Bitcoin: Cryptopayments Energy Efficiency

Michel KHAZZAKA*
khazzaka@valuechain.pro
April 20, 2022

ABSTRACT

Bitcoin introduced a cryptographic peer-to-peer version of money that allows online

payments to be sent directly from one party to another without going through a
nancial institution. Many recent studies evaluated and criticised Bitcoin’s energy
consumption1 through its Proof of Work (PoW) consensus mechanism without
evaluating its ef ciency compared to classical electronic payment system.

Based on physics, information science and economics, we compute and compare the
energy consumption and de ne what is the energy ef ciency of both the current
monetary payment system and Bitcoin cryptopayment system. We demonstrate that
Bitcoin consumes at least 28 times less energy and can run today with 60 times less
energy than the classical system. At a single transaction level and with total volumes
accounted for, Bitcoin produces equivalent energy ef ciency rates or better. When
Bitcoin Lightning is compared to Instant Payment scheme, Bitcoin gains
exponentially in scalability and ef ciency, proving to be millions of times more
energy ef cient per transaction than Instant Payments.

INTRODUCTION technology4 (DLT) in payments, banking and

nance. The DNB paper did not compare Bitcoin
PoW energy ef ciency with any parts of the classical
Bitcoin is designed and built to function as a world
monetary and payments system. What is needed is a
global currency and an online payment system. This
correct evaluation of Bitcoin functions and their
is the promise declared in the 1st sentence of the
energy consumption compared to their counterparts
Bitcoin white paper abstract: “A purely peer-to-peer
in the classical electronic cash and payments systems.
version of electronic cash would allow online payments”.
Many have tackled this challenge without completing
While Bitcoin is still representing ≈ 42% of the total
it. Changpeng Zhao the founder of Binance recently
cryptocurrencies’ market cap, many of its detractors
a s k e d f o r a ny d a t a a b o u t p a y m e n t s ’ v s.
continue their criticism of its Proof of Work
cryptopayments energy consumption and Institut
consensus mechanism accusing it of being power-
Sapiens the French think “tech” recommended in its
hungry up to megalomania. The central bank of
publication “Bitcoin, totem & tabou” for this work to be
Netherlands DNB compared its energy consumption
performed: “banking industry, whose energy cost is
to a whole country like Denmark or the Netherlands
considerable but never evaluated, recognized, nor published. It
in the De Nederlandsche Bank paper “The carbon
would be interesting to calculate the energy cost of the banking
footprint of bitcoin”2. Although most3 central banks do
sector…”
not recognise Bitcoin as legal tender, yet they are
convinced of the capabilities of the distributed ledger

1 In march 2022, EU Markets in CryptoAssets regulation (MiCA) discussed banning completely PoW based on energy inef ciency claims.
2 By Authors Juan Pablo Trespalacios and Justin Dijk, 2021
3 Central banks of Salvador and Central African Republic recognised Bitcoin as legal tender. Some countries recognize Bitcoin as analogue
to foreign currencies such as Russia.
4 See our Cryptopayments Glossary issued by France Payments Forum (in French) for: blockchain, DLT, legal tender keywords.

Bitcoin: Cryptopayments Energy Ef ciency 1/28 Michel KHAZZAKA — Valuechain

Electronic copy available at: https://ssrn.com/abstract=4125499

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 The weaknesses in the previous studies are as follows: SCIENTIFIC APPROACH

Use of inaccurate numbers or incomplete

In order to study the energy consumption of Bitcoin
methodologies: for example the Cambridge
PoW cryptocurrency system and the classical
Bitcoin Electricity Consumption Index (CBECI)
electronic system, we start by setting the governing
which is based on a world average of electricity
mathematical and scienti c equations into play that
prices in USD and an average distribution of
will be used hereafter.
mining hardware leads to inaccurate results
varying between −50% (lower bound) up to
Work in physics, is the energy transferred to or from a
+120% (upper bound). This is a known limitation
system via the application of force along a
of the CBECI methodology in addition to its lack
displacement in spacetime6. In our case, a payment
of comparing 2 similar systems ef ciency. This
work is to transfer an amount of value money from a
paper will address both of these issues.
payer to a payee along a displacement over time. Note
Often partial or anti-bitcoin position: and that by nature an electronic transaction (noted Tx) can
usually do not account for both monetary systems travel the globe in near real-time so the notion of
and payments systems. For instance the central displacement in distance measured in kilometer has a
bank paper by the DNB “The carbon footprint of lower weight in the equation compared to the
bitcoin”, compares Bitcoin energy consumption to displacement in time which will be more weighing in
the debit card payment system alone basing their the equation. Here time is the time span δ t required
statements on the Cambridge index and the study to nish the payment work.
“The Energy Consumption of Blockchain Technology:
Beyond Myth” 5. Yet card payments are just an A payment work is to transfer an amount
intermediary step of the payment transaction, they of value called money from a payer to a payee [A]
mainly provide an authorisation of a transaction along a displacement over time.
and will at least require later inter-banking clearing
and settlement to become nal. On the other hand
The physical force7 applied is provided mainly
a bitcoin transaction is nal and covers end-to-end
through an electrical force causing a differential of
steps of the transaction, so the comparison is very
energy. From Newton's second law, it can be shown
incomplete.
that work on a free (no elds), rigid (no internal
degrees of freedom) body, is equal to the change in
It’s essential to compare Bitcoin energy consumption
kinetic energy Ek corresponding to the linear velocity
with all the aspects of the classical monetary
and angular velocity of that body W = ΔEk , where
payment system. This covers: banknotes and coins
the energy is the quantitative property that must be
cash management in ATM systems, card payments,
transferred to the system to perform work (and/or to
point of sale (POS) payments, banking and inter
heat it)8. It’s important to insist that energy is a
banking energy consumption etc. (see
conserved quantity; the law of conservation of
METHODOLOGY below)
energy states that energy can be converted in form,
We’ve endeavoured in our paper to answer but not created or destroyed. Energy like work is also
mathematically and scienti cally all these challenges measured in Joules in the international system9 but
for the bene t of decision makers, researchers, can also be measured in Wa t t × h o u r or kWh10
politicians, legislators and industry representatives. which is 1000Wh. Power is the amount of energy
transferred or converted per time unit:

5 The research used by DNB to criticise the PoW actually concludes by stating: “While their energy consumption is, indeed, massive, particularly when
compared to the number of transactions they can operate, we found that they do not pose a large threat to the climate, mainly because the energy consumption of PoW
blockchains does not increase substantially when they process more transactions”. But the central bank seemed to have missed this detail.
6 In its simplest form, it is often represented as the product of force and displacement.

7 Power and energy are scalar quantities in opposite to the vectorial form of the force.

8 Heat and mechanical work are special forms of a same value that is conserved and is called energy by Lord Kelvin and he called thermodynamics

the science that studies it.

9 One Joule is the energy transferred to an object by the work of moving it a distance of one metre against a force of one newton.

10 The conversion rule is 1kWh = 3 600 000 Joules or 1Wh = 3600J

Bitcoin: Cryptopayments Energy Ef ciency 2/28 Michel KHAZZAKA — Valuechain

Electronic copy available at: https://ssrn.com/abstract=4125499

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 E n erg y dW [0] The correct way to compare the classical monetary
Po w e r = = = F.v
Time dt and payments system to Bitcoin is to compare all
their common capabilities in terms of energy
Power is measured in Watts, joules per second, and consumption15. Bitcoin serves as a:
also in watt-hour/day or terawatt-hour per year
(TWh/yr) for example when quantifying the Monetary System: issuing, burning, and
electrical power of a data center or a country. For circulating the cryptocurrency bitcoin comparable
instance, the energy consumed by the biggest to a central bank with various commercial banks
datacenter in the world Equinix is 6.46 TWh/yr. The issuing and distributing central bank money and
whole digital services on the internet consume 2,000 commercial money.
TWh/yr. In France digital services consume 10
TWh/yr which is 0.5% of total digital energy. We Means of Payment allowing the transfer of the
will use the megawatt: MW or the version of TWh/ cryptoasset bitcoin from a payer to a payee. The
yr to measure power (power being an energy blockchain nodes serve as Payment Service
consumption here per year see [0]). We will also use Providers (PSP) similarly banks use card schemes,
kWh to measure energy.11 clearing and settlement mechanisms in the classical
electronic payments industry with central banks.
If Δ is the amount of work performed during a
The high level work breakdown structure of the
period of time of duration Δt, the average power Pavg monetary system can be simpli ed to the following
ΔW functions:
over that period is given by the formula: Pavg = .
Δt
Monetary mass issuing and circulation of
What follows is the evaluation of the total consumed
electronic money as well as the paper cash money
energy — that is power — of the monetary and
and coins,
payment systems worldwide compared to the energy
consumption of Bitcoin. Monetary distribution and lifecycle
management through the economy based on
METHODOLOGY supervised and regulated banking and nancial
institution service providers. This covers the
physical form of money distribution in secured
Money in the economy is a measure of work12, a value
vehicles, vaults, and ATMs as well as an electronic
commonly called price13. Today money is considered
form of money.
to be a nancial instrument issued by special monetary
authorities such as central banks. In this paper, we Bookkeeping services with central bank accounts
argue that money can be quali ed as a social in wholesale using central bank money, and
contract, in essence, and thus can be de ned as an customer banking service bookkeeping in retail
asset with an intrinsic power differential between two using core banking and online banking.
economic agents. Traditionally money serves three
functions: A unit of account as the foundation for Non-card payment services such as wire
economic metrology, a medium of exchange allowing to transfers, instalment automatic withdrawal like
transform a value into work through space in the form direct debit and other cross border or nancial
of payment transactions and a store of value messages operations using third party providers
transporting this value through time. It can be easily like Swift in addition to Clearing and Settlement
seen that there are natural relations between money, Mechanisms (CSM)
work14, energy and power.

11 To help understand the meaning of energy ef ciency and power vs energy, note that burning 1Kg of coal releases much more energy than
detonating 1Kg of TNT, but because the TNT reaction releases energy much more quickly, it delivers far more power than the coal.
12 Plato de ned it as a social convention while Aristotle as a measure of work See Aristotle's text here

13 Some time the price of money means the interest rate

14And also Proof of Work PoW

15It’s not in the scope of this paper to demonstrate that Bitcoin can serve as a currency and as a payment system. This is taken as a
hypothesis and as the promise of its Blockchain as stated by Satoshi’s white-paper.

Bitcoin: Cryptopayments Energy Ef ciency 3/28 Michel KHAZZAKA — Valuechain

Electronic copy available at: https://ssrn.com/abstract=4125499

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 Card Payment services which include point of replaced by blockchain wallets. So they are out of
sales (POS) acceptance solutions and terminals, in scope for simpli cation reasons and to ensure an
addition to plastic card issuance and distribution, homogenous methodology.
vicinity and online payments authorisation through
a card scheme such as Visa, MasterCard or Carte Most of the studies16 available missed the point that
Bancaire locally in France. It also includes the it is a mistake to compare Bitcoin to Visa only since a
collection, clearing and settlement of those card scheme does not execute a payment transaction
transactions through clearinghouses. from end to end as Bitcoin does. A card scheme
ensures an authorisation in real time between the
It is important to note that this paper is a global actors of the payments value chain: the bank of the
evaluation of payments worldwide, but in reality cardholder called the Issuer and the merchant’s
electronic payment systems are very fragmented and Acquirer bank. But most17 of the time the card
have different features and levels of ef ciencies in scheme and the two banks need to settle the
different regions and countries around the world. In transaction in a delayed step using central bank
addition, the carbon foot print in CO2 for instance is money and sometimes between corespondent banks
not a reliable approach, since many companies and and different central banks in case of a cross border
industries cover their carbon footprint by buying payment. In comparison, a transaction in bitcoin is
carbon credits. Their resulting carbon footprint is not nal in near real-time, it is a push payment in only
their real carbon emission. The only scienti cally one step and the nality time is set to be about 10
reliable approach is by the computation of the energy minutes on average (or much less through Lightning).
in terawatt-hour (TWh) per year required by each
system to function, and to compare their work Electronic System Crypto System
accomplished in this pure form of input energy
without taking into account the energy sources. Annual Issuing Included Included

Distribution ATM and POS N/A

SCOPE Bookkeeping Banks Blockchain

Card payments Acceptance, POS, N/A

The chosen scope is to compare the “Run” of both authorisation & CSM
Bitcoin and the existing electronic system: this means
Other payments Wiretransfer, debit, etc. Cryptopayment
to compare the energy consumption of the similar
running operations and to leave out of scope the Cheques Excluded N/A
“Build”of each system, such as the manufacturing of
ATM or miner units, the printing of banknotes and Finance services Excluded (insurance & Excluded (DeFi)
minting of coins. Although comparing the Build loans, etc.)

would have been bene cial for Bitcoin, it confers to it In scope of capabilities included for energy assessment
an unfair advantage. The issuance of bitcoins, called (highlighted) [T0]
mining is included since it is a part of the running
operations. The annual printing of banknotes and
Note that credit services are kept out of the scope of
minting of coins are included, the cash distribution
this study as well as DeFi nancial services and web
to ATMs and acceptance at electronic Point of Sales
3.0 use cases in order to focus only on Bitcoin vs
are also included to cater for the running of
monetary and payments industries. Electronic
electronic cash management. In addition all Payment
cheques payments are also kept out of scope for
Service Providers such as PayPal or any other
simpli cation considering their adoption decrease
marketplace payment or acceptance solution
(yet they still consume a considerable energy
providers are left out of scope since these can be
especially through printing, distribution and transit
proposing cryptopayments solutions also, or can be
back to bank).

16 For example DNB paper “The carbon footprint of bitcoin” or Arcane Research “The State of Lightning” — Oct 2021
17 There exist a card payment mode called “single mode” that allows the cardholder to be instantly debited and the merchant account to be
directly credited, but most of card payment transaction are in “dual mode” requiring to distinct steps: authorisation followed by collection of
translations at the end of day, then a request to a clearing and settlement mechanism for compensation with central bank money. This
distinction will not impact the energy consumption of the actors in general but only increase the speed of certain electronic payments
compared to cryptopayments.

Bitcoin: Cryptopayments Energy Ef ciency 4/28 Michel KHAZZAKA — Valuechain

Electronic copy available at: https://ssrn.com/abstract=4125499

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 An approach that compares the transacted values in ENERGY OF PRINTING & MINTING CASH
equivalent USD, not just transactions volumes is also
unsuitable. In both systems, energy consumption
Let’s start by calculating the energy consumption of
won’t be affected by transaction value. We have
the renewal rates of banknotes and coins. Note that
managed to exclude from this research 100% of this
we will not take into account the initial printing and
research any exchange value rates and transacted
minting of cash money already in circulation
amounts between Bitcoin and classical payments in
according to our methodology of comparing only the
dollars or euros for instance.
run time energy consumption of both systems.

Finally energy sources and energy mix are kept out

Although, you might consider that notes and coins
of scope for a total focus on the most fundamental
are not an electronic form of money and shouldn’t
questions: energy input & energy ef ciency.
be accounted for, yet this form of central bank
money is used in retail electronic payments such as
Our research follows the journey of a classical
automated teller machines, or electronic point of
monetary and payments transaction from money
sales terminals. Therefore they are accounted for in
issuance (yearly renewal) to its transit into an ATM or
electronic payment transactions.
a cash point, followed by its acceptance in payment
as cash. Then we switch to card payments and the
In order to estimate how much energy per year is
energy of schemes like VISA and Mastercard, and
required yearly to print and mint we need to
ePoS acceptance, then we continue the journey
estimated the total number of coins and banknotes in
through the banking system up the stream to central
use worldwide and their current renewal rate. These
bank clearing and settlement mechanisms. Finally we
numbers are not easy to estimate given the lack of
will consider the important update of classical
information from certain countries, the differences in
payments into instant payments. For a Bitcoin
currencies values and consumer preferences for coins
transaction we will consider simply the total
or banknotes which differ largely from one country to
hardware used in mining and processing and
another. To succeed in this critical challenge and to
compute the exact energy consumed by the
reduce the error margin we’ve used 2 different
Blockchain PoW. Later will we also assess the
sources and methodologies to narrow down the
important improvement brought by Bitcoin
evaluation.
Lightning.
According to the ECB there are today 28.67 Billion
At the end we will compute and compare the energy
banknotes and 141.97 Billion coins in circulation in
per a single transaction in both systems: Classical vs
the eurozone representing respectively €1.587 Billion
PoW then Instant vs Lightning. Then we will propose
and €31.426 Billion. After the COVID period the
an energy ef ciency equation that will allow us to
demand for cash increased to reach a total of 16% of
arbitrate on both capacity , speed and energy
the GDP of the eurozone in 2022 counting 342.56
consumption per transaction of both systems.
million persons using the euro. According to Central
Bank of India there were about 124.36 Billion
1 INTRODUCTION 10 ENERGY OF BANKING OFFICES banknotes and 122.99 Billion coins in circulation in
2021 in India. The Federal Reserve Bank published
2 SCIENTIFIC APPROACH 11 ENERGY OF BANKING COMMUTE
that there are 67.68 Billion banknotes in 2022
3 METHODOLOGY 12 ENERGY OF BANKING IT labeled in dollar and worth $2,750.27 Billion. For
coins in the USA, there were about 28 Billion coins
4 SCOPE 13 ENERGY OF INTER-BANKING
in circulation in 2016 but with 15 to 20 billion coins
5 ENERGY OF PRINTING & MINTING 14 RESULTS OF CLASSIC PAYMENTS minted yearly according to the US Department of
Treasury.
6 ENERGY OF ATMS 15 ENERGY OF BITCOIN

7 ENERGY OF CASH IN TRANSIT 16 COMPARING TX LEVEL Based on the above numbers and through
extrapolation according to population we reach a
8 ENERGY OF CASH AT EPOS 17 LIGHTNING VS INSTANT
total of 842.6 Billion banknotes in circulation
9 ENERGY OF CARD PAYMENTS 18 CONCLUSION worldwide. To con rm our estimation we’ve checked

Content Summary [T1]

Bitcoin: Cryptopayments Energy Ef ciency 5/28 Michel KHAZZAKA — Valuechain

Electronic copy available at: https://ssrn.com/abstract=4125499

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 with a second source18 that estimated at 576 Billion will account for cash in transit later). But an easier
banknotes worldwide in 2018. Several central banks approach that can give us the lower bound, is by
con rmed a growth rate of 12% to 16% per year of estimating the energy consumption of industrial
banknotes printed since 2018. This leads to a count magazine manufacturing. We’ve calculated that
of notes between 1015 Billion and 1210 Billion printing 35,000 copies of a 96 pages magazine
banknotes according to this second source. consumes about 0.0372 KWh per page. Based on
Accounting for destroyed banknotes this con rms our this source, printing [1b] can consume up to 8.16
range of 842.6 Billion banknotes as a safe lower TWh/year. About 83% of this energy is consumed in
bound estimation with an average growth rate of making the paper that goes through the press. Only
11.57% per year in the last 4 years. 11.1% are needed to print, cut, collate.

For coins in circulation applying the same This rst approach is interesting in giving us an
extrapolation leads us to ~1,507.7 Billion coins initial order of magnitude of the energy
worldwide in 2022. We conclude that globally the consumption of banknote printing, but it is not
ratio of coins to banknotes is ≈ 1.79× although this precise enough for 2 reasons: magazine printing is
ratio differs largely around the globe between ~1× in not totally comparable to money printing, and any
India to ~4.9× in the EU. error margin in the energy cost per banknote is
ampli ed tens of billions of times given [1b]. A
What is important for us is the renewal rate of this better approach is to use of cial central banks real
cash mass. It’s estimated that the renewal rate of energy consumption gures on this activity. This data
banknotes is ~26.04% per year. This leads to 219.42 is not openly available worldwide but a recent french
Billion banknotes per year being printed to replace central bank report stated that the Banque de France
the worn notes taken out of circulation and to consumed 172.2 GWh/year in 2017 on activities
answer new demand. including banknotes paper manufacturing at
Auvergne and Vic-le-Comte and printing at
Coins have a slower renewal rate. A circulating coin Chamalières. In order to estimate how much
has an estimated 30 years lifespan or more and today banknotes were printed in 2017, we know that at
the US Mint issued 15 billion coins in 2021 giving a Chamalières site 1.25 billion euro banknotes are
renewal rate of about 11.54% for the dollar and printed yearly as well as 1.25 billion banknotes in
2.52% per year for coins based on European Central other currencies. This leads to an energy cost of
Bank’s data. Different countries might have larger 0.069 kWh/banknote.
increase rates but we base our calculations on a
renewal rate of ~7% and this leads to a global It is safer to extrapolate based only on the more
minting rate of 106 Billion coins per year. So the energy ef cient french central bank gures although
results are as follows: other central banks might be less modern and less
energy ef cient. This leads to a total of at least 15.1
Count(notes) ≈ 842.57 Billion notes [1a] TWh/year of all banknotes renewal worldwide.

New(notes) ≈ 219.42 Billion notes/year [1b]

Energy(PrintNotes) ≈ 15.1 TWh/year [1e]
Count(coins) ≈ 1,507.7 Billion coins [1c]
According to “The United States Mint’s 2011
New(coins) ≈ 106 Billion coins/year [1d]
Sustainability Report” the US Mint’s total energy
consumption in 2011 was 192,906,111 kWh. This
Let’s now estimate the energy consumption of [1b] includes consumption of natural gas, diesel, lique ed
and [1d]. petroleum, electricity and steam. In 2011, there were
8.7 billion coins minted by the US Mint. This gives
Energy consumption of secure paper money printing us an energy cost per coin of ≈23.53 Wh/coin, and
is dif cult to estimate precisely. Paper fabrication, a total energy consumption for yearly minting
printing, cutting, collating, counting, testing and worldwide today of about 2.49 TWh/year. It is
binding is a complex and heavy industrial process (we

18 Source is Hermann Giesecke and Alphonse Devrient founded Giesecke+Devrient (G+D) in Leipzig in 1852. The company is specialized
in printing banknotes.

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Electronic copy available at: https://ssrn.com/abstract=4125499

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 important to understand that this excludes the energy ENERGY OF ATMS
consumption of metal mining and re ning. The
metals are mined as ore before being re ned to
We’ve computed and veri ed in our study that the
remove impurities. These include iron, gold, silver,
total number of cash dispenser machines worldwide
nickel, and copper, among other metals and requires
is estimated to be 4,823,564 ATMs. This number
large amounts of energy that could have been
can be reached based on country-by-country studies
included into the benchmark. We have ignored these
of the number of ATM machines per 100,000
energy costs to simplify the complexity of giving a
individuals. We’ve veri ed this by double-checking
proper ratio of gold, silver, etc. mined for coins work.
central banks sources of 35 representative countries
We have covered only then the minting process and
covering more than 5 billion persons on all
transformation into central bank coin.
continents and based on of cial central banks
reports. Our calculations reached an average of 60.7
Energy(MintCoins) ≈ 2.5 TWh/year [1f] ATMs per 100,000 persons in the total serving the
world’s population of 7,939,000,000 people. This
estimation takes into account the drop of ATMs
In conclusion the total energy consumption of
usage in several countries worldwide.
printing and minting cash is at least:
For a small bank an ATM machine has an average
Energy(Print&Mint) ≈ 17.61 TWh/year [1] daily power19 of about 250W maximum according to
a rst source. We consider 230W per ATM on
Note that on yearly bases, minting is using less energy average for our calculations and evaluate that the
than banknote printing because of a very large energy consumption of world ATMs to be around
demand on banknotes compared to coins and 9.72 TWh/yr. A second source is Diebold, the ATM
because coins require no maintenance and are not vendor estimates that an ATM has an average
recycled, their lifecycle virtually ends at production, consumption of 1620 kWh/yr leading to 7.81 TWh/
while banknotes deteriorate quickly and are yr. We’ll consider an average of 8.77 TWh/yr.
frequently renewed. We’ve excluded from the
But in practice, ATMs are not used alone, they
evaluation the energy consumption of the mining of
require two air conditioners and lighting (that can be
the metal coins and the manufacturing of paper
in a branch or out of bound of a bank branch). A
notes according to our methodology. We’ve also
medium air conditioner consumes about 900W.
excluded the initial printing and minting of total
Since running one air conditioner for 24/7 reduces
cash in circulation and only evaluated the new cash
its life span, two AC are used working20 alternately to
entering into circulation yearly.
achieve full time coverage. By taking the average
Finally we’ve kept out of scope gold stocks mining consumption of all ATMs and including only 1 AC
and maintenance by central banks for several unit this leads to a more realistic range of 46.8
reasons. Gold mining industry consumes about 265 TWh/yr for all ATMs worldwide.
TWh/year. But although gold is still an important
asset used massively by central banks to provide trust Energy(ATM) ≈ 47 TWh/yr [2a]
in the stability of a given currency, it is not pegged to
the real value of any major currency today. In
This estimation does not take into account: server
addition central banks do not mine gold directly, they
side consumption, cash handling, or any
buy and store large amounts of already minded units
maintenance interventions on ATMs. Therefore it
and it is dif cult to extract the precise impact of
can be seen as a minimal energy requirement to run
central bank demands on gold mining and what ratio
world ATMs today.
of this gold is covering indirectly any payment
transactions. For all these reasons the 265 TWh/year
of gold mining are not accounted for.

19 These estimations ignores for now the energy consumption on the server-side of ATMs Manager by Diebold Nixdorf or NCR for instance
20 Note that these AC units are not used in the bank branch itself by only dedicated to the ATM

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 ENERGY OF CASH IN TRANSIT [1a]. We’ve estimated that the velocity of banknotes
is ≈ 1.5 × , meaning that a banknote circulates and
returns back to its starting point (ex. an ATM) 1.5
Now let’s assess the physical cash management
times per year.
energy consumption and focus on cash-in-transit
(CIT), the physical transfer of banknotes, coins,
Loomis eet in the USA has 3000 vehicles (50% of
credit cards and items of value from one location to
their world eet) and process 25 million banknotes
another. The locations include cash centers and bank
per day in the US. This leads to an average capacity
branches, ATM points, large retailers and other
per CIT vehicle ~3,041,667 banknotes per year.
premises holding large amounts of cash, such as
Taken into consideration the velocity of banknotes
ticket vending machines and parking meters.
and the total number of banknotes worldwide we
Companies such as Loomis and Brinks are the main
estimate that there are about 6.03 million CIT
providers in this sector and are representative of the
vehicles in the world including a safe estimate of 1
workload necessary.
bank car for each 2 armoured trucks counting 5.4
million trucks. When we take a moderate hypothesis
Loomis has more than 200 cash processing centers
that an armoured vehicle transports the cash for ~40
equipped with technology to count, authenticate, and
km per day over 220 days per year, and the banalised
check the quality of banknotes and coins. We will
bank car accompanies the truck only for half of the
ignore the veri cation and authentication machines
path our estimations lead to a total cash-in-transit
consumption as an additional simpli cation of our
power of:
model and focus only on the transit energy
consumption. Loomis handles up to 50 million
banknotes per day in the processing centers and has CIT(Vehicles ) ≈ 6 million vehicles [2b]
6000 secure transport vehicles. Brinks has 1100
Energy(CIT) ≈ 166 TWh/yr [2c]
operations facilities, and a eet of 13,300 vehicles.
These vehicles consume signi cant amounts of
energy. A diesel armoured car can be consuming This gure does not account for processing centres
~3.3 kWh per kilometer. Note that kinetic energy is and employees managing the cash and the
only 30% of the input energy required for the truck, distribution from central banks. This excludes also
the remaining is lost mainly in the exhaust. Estimates the energy consumption for the maintenance
computed an average of ~35 litres of diesel every activities for these vehicles, so [E] should be
100 km. One litre of diesel fuel has an energy of ~10 considered as a minimum energy requirement for
kWh. This con rms the estimate around 3.5 kWh/ global CIT activity.
km.

CIT is a complex process with multiple steps. Cash ENERGY OF CASH AT EPOS
vehicles can be transporting banknotes and coins
from cash centres to banks, or from retailers to bank Physical cash payments are private by nature and
for instance. Almost all the eet is used daily, CIT (without electronic traceability) are harder to count.
companies optimise the number of vehicles for these In our research we’ve found that the share of cash
rotations without counting the energy cost for their transactions at an electronic POS is more frequent
maintenance as an additional simpli cation. In the than the cash distribution by banks and even more
majority of the time an additional step is added to frequent than electronic vicinity payments at shops.
the CIT process and a banalised vehicle belonging to In Europe, cash transactions are on average about
the bank, drives along the armoured car thus almost 68.1% of all vicinity payment transactions at POS21.
doubling the number of vehicles involved but not to Globally, les notes and coins represent more than
all the path of transit. 50% of transactions in most OECD countries. To
verify this initial estimate we refer to the European
It is a very dif cult task to estimate the number of Central Bank report that estimates the share of
armoured trucks for CIT worldwide. A good payment instruments used at the POS and P2P in
educated guess is to take into account the total terms of the volume (count) of transactions to be
number of banknotes in circulation worldwide, see

21 Going from 88% in Malta to 77% in Germany to as low as 34% in Netherlands (59% in France)

Bitcoin: Cryptopayments Energy Ef ciency 8/28 Michel KHAZZAKA — Valuechain

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 about 73% of all payment transactions including ENERGY OF CARD PAYMENTS
POS (and 48% of the transactions’ value). We
compute the average number of POS and P2P
After estimating cardless PoS electronic cash
transactions per person per day, per country, to be
management, we will estimate in this paragraph the
about 1.14 cash Tx/day/person in Europe with large
energy consumption of card payment transactions.
disparities between countries cash appetite: Greeks
The card payment leader Visa has 4 data centers
Italians and Portuguese make 1.6 cash Tx/day per
located in Central US, East US, UK, and Singapore,
person (compared to 0.5 for Dutch and Estonians).
with a private communication network of 10 million
Based on the 1.6 gure as an average worldwide we
route miles (400 times earth circle23). Although Visa
extrapolate to world population, this leads to a
keeps con dential the exact energy required by its
3.3 Trillion cash transactions on electronic point of
datacenters, it is possible to compute that Visa’s they
sale per year. But since Europe has fewer cash
require on average 305 MW per data center to
transactions than the rest of the world the real
operate [4c]. These calculations are based on Visa’s
number can be considerably higher.
annual report (Visa Green Bond Report — July 2021)
stating that Visa’s datacenter energy consumption
PoS(CashTx) ≈ 3.3 Trillion Tx/yr [3a] stayed stable between 2017 and 2020 totalling 446
million kWh. This estimation leads to an energy
The total energy for a cash peer-to-peer transactions consumption by Visa ≈ of 2.7 TWh/yr [4a]. Visa’s
in the economy is more dif cult to estimate since they market share can be estimated to be about 15% of
are private by design, and not all of them are total cards in the world. This can be obtained
accounted for electronically. But it’s important to through Visa’s declaration that is processes 3.8 Billion
account at least for the part that is processed by cards and we know that the total number of payment
electronic point of sales desks because the cash cards was 25.2 Billion cards in 2021. Now we can
management has a high cost effort for merchants too, extrapolate [4a] and see that the total card schemes
not only banks. Today Visa alone serves 100 million payments datacenter consumption is ≈ 17.72 TWh/
merchants worldwide, a number in the rise largely yr to operate all card payments worldwide.
driven by government initiatives to promote cashless
payments. An educated guess of how many Power(Schemes) ≈ 17.72 TWh/yr [4]
merchants accept cash payments only, can be the
majority of the very small shops around the world
So based on Visa numbers we can extrapolate that
that still do not accept card payments. Based on
the total payment cards generate 1.54 Trillion
ECB estimates that 27% of vicinity payments are
transactions per year (Tx/yr) [4d] or about 48,891
card transactions and 73% are cash at ePOS we can
Tx/s moving USD 86.2 billion/yr. This leads to an
estimate that 370 million merchants accept cash
average of 56 USD/Tx (in card payments) [4e].
using a PoS electronic system worldwide. If we
consider that a PoS cash desk works 8 hours per day
As a reminder these transactions are not nal, they
on average and uses as little energy as a PoS terminal
are most of the time online authorisation requests to
about 111.6 W (see references thereafter) this leads to at
the Issuer on behalf of the Acquirer24 and the
least 72.75 TWh/yr for electronic cash desks at PoS
payment will complete later with the collection,
working 220 days per year 8 hours per day and
clearing and settlement transactions with central
counting only 1 e-cash ePoS per merchant.22
bank money. We will estimate the energy of these
steps later in our study. As a result, card payment
Energy(CashPayments) ≈ 72.8 TWh/yr [3b] transactions (which is only an intermediary step of
the end-to-end payment transaction) require globally
Energy(ePosCashTx) ≈ 22.03 Wh/Tx [3c]
about 11.49 Wh/Tx in energy to process through a
card scheme like Visa or Mastercard for instance.

Energy(SchemeTx) ≈ 11.49 Wh/Tx [4a]

22 We will not account for cash transport by merchants between branches and by client since this could impact highly the results without
being completely in scope for comparing with Bitcoin payments.
23 That is 5 096 800 Km of cables only between servers at the datacenter

24 In card payments Issuer is the issuing bank of the card and the Acquirer is the bank of the merchant acquiring the payment on his behalf

Bitcoin: Cryptopayments Energy Ef ciency 9/28 Michel KHAZZAKA — Valuechain

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 To complete the estimation, a card payment operate. Commercial bank branches according to
generally originates at a point of sale (POS) terminal International Monetary Fund, is about 10.8 branch
in the case of vicinity payments25. We’ve estimated per 100K individuals in 2020. Based on world
the global installed base of POS terminals to be population we can estimate that there are 857,412
about 207 million units in 2020. Then we’ve bank branches [6b1]. To double check this initial
computed that the minimum POS energy estimate we’ve analysed the banking industry in the
consumption per transaction ≈ 0.9401 Wh/Tx. In a following 45 countries (totalling 3.78 billion citizens):
different and more accurate method, the average European Union (28 countries), USA, India, China,
POS terminal energy consumption26 is ≈ 111.66 W. Japan, Brazil, Indonesia, Egypt, Mexico, UK,
If a terminal works 8 hours/day on average and is Switzerland, Russia, South Africa, Nigeria,
online 80% of working hours, we compute that the Philippines, Hong Kong, Canada and Turkey. We
total POS terminals energy consumption is more have reached an average of 59.17 branches per bank
precisely 54 TWh/yr for the 207 million terminals. for a total of 25,872 registered banks in 45 countries.
When pondered to representing 80% of banks
Energy(POS) ≈ 54 TWh/yr [4b] worldwide this leads to an ~1,740,000 branches
[6b2] worldwide.

Based on [4] and [4b] we conclude that card Note that [6a] is then to be considered a minimum
payment transactions consumes 71.71 TWh/yr. estimation of bank count and that banks-like entities
such as credit unions and electronic money issuers etc.
Energy(CardSchemes) ≈ 71.71 TWh/yr [5] can increase the number of what is commonly
known as a bank to the range of 55,000 to 62,000
Energy(CardSchemeTx) ≈ 46.51 Wh/Tx [5a] entities worldwide. To remain on the safe side we
took the hypothesis that these 45 countries represent
Note that the difference between electronic cash at about 80% of all banks worldwide. This leads to a
PoS and ePoS is that one is only at cash desks energy pondered estimation of 36,760 banks worldwide
consumption [3b] and the ePoS is for energy excluding other nancial electronic money and
payment terminals accepting card payments [4b]. payment entities. We take the average of [6b1] and
And these are 2 different hardware serving different [6b2] giving ~1.3 million branches.
means of payments at the point of sale.
Count(Banks) ≈ 36,760 [6a]

Count(Branches) ≈ 1,298,667 [6b]

ENERGY OF BANKING OFFICES

Energy consumption of banking branches can be
evaluated through the average number of kilowatt
We need to complete the estimation with the end-to- hours per square meter for a commercial building.
end work ow through banks and other cross nancial According to the Department of Energy (DOE), this
institution actors such as clearinghouses and Swift electrical energy is approximately 242.2 kWh/m2.
like service providers. This does not include all the
services provided by banks such as insurance, loans Traditionally, bank branches have ranged27 in size
or trading, but focuses on the accounts and payments from 371.6m2 to 557.4m2. We have veri ed from an
management services. The banking industry counts different source, a major French bank, that an
more than 25,000 banks around the world [6a]. average size bank can consume about 21% of its
Banks manage globally a high number of branches energy on of ces and branches28 and according to
that also consume a large amount of energy to banks roadmaps of improving its energy ef ciency of

25 Since online payments originate in the same way as Bitcoin cryptopayments and e-commerce card payments they are kept out of the
scope of the calculations.
26 Source: Energy Losses Due to Imperfect Payment Infrastructure and Payment Instruments by Oleksandr Melnychenko, Oct 9, 2021

27 We’ve based the calculation at 6000 square feet instead of 4000 to account for HQ and additional dependencies other than the bank
branch of ces for public.
28 Source: Internal of cial information of one of 12 major French bank according to their program for improving energy ef ciency.

Bitcoin: Cryptopayments Energy Ef ciency 10/28 Michel KHAZZAKA — Valuechain

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 its of ces and branches, it is targeting an average of Payments ≈ 1.2 Million employees [7b]
137.14 KWh/m2 in 2024. This con rms the range
and although banks worldwide are improving their
carbon impact using their resources large disparities These estimations account for direct internal bank
worldwide still remain between them. We will employees and ignore the somewhat signi cant
consider the average of 242.2 kWh/m2 in 2022 number of external providers and consultants such as
worldwide. This leads to an energy consumption by security and guards, CIT employees, consultants etc.
total bank of ces and branches worldwide of 151 it also ignores all bank-like employees working in
TWh/yr, excluding for now IT services and banks electronic money issuers etc.
data centres.
It is important to distinguish only the count of
employees in [7a] working at least partly on
Energy(BankBranches) ≈ 242.2 KWh/m2 [6c]
payments and accounts management. We consider
Energy(BankBranches) ≈ 175.3 TWh/yr [6] that employees working on security, fraud,
maintenance, risks, marketing, accounting,
c o m p l i a n c e, a n d o t h e r c ro s s s t r e a m s o r
administrative functions fall in the same domain of
payments and cash management since they are
essential for these services to run. Although branch
ENERGY OF BANKING COMMUTE
employees work also on loans and insurance sales yet
they are still essential in the cash management,
The number of employees working in banks as distribution and management of credit cards, in
per manent employees can be estimated by addition to the execution of certain wire transfers
extrapolation from the same 45 representative and book keeping services.
countries representing more than 3.78 billion people.
We have reached the result that 0.703% of the world It is legitimate to reduce [7a] by subtracting banking
population working in banks, with a variation functions solely related to loans, insurance and
between Nigeria (0.046%) and Hong Kong (3.67%). trading. Worldwide there are about 9.6 million
A pondered extrapolation leads to 55.9 million traders, but not all of them work in banks. For
employees worldwide working in banking. Using 2 example at the main large banks in France the
other separate methods we can verify that the total Société Générale has 351 employees out of 133,000
numbers of employees is certainly above 35 million employees worldwide, and 353 employees at the
using basic employees over population ratio and BNPP are traders out of the 193,319 total employees
below 174 million employees based on banks count count. On average we can see that 0.22% of the total
per 100,000 people of cial countries declaration. We headcount is in trading which is negligible 122,980
have reached the conclusion that the best educated traders working in banks. In another approach we
guess is ~ 55.9 million bank employees [7a] and this can consider that about 25% of banking
is con rmed also with sample countries based on headquarters work on loans, insurance and trading,
major American bank reports, central banks in but almost 100% of branch employees fall into cash
China, India, Eurozone, and Japan about the average and payments operations at least part time.
number of employees working per bank. Therefore this demonstrates that the strictly non-
banking and non-payments related employees can be
In addition, we have researched a list of about 100 considered to be at the margin and that [7a] can be
top payment service providers worldwide, the reduced by a factor of 0.54% to focus only on
average number of employees per PSP is about employees concerned in the fundamental banking
12,000. We have estimated the total number of and payment services. As a safety measure we will
employees working in payments industry to be more ignore [7b] and ignore all part time employees and
than 1.2 million employees worldwide ranging from consultants working in payments and banking and
ATM manufacturers, ePOS manufacturer to we will base our evaluation on [7a] as the narrow
payment switches and processors etc. estimation of payments and banking employees.

Bankers ≈ 55.9 Million employees [7a] The average commute distance in transport per
employee is known to be approximately 24.14 km

Bitcoin: Cryptopayments Energy Ef ciency 11/28 Michel KHAZZAKA — Valuechain

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one-way. This is an average distance between large simply just powering it on) to about 2,600 kWh/yr
city centres, suburbs and far country sites. According [8e]. IBM servers’ idle energy usage is related to the
to major french bank internal numbers, commute number of Central Processing Unit (CPU) sockets
energy is 57% due to car travels, 26% air travel, 17% and has remained static since 2007 at 365W for two
train totalling 4400 Km/year per employee on socket servers (Shehabi et al, 2016; Shehabi et al,
average or 20 km/day con rming and falling in the 2018). But in reality a server in a data center facility
same range of our estimate above. requires more power. A more accurate estimate
might come from calculating how many servers could
We will ignore airline and train travel energy be used with a given energy capacity. If a similar
consumption and estimate based on a transport mix high tier data center has an 850 MW capacity, and
of employees basically made through petrol and each rack was using 25 kW of power, that institution
diesel with a ratio of 2 wheels and 4 wheel transport could operate 1,768,000 servers. This leads to a
vehicles. Given the results observed in a bank case minimum required energy of 0,481 kW/server that
study, petrol 2 wheels represent 33.8% and requires then consumes 4,212 kWh/yr [8b]
0.45 Litre/Km and the remaining 66.2% are diesel
and petrol 4 wheels and they require 0.147 Litre/Km To count the total number of servers used in banking
each. This leads to a median calibrated ratio between we proceed as follows in a different approach to
diesel and petrol of 9.87 kWh/Litre. Another source validate our estimations. While Amazon and
reached an estimate of about 10.83 kWh/Litre. Alphabet devote 12% and 20% of their operating
Based on the case study observation of 231 worked costs respectively to IT, banks are devoting 29% of
days per year and the energy consumption this leads their operating costs to IT spending. This informs us
to a minimum of 1535.79 TWh/year for round trip that banks’ IT budgets are 2,42 × times higher than
commute. GAFA and other industries [8c]. There are 100
million servers that are currently being used all
Energy(Commute) ≈ 1,535.79 TWh/yr [7] around the world. A substantial number of these
servers are owned by Google and Microsoft. In total,
we’ve estimated that bank data centres use 8.822
million servers [8d], less than 9% of all servers
worldwide, a logical gure based on [8c].

Let’s adopt a different approach. We have veri ed

ENERGY OF BANKING IT with a major French banks that it possess 2
datacenters consuming 1250 KW each. Leading to
Banks also possess data centres either in the vicinity 21.9 GWh/year. Using [6a] this extrapolates to 547.5
internally or outsourced or on the cloud. The most TWh/year for all banks datacenters. But not all
precise way to calculate the energy consumption of a banks are major banks. For instance in France the
bank’s data centre is to estimate the average number ratio is 3.13% major banks and this gives us about
of servers used per bank. Based on our knowledge 1,152 major banks worldwide out of the 36,760
and our consultation with small and large banks we banks. This allows us to estimate that major banks
can estimate that each bank (relatively small banks) consume about 25.22 TWh/year on their
has a minimum of 300 servers varying between large datacenters. While smaller banks consumes much less
IBM mainframes to rewalls, database servers, but are much more numerous. Based on [8d] and
routers, core banking and online banking, backup [8b] we compute that the minimum bank data
servers such, NAS storage etc. we will consider the centres energy consumption is ≈ 37.2 TWh/yr on
lower bound of29: average for all banks worldwide. Major banks
consumes more than 65% of this energy.
Count(BankServers) ≈ 300 servers/bank [8a]
Energy(BankDatacenters) ≈ 37.2 TWh/yr [8]
In terms of annual energy usage, a two-socket server
may use approximately 1,314 kWh/yr (which is

29 This is the average for small banks, so in reality the numbers are at much higher

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 ENERGY OF INTER-BANKING the lower and upper bounds of energy consumption
for CSM messages to be between 36.2 TWh/yr and
79 TWh/yr. It’s safe to consider the average31 equal
Inter-banking communications using nancial
to 57.4 TWh/yr. The rationale of this approximation
messages for wire transfers clearing and settlement
is that certainly a large clearing batch le consumes
are also required to complete the study. Swift
hugely more than a single card authorisation call as
operates three data centers - one in Zoeterwoude,
found for a single Visa transaction [4a], Power(CSM)
Netherlands; another in Culpeper, Virginia, United
> 36.2 TWh/yr. And it’s since the transactions for
States; and a third in Thurgau, Switzerland. It also
CSM are grouped by thousands, to tens of thousands
has a Command and Control center in Hong Kong.
each transaction will consume much less than a 1MB
Not all banks are connected to Swift but only 11,000
email as in [10a] so the Power(CSM) < 79 TWh/yr.
banks. We can conclude from the above sources that
So the average is clearly near the real value.
Swift represents 44% of this use, based on [6a].

Using [4c] we estimate a minimum of 31.3 TWh/yr Power(CSM) ≈ 57.4 TWh/yr [10]
of the energy consumption of Swift-like messages in
data centres alone.
Finally, banking employees use personal computers,
as well as banking software relying on backend
Energy(FinDataCenters) ≈ 31.3 TWh/yr [9] servers usually on the cloud. On average, there are
20 deployed computers for one server leading to 2.8
Clearing and settlement mechanisms (CSM) are used million servers in the backend for banking as well as
by banks to complete payment transactions like EBA 55.9 million personal computers for bank employees
in Europe and STET in France for instance. As a (see [7a]). Using [8e] this translates into 7.27 TWh/yr
reminder sending a simple email on the internet for total backend servers and cloud energy used by
requires 25 Wh of energy [10a]. As a sample, STET, banks for AWS, Azure and other SAP like SaaS. In
the French CSM processed in 2020: 16.74 billion addition, desktop computer consumes about 600
transactions per year [10b]. The total card volumes30 kWh/yr in 8 hours of work per day [11c] leading to
according to Banque de France is 49% of total 33.57 TWh/yr.
payment transactions. Based on [4d] this means that
the total number of world payments is 3.146 trillion Count(BankITServers) ≈ 2.8 million [11a]
Tx/yr, including card and non-card payments, such
as wire transfers and direct debits, requiring clearing Count(BankPC) ≈ 55.9 million [11b]
in most cases. Energy(FrontToBack) ≈ 40.84 TWh/yr [11]

Count(PaymtTx) ≈ 3.146 Trillion Tx/yr [10c]

CSM messages are cleared in batch le mode in

general, yet now they are becoming instant payment
transactions like Faster Payments in UK and SEPA
SCTInst Scheme in Eurozone. We can either use a
methodology of estimating energy consumption of
encryption and transfer of large data transfers
between banks and CSM or use a simpli ed
approach using individual level transactions. Based
on [10c] and both [4a] and [10a], we can evaluate

30 Number of transactions not amounts

31 As a reminder a single payment clearing transaction requires several API calls between small bank to the primary bank to CSM then to
the central bank and back to the bank and the payer and the payees accounts, batch le calls also uses streaming of les over the internet
which consumes much more energy than a simple and small single transaction authorisation the quantity of data in EMV norm of card
payments contains much less data then a batch grouping tens of thousands of transactions per hours or day. So it’s a moderate estimation to
only use [10a] and [4a] instead of n times for n API calls energy costs. Here we used an approximation because such energy consumption
differs very highly between banks.

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 RESULTS FOR CLASSICAL PAYMENTS Circuit). Therefore, we can exclude today Bitcoin
mining through CPU or GPU since they are out of
the network or extremely marginal.34
Finally, we have completed the evaluation of the
energy consumption for all the classical monetary
After China’s mining ban, Bitcoin Mining Map
and payment systems. In conclusion, we can estimate
shows that USA became recently the leading Bitcoin
that the total energy consumption is the sum of
mining country with 35.4% of global hash rate
intermediary results32 in TWh/yr.
power of the Blockchain. It’s important to escape
listing all currently in use ASIC hardware according
Energy(ClassicSystem) ≈ 2,252.75 TWh/yr [12] to their pro tability. This approach requires to cater
for electricity prices and we do not need to use this
Next we will evaluate Bitcoin PoW energy. inaccurate path in our research. A better path is
simply hardware ef ciency: that is Watt consumed
per Terahash and the release dates of each model.
ENERGY OF BITCOIN Non pro table miner units are most probably today
switched off, because by de nition the miner will be
Let’s now analyse the Bitcoin blockchain PoW energy literally loosing money if they switch them on,
consumption, excluding its layer 2 for Bitcoin depending on electricity costs. That said, we’ve
Lightning for now. The most referenced assessment veri ed with industrial miners that they are still using
work is Cambridge Bitcoin Electricity Consumption certain older ASIC models considered today non
Index (CBECI). In April 2022, according to pro table based on average electricity price. That’s
Cambridge, Bitcoin power is supposed to be equal to possible because certain industrial miners negotiated
144.82 TWh/yr [13] with a lower bound of 53.29 very low cost of energy rendering pro table older
TWh/yr and a higher bound of 356.83 TWh/yr. models.
This large range seems more as a guess33 work by
Cambridge than a precise evaluation and these Let’s call i the index of a mining unit model mi out of
numbers are continuously used to criticise the PoW Nt models at time t. We call the Power Ef ciency πi
of Bitcoin. Cambridge acknowledges using different of a mining unit m i , the amount of power required
hypothesis of electricity prices for pro tability to reach a rate of 1 tera-hash.
estimations and “uses simplistic weighting of pro table
hardware” yet Cambridge is aware that “assuming that Po w e r (m i ) [14]
πi = (in W per TH)
all pro table equipment is equally distributed among miners is Ha sh r a t e (m i )
unrealistic given that not all hardware is produced in equal
quantities and readily available”. So there’s plenty of Let’s start by building the mathematical model and
room for improvement on their work and that’s what theory of Bitcoin PoW mining. Let at any point in
we will undertake in this paper with a completely time t:
different methodology.
Mt = {m 0 , m1, . . . , mNt} |M | = Nt miner models
The best and most scienti cally precise method is to
count Bitcoin miner nodes and hardware units and Where M is the set of miner unit model m i and Nt is
then based on the required computing power (PoW the total count of models available at any point of
dif culty) of the installed base of miner units, we can time t since the mining started in 2009 until today in
precisely estimate the kWh actually used by each 2022.
mining unit available on the Blockchain. Today
100% of mining units are a special hardware model Let Rt = {r0, r1, . . . , rn} |R| = |M |
called ASIC (Application-Speci c Integrated

32 Note that many estimates even [7] can be considered as a lower bound since we didn’t take into account all central banks energy
consumption nor all the additional registered Electronic Money Issuers not Payment Service Providers data centres (such as Stripe, or PayPal
for instance) and we didn’t take into account any non internal full time bank employees.
33 Cambridge Index speaks of constructing a “best-guess”

34CPU and GPU mining represent considerably less than 0.000000001% of mining power and they are completely inef cient and not used
actively in mining. We will only consider CPU and GPU mining in our research to compile initial mining data in the rst 5 to 6 years of
PoW mining

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 Such that ∀m ∈ M, f : M → R give us the release the current block dif culty. More speci cally, given
date and allows us to determine the age αi of the the average time T between mined blocks and a
mining unit in order to determine later its market dif culty D on Bitcoin PoW, the estimated hash rate
share of the hash power and its energy consumption. per second H is given by the for mula
Give a time t, we can model all miners attributes D
H (t ) = 232 × . Where T ≈ 10 min but in the
using this approach: T
calculation of hash rate the real value on the
Mmodel = {m 0 , m1, . . . , mNt} blockchain are used and that can be for example less
Mrelease = {r0 , r1, . . . , rNt} than 10 min. Therefore the hash rate although
calculated, is extremely precise for our work up to 10
Mhash = {h 0 , h1, . . . , hNt}
Mi n e r s (t ) → minutes periods, while we are working on monthly
Mpower = {p0 , p1, . . . , pNt}
rates and numbers over 13.3 years period.
Mef f iciency = {π 0 , π1, . . . , πNt}
Mcount = {C0 (t ), C1(t ), . . . , CNt (t )} The hashing Dif culty is a measure of how dif cult it
is to mine a Bitcoin block, or in more technical
terms, to nd a hash below a given target. A high
Fo r e a c h m i n e r w e c o n s i d e r t h e s e t dif culty means that it will take more computing
m i → {ri , αi , h i , pi , πi , Ci (t )} where Ci (t ) is the count power to mine the same number of blocks, making
of the model m i at a given time t, online and the network more secure against attacks. The
contributing to the Bitcoin Blockchain PoW. ASIC dif culty adjustment is directly related to the total
miners life expectancy is between 3 to 5 years and mining power in the Total Hash Rate (TH/s). When
we’ve veri ed this information with the mining the Bitcoin hash rate increases or decreases by ΔH (t )
industry directly. So in our research we’ve accounted this is due to the fact that the installed hardware park
for Nmax = 95 miner models with a release date increased in the total count of mining units across all
between July 2014 and July 2022 (αma x ≤ 5 years models m i . This delta increase or decrease will be
period). Other older models can be safely considered distributed among older and newer hardware
out of the Bitcoin network today (or not impacting released.
the results).
These considerations lead to one equation with up to
Nma x = 95 m o d el s 91 or more variables making it impossible to
ri ∈ [rmin, rma x ] = [2014.07, 2022.08] compute each Ci (t ) . Yet the total hash rate is
αi = t − ri , αma x ≈ 60 m o n t h s distributed over the available models Nt. This fact can
Mi n e r s → h i → T H /s lead us to a rst average calculation but we can
pi → Wa t t achieve a much better evaluation. We note that for
πi → Wa t t /T H t ≤ Ju l y 2014 all old miners are not online anymore,
Cm (rmin ) = Cm (rma x ) ≈ 0 , ∀i ∈ [1, 95] therefore it’s allowed to estimate them as one uni ed
i i
virtual model. Let’s call m 0 the virtual miner
hardware starting since the r0 = rmin = 2009.02
The most precise way to evaluate the Bitcoin PoW (month 1 of Bitcoin going online). Since this virtual ASIC
energy consumption is to calculate the most accurate miner can be considered alone in the market until
count Ci (t ) of installed units for each model over r1 = 2014.07 (month 68), it’s now easy to compute the
time. But since sales data are not available and the count of m 0 for all the period C0 (t ) ∀t ∈ [1, 68] using:
Blockchain does not register the mining model this
approach seems impossible. Yet we’ve found that the H (t )
C0 (t ) = ∀t ∈ [1, 68] total months [16]
increase of the total hash rate ΔHt of Bitcoin can h0
give us a precise indicator of the growth of the hash
power of the total installed miners: At any point t in In the example above we see that in this model the
Nt virtual m 0 with its 0.18 TH/s is allowed to have a
time, H (t ) = ∑ hiCi (t ) . [15] where H (t ) is the hash count of units less than one (until Feb 2011) since it
i=0
simulates all older models: 2 ASIC models, some
rate available on Bitcoin at time t. This data can be GPU and CPU models. And since m 0 and all these
reliably read from Bitcoin Blockchain in near real models combined are no longer online, it’s still a very
time. The hashing power is estimated from the
number of blocks being mined in the last 24h and

Bitcoin: Cryptopayments Energy Ef ciency 15/28 Michel KHAZZAKA — Valuechain

Electronic copy available at: https://ssrn.com/abstract=4125499

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 accurate start to build on for the next released Since the sales are not known and the average
models. distribution is not precise enough, we’ve
demonstrated that Bitcoin hash rate variation ΔHt is
So m 0 equations become as follows: directly proportional to the sum of all ΔCm (t ) that
corresponds to the total miners installed and taking
Nma x = 1 m o d el into account new hardware, minus older miners gone
r0 = rmin ∈ [2009.02, 2019.05] of ine. This leads to ΔHt = Ht − Ht−1, ∀t ∈ [1, 160]
αma x ≈ 120 m o n t h s months being directly proportional to Δ Count of
h 0 = 0.18T H /s miners at t :
m0 → p0 = 360W
π 0 = 2000W /T H Nt

∑ i
H(t)
ΔHt = h × ΔCi (t ), and:
C0 (t ) = i=0
h0
∀t ∈ [1, 163] m o n t h s Nt Nt Nt

∑ ∑ ∑
Ci (t ) − Ci (t − 1) = ΔCi (t )
i=0 i=0 i=0
Note that exceptionally the maximum age of m 0 is
10 years instead of 5 years. It is legitimate to allow Nt

∑ i
for new models to replace it in the market and C (t ) being the total count of mining units at any
i=0
because the last miner issued more than 5 years ago
time t.
is the Bitmain AntMiner S1 with 0.18TH/s model
and released in Nov, 2013, this model is used as m 0
Since hi and pi are given by the manufacturers for all
unifying all older ASIC, GPU and CPU inef cient
models, we need to nd the most accurate approach
hardware. At the same time, Bitcoin total hash rate
to calculate ΔCm (t ) for each one of all Nt miner
was millions of times smaller growing from H(1)=
models at a given36 time t.
0.0000044 TH/s in 2009.02 to H(58) = 2,559 TH/s
in 2013.11, an increase of 581 million folds in about
If the distribution of new hardware to the market is
4 years. This con rms our approach for m 0 and its
made evenly (which is not) and before we apply
0.18TH/s capacity as the uni ed model of all older
additional improvements to this method, it is possible
hardware no longer online since 2019.05.
to solve an approximation of the many variable
equations using the series based on m 0 information :
For example, the virtual number of miner units is:
ΔHi ΔHi
H (20) 0.00417 T H /s Ci (t ) = Ci−1(t ) + giving us ΔCi (t ) = [17]
C0 (20) = = = 0.0232 miner units Nt h i Nt h i
h0 0,18 T H /s

H (61) 15,943 T H /s Let’s now nd a very accurate solution for the

C0 (61) = = = 88,570 miner units35 equation. For m 0 , the C0 (t ) is determined 100%
h0 0,18 T H /s
accurately thanks to blockchain data until the release
Once a new miner model m1 is released to the date of m1 at r1 = 68 . Until α 0 = 68 , m 0 is the only
market at least 1 to 3 months are required for it to be mining virtual model in the market. This will allow
part of the Blockchain hashing power, and will follow us to compute a rst (but unsatisfying) estimation of
a growth rate replacing gradually m 0 market share all mining units over time. In order to improve this
and hash rate until it leaves the installed park of model to the maximum extent, we need to nd a
miners and goes of ine ~60 months (5 years) later. precise distribution model of miner units installation
Using its life time, it will share the hash power with usage and gone of ine.
newer models m i launched after its market entry.

At this stage this is a virtual model count. Miners here are not nodes. Nodes are often pools of mining hardware of ASIC models. At
35

month 61 we can estimate that 88,570 miner units were online actively participating in PoW on Bitcoin nonstop.
36 Overclocking miners will increase the hash rate and increase the consumption. We did not take this into account in the model since the
Power Ef ciency remains relatively the same thus not affecting the total energy consumption of Bitcoin in total but only requiring marginal
less hardware consuming marginally a little more power but ending with an equivalent energy consumption globally.

Bitcoin: Cryptopayments Energy Ef ciency 16/28 Michel KHAZZAKA — Valuechain

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 In economy and in physics new products entering a We still need to determine the σi . The standard
market follow globally the normal37 distribution law deviation is a measure of the dispersion of a set of
in general. We will not undergo a full demonstration miner model m i . A low standard deviation indicates
here, but let’s state that this has been veri ed for that the values tend to be close to the mean μi = 30
many products in logistics and here’s a quick logical months, while a high standard deviation indicates that
veri cation for the miners products: the values are spread out over a wider range. Since
we are looking for an αma x ≈ 60 months as the wide
Once a new mining unit is released, it takes a spread of the normal curve, this solves to a
certain delay to be pre-sold, sold, manufactured, σi ≈ 6.5 m o n t h s ∀i > 0. The interpretation of this
stored, shipped and delivered, thus initiating the value is that between −σi and +σi , a period of 13
start of the bell shape with an exponential growth. months, 68.2% of the total model m i sales are in
Mining market information shows a delay of 1 to 3 production and online on the blockchain. And
months to start a growth penetration phase of the between −2σi and +2σi (26 months period) 95.4%
product. are in production. This leaves a long tail outside the
range ± 2σi (more than 2 standard deviations) for
Then once it becomes largely available in the entering the market and exiting the market on the
market, it grows relatively exponentially in sales borders of the curve, and this was veri ed with
and installation before its growth rate decelerates mining centres still using almost 5 years old
and then gets limited due to 2 factors: market hardware. Given in our model σi = 6.5 months and
saturation, price to power ef ciency (πi), and new μi = 30 months we can now compute the percentage
better models entering the competition limiting the each product sales and installation. We need now to
demand on the previous models. correlate the product market penetration rate with
different competing models and determine the most
Once the interaction of several competing models precise count of each model in time, that is to solve
occur, the previous model decelerates its growth to Ci (t ) , ∀i ∈ [1, Nt ], ∀t ∈ [1,163] months.
halt at a maximum marketshare then the curve
starts reversing while the new models grow Nt
exponentially and the older model starts getting Since the ΔHt = ∑ hi × ΔCi (t ) and since we know
out of market following the reverse process is i=0

sensibly symmetric, until the same process occurs the value of C0 (t ) ∀t ∈ [1,68] , it is possible to
in loops also for the newer models. compute one by one the series Ci (t ) based on Ci−1(t )
using the proportion of each model sales given by
The maximum age on average of any m i is ~5 years γi (t ). We’ve demonstrated that the solution for this
of full-time run thus giving us a knowledge of the complex equation is in [19] below.
Gauss curve span. This important piece of
information is crucial to solve the complex equations. H (t ) = C0 (t )h 0 + . . . + Ci (t )h i + . . . + CN (t )hN ⇒
A normal distribution curve requires 2 variables to be Nt
modelled:
∑ i
H (t ) = C (t )h i , ∀t ∈ [0,163] & ∀i ∈ [0,Nt ] [β ]
i=0

t − μi 2
2 ( σi )
1 −1 We solve for the count of each mining unit as Ci(t) for
γi (t ) = e [18]
σi 2π each model i over time t :

H (t ) γi (t )
Where π = 3.14159265359... and e an exponentiel Ci (t ) = × ∀i , j ∈ [0,Nt ] veri es [ β ]
hi N t γ (t )
∑ j=0 j
function related to Euler’s number e = 2.71828…
then σ is the standard deviation and μ is the mean
Nt
value of the distribution (median). Since we know H (t )
i γ (t )
Proof: ∑ × × hi =
that a miner age αma x ≈ 60 months, we can consider h i
Nt
∑ j=0 γj (t )
i=0
that μi ≈ 30 months on average for any Bitcoin
miner.

37 Also called Laplace-Gauss law, Gauss Law or simply bell shape curve

Bitcoin: Cryptopayments Energy Ef ciency 17/28 Michel KHAZZAKA — Valuechain

Electronic copy available at: https://ssrn.com/abstract=4125499

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 ∑Nt γ (t )
i=0 i ∑ γi (t ) each mi model. Here are the values today at t = 163
H (t ) × = H (t ) since = 1 ∀t ∎ months.
∑Nt γ (t )
j=0 j
∑ γj (t )

To see the evolution of PoW Power Ef ciency over

H(t) γi (t) time see πPoW graph in the diagram [D5] above.
Ci (t ) = ×
hi ∑N t
j=0 γj (t) The importance of the count of hardware per model
t − μi 2
2 ( σi )
is that it allowed us to calculate that there are ≈ 3.2
−1
1 million miner units of the different models today
γi (t ) = e
mi → σi 2π [19] worldwide grouped in the 14,491 reachable Bitcoin
∀i , j ∈ [0, Nt ], ∀t ∈ [1, 163] nodes. Note that our approach do not require any
σ standard deviation of model i mapping per country nor uses electricity pricing
μ norm. dist median of model i directly or indirectly in anyway.
H(t) = hashrate at time t
Since the power of a hardware is determined by the
manufacturer and veri ed by the mining community
This important mi equation allows for an accurate
we can consider its value precise with a very low
description of Bitcoin energy consumption based on
error margin (less than 2%). The error margin of
the precise number of miner units for all miner
bitcoin energy consumption can originate from 2
models. The equation results are con rmed for all
sources:
calculations up to 0.00000001 precision at any point
in time t during the 160 months period.
Our Ci (t ) estimation and the precision of the pi in
Watts provided by the manufacturer39. In our
Bitcoin Blockchain Explorer indicates that the
approach we do not need to consider that the
current miners network hash rate ≈ 198.7 million
hardware up time rate per year (~ 99.9%) since
tera-hashes per second38. And we can read on the
we’ve computed the exact real ASIC miners
blockchain all H(t) values daily since the genesis
uptime consumption and real hash rate delivery
block. Now we can nally compute the energy
(counting only uptime).
consumption of Bitcoin PoW using [20]
Varying the values of σi and μi generate results
Nt
deviating by ϵ < 5 % comforting the precision of
∑ i i
P (t ) = p C (t ) [20]
i=0
our calculations. In contrast, the error margins of
Cambridge index are very large with
H (163) ≈ 198.7 × 1018 H /s [21] ϵCBECI ∈ [−63.2 % ,146.4%].
To t a lCo u n tM (163) ≈ 3,268,000 miners [22]
Note also that not all the 95 ASIC miner models
EBitcoin (163) ≈ 80.69T W h /y r [23] used are solely for Bitcoin mining, many of them are
not that ef cient for Bitcoin and are mostly used to
EMin ( Bitcoin) = 37.4 TWh/yr [23a] mine other cryptocurrencies. Based on this principle
Cumulative miner models count = 96 models alone we can see that [23] is actually an upper
[24]
bound. And if we take this argument into account,
Current miner models online today = 87 models [25] miners with lower πi will be used more in mining
Bitcoin and this will improve the actual Bitcoin
πM ≈ 46.36 W/TH (average of all miners) [26] energy consumption overtime.

Where P(t) is the electrical power of Bitcoin’s PoW in Hypothetically if all mining units were replaced by
Watt at time t. We were able to compute the number the most ef cient ASIC (having the lowest πi possible
of each installed miner units during 163 months for today), Bitcoin energy consumption would drop to
πi = 21.5W /T H instead of [26]. This leads to the

38 That is 198,689,000,000,000,000,000 cryptographic hashes/second

39Note that overclocking ASIC miners may improve the hash rate capability and increase the required energy consumption value of the
miner unit but the power ef ciency remains relatively constant thus not affecting the nal result especially that all us bound by the Bitcoin
total hash rate. So this can produce a variation less then the error margins of our Ci(t)

Bitcoin: Cryptopayments Energy Ef ciency 18/28 Michel KHAZZAKA — Valuechain

Electronic copy available at: https://ssrn.com/abstract=4125499

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 same H(t) work with a large drop of Bitcoin energy
consumption by 40% to only 37.4 TWh/yr. So it is
possible to run all Bitcoin network today with 37.4
TWh/yr without triggering the dif culty adjustment
of the PoW [23a]. Note that this is not an actual
lower bound but minimum required energy today
and the hardware uses actually 80.69 TWh/yr to do
the same work40.

EClassic ≈ 28 × EBitcoin [27]

Bitcoin can run today with 60 × less energy

We conclude that Bitcoin PoW consumes at least

[D1] Calculation of Ci (t ): Count of miners for 96 ASIC ~27.9 times less energy than the classical electronic
models (left to right columns) in [0, 163] months (top monetary and payment system and can run today
down rows) using 60 times less energy based on [23a].

Bitcoin Hashrate in TH/s between months 0 to 163

0
00
00
50

198.7 EH/s
22

0
00
50
87
16

0
00
00
25
11

00
00
25
56

t 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 91 96 101 106 111 116 121 126 131 136 141 146 151 156 161

[D2] Bitcoin PoW real hash rate as observed at its Blockchain over 13.5 years
0
00
00
35

7
66
16
29

3
33
33
23

0
00
50
17

7
66
66
11
33
33
58
0

1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 91 96 101 106 111 116 121 126 131 136 141 146 151 156 161

[D3] Count Ci (t ) of each one of the 92 ASIC miner models contributing to PoW over [0, 163] months

40Note also that commute energy consumption of employees running the ~ 15K nodes is negligible compared to 55+ million banks
employees without counting the very high number payment service providers employees. In addition most of the nodes management work is
done remotely in monitoring and remote maintenance. We did not include on this paper the physical maintenance energy required for
banking and Bitcoin for complexity reasons by it is in the disadvantage of the classical payments system.

Bitcoin: Cryptopayments Energy Ef ciency 19/28 Michel KHAZZAKA — Valuechain

Electronic copy available at: https://ssrn.com/abstract=4125499

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 0
00
00
90

0
00
00
75

0
00
00
60

0
00
00
45

0
00
00
30

0
00
00
15

1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 91 96 101 106 111 116 121 126 131 136 141 146 151 156 161

[D4] Total count of mining units over time (accumulation of the count for the 96 ASIC miner models) over 163 months

Power Ef ciency of PoW in W/TH (all miners combined)

00
22
80
19
60
17
40
15
20
13
00
11
0
88
0
66
0
44

46.3 W/TH
0
22
0

1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 91 96 101 106 111 116 121 126 131 136 141 146 151 156 161

[D5] Evolution of PoW total miners Power Ef ciency πi of all models (163 months) see [26]

Annualised Total Bitcoin PoW Energy Consumption in TWh/yr (compared to Bitcoin hash rate in dashed line)
0
14
0
12
0
1080

80.69 TWh/yr
60
40
20
0

1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 91 96 101 106 111 116 121 126 131 136 141 146 151 156 161

[D6] Energy consumption of Bitcoin PoW between [0, 163] months. Notice the 2 curves inversion at month 151 demonstrating
the higher usage of modern miner units with lower power πi see [D5]

Bitcoin: Cryptopayments Energy Ef ciency 20/28 Michel KHAZZAKA — Valuechain

Electronic copy available at: https://ssrn.com/abstract=4125499

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 COMPARING AT TRANSACTION LEVEL The minimum power per Bitcoin transaction can
occur when the maximum capacity of a block is
used. Note that [33] and [34] cannot be extrapolated
Let’s compare now the work and power of the 2
to larger volumes since Bitcoin transactions are
systems. It is not enough to compare only the total
grouped in blocks and a single block can contain up
energy usage of both system. We have to compare
to ~10K Tx. We will see below the method that
the energy ef ciency per transaction level and the
Bitcoin can scale above this block limit using Bitcoin
quantity of work and power involved in these 2
layer 2 called the Lightning Network.
systems.

The current monetary payment system is at least

Let’s start by comparing the energy consumption at a
5,775 times bigger than Bitcoin in terms of payment
single transaction level. For Bitcoin, the current block
transaction volumes [30] and [10c], and had 60 years
size is between 1 MB to 1.52 MB and hosts today
more time to get optimised and to scale yet consumes
about 2,591 Tx per block. A Bitcoin block now have
at least 28 times more energy than Bitcoin PoW does.
a theoretical maximum size of 4 MB and a more
realistic maximum size of 2 MB41. The exact size
Comparing energy ef ciency per transaction of the
depends on the types of transactions. So the
two competing systems is not a direct calculation of
maximum capacity of bulk processing per block can
the total transactions count per year over the total
be about ~10,380 Tx/block. This result is obtained
energy consumption. Although this might seem
using a variable size of a bitcoin transaction between
logical to compare energy on a single transaction,
303 and 454 KB/Tx (from median to average).
doing so is incomplete because it would be
We’ve computed that Bitcoin can process up to
comparing apples to oranges. A bitcoin transaction
544,879,300 Tx/yr and currently is processing about
and a classical system transaction do not have the
136.22 million Tx/year (operating at ~24% of its
same number of steps, pre-requisites and most
capacity). So on average a single Bitcoin Tx requires
importantly do not get settled at the same duration.
today 592 kWh/Tx but can be executed with 101.5
A Bitcoin transaction gets settled in near real time
kWh/Tx with more adoption of cryptopayments.
within 10 minutes on average42. While in a classical
payments transaction the settlement occurs in about
Note that [33a] is obtained through the current total
1 to 5 business days i.e. up to 7 days43. Most of local
power of PoW 9.211 GW in [33b] and a currently
transactions are usually settled in T+2 which is in 2
low Median Block Con rmation Time ≈ 6.82
days. Cross border payments settle slower due to
minutes/block instead of 10 minutes/block.
additional barriers. Classic payments can be
Co u n tcurrent (B i t c o i nT x) ≈ 136.22 × 106T x /y r [29] settled up 1008 times slower than a Bitcoin
transaction. This is the case for cross-border
Co u n tma x (B i t c o i nT x) ≈ 544.88 × 106T x /y r [30] payments for example. They are ≈ 2% of total
payments worldwide but increasing extremely fast
Pe a kreal (B i t c o i n Ca p a c i t y) ≈ 4.32T x /s [31]
due to massive adoption of online payments and
Pe a k ma x (B i t c o i n Ca p a c i t y) ≈ 17.3T x /s [32] mobile payments with global marketplaces and
immigration working force. But in the larger case, we
Energyavg (1T x) ≈ 592 kWh/Tx [33] can consider that the settlement duration of classical
payment transaction is on average 2 days. A classic
Energymin (1T x) ≈ 67 kWh/Tx [34] payment transaction is on average 288 times
EPoW (163) ≈ 1,045,529 kWh/block (today) [33a] slower than a Bitcoin transaction [35] (and
currently 422 times faster) given the recent block
PPoW (163) ≈ 9.211G W [33b] mining duration in 410 seconds.

41 This difference is due to the fact that Bitcoin uses now a maximum “weight limit” of a block. Block weight is a measure of the size of a
block, measured in weight units. The Bitcoin protocol limits blocks to 4 million weight units, restricting the number of transactions a miner
can include in a block. Four million weight units is equivalent to 4MB of data, meaning the maximum size for a block is now 4MB.
42 The current Median Con rmation Time on Bitcoin Blockchain has recently dropped below 7 minutes. Bitcoin PoW mining dif culty is

adjusted every 2016 blocks (every 2 weeks approximately) so that the average time between each block remains 10 minutes.
43Swift GPI hasn’t been adopted yet but will allow in the future for faster cross border transactions within minutes too. Central Bank Digital
currency experimentation (Donbar Project by BIS) tested a different approach using multi-CBDC between central banks directly. But these
systems are not yet in production. See also Swift How long do wire transfers take?

Bitcoin: Cryptopayments Energy Ef ciency 21/28 Michel KHAZZAKA — Valuechain

Electronic copy available at: https://ssrn.com/abstract=4125499

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 In physics power is the energy consumed in a given vicinity or online transactions. Similarly it is
duration, and the work is a form of change in energy important to understand that the only sound
that also when divided by time gives power. So let’s estimation of energy consumption for Bitcoin is per
compare work done by Bitcoin and the work done by block. Since a block can contain 0 to 10,380 Tx yet it
the classical electronic payment and banking system. consumes the same amount of energy per block (see
Based on [0] [33] and [33a]

The classical electronic system consumes at least 0.7 First conclusion, Bitcoin is not used to its full
kWh/Tx on average (see [12] and [10c]) but potential. Since we can increase the
completes the work in ~48 hours on average. Bitcoin transaction volumes ×4 without increasing its
consumes currently between 406 kWh/Tx and 592 energy consumption. Block size is underused
kWh/Tx and nishes the transactions in ~10 today and Bitcoin adoption can grow without
minutes on average (currently in 6.82 minutes). When increase in energy. When this maximum limit is
blocks are full a single Bitcoin transaction would reached this will be the highest volume capacity
consume 101 kWh/Tx at the current dif culty level Bitcoin can handle, and that’s why we cannot
and with current miners mix. When old miners are extrapolate energy growth to be converted to more
replaced only 47 kWh/Tx would then be required at throughput above this cap. Bitcoin solved this limit
the same dif culty level. by introducing Lightning Network at a layer 2 that
we will cover in the next paragraphs.
It is also important to understand the meaning of the
average 0.7 kWh/Tx for the classical system. This Based on [0], we’ve de ned that: the same work done
average is based on all 3.146 Trillion Tx/yr that the by both systems is moving money through a
banking and payments system processes while displacement over time, instead of moving a physical
consuming 2,252 TWh/yr (see [10c] and [12]). And is object through space. The proper methodology in
computed as the lower bound estimation after several order to compare apples to apples is to compare the
simpli cations. It is clear that the banking system as a energy consumption relative to the settlement time of
whole can sometimes consume much more or much the 2 systems. Let’s call Compared Energy
less energy per transaction depending on the Ef ciency or energy conversion ef ciency (η) a number
different nature of the payment act: cross border, without a unit obtained as a ratio of the useful work
card, or non-card, instant payment, cash transaction, output of an energy conversion system compared to
another system, here Bitcoin compared to the global
monetary and payment system.
Energy in kWh/Tx
0
80

Pc tc2 ΔWc . d tc A
η = = = ηe × ηd = c
6
68

PB tB2 ΔWB . d tB AB
1
57

Current PoW energy per Tx is between 406 to 592 kWh/Tx ΔWc dt

Where, ηe = and ηd = c .
7

ΔWB d tB
45
3
34

Note that dt is the displacement in time as in [0], e is

for energy, c for classic system and B for Bitcoin. ηe, is
9
22

101 the energy ef ciency per transaction and ηd , is the

4

duration ef ciency per transaction (distance in time).

11

Note also that A = P . t 2 is called action in physics.

0

1 400
1 900
2 400
2 900
3 400
3 900
4 400
4 900
5 400
5 900
6 400
6 900
7 400
7 900
8 400
8 900
9 400
9 900

The action is the momentum of the transaction

times the displacement it moves through time and
Transactions per block has dimensions of energy × time, and its unit can be
in joule-second (like the Planck constant h).
[D7a] Current energy consumption of a single Bitcoin
transaction using PoW in kWh per Tx versus the number
Ac [35]
1,400 to 10,100 Tx/block. (Bitcoin can run today at Energy Ef ciency is: η = ηe × ηd =
47.1 kWh/Tx with the newest miners at same dif culty) AB

Bitcoin: Cryptopayments Energy Ef ciency 22/28 Michel KHAZZAKA — Valuechain

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 η (function of Bitcoin PoW energy ef ciency per transaction)
3,0
by newer more ef cient models and without
2,7 increasing the hash rate nor the transaction count
2,3 per block, ηBitcoin is becoming much higher per
transaction based only on PoW. Then 37.4 TWh/yr
2,0
would be consumed by PoW instead of the current
1,7 value and ηmax = 4.37× see [23a].
1,3
η ∈ [0.5, 3]
1,0 Energy Capacity Tx Time Ef ciency
Energy
0,7

0,3 TWh/yr Tx/yr kWh/Tx Min η

0,0 Classic 2252 3.146 0.7 2880 1×
1 400
2 000
2 573
3 200
3 800
4 400
5 000
5 600
6 200
6 800
7 400
8 000
8 600
9 200
9 800
Trillion

Transactions per block Bitcoin 80.69 133 407 6.82 0.74×

Current Million
[D8] PoW η energy ef ciency vs Classical system,
Bitcoin 80.69 794 101.6 6.82 2.97×
Current average, max and break even η depending on
Max Million
count of Tx/block. (current miner models mix). Break
even is reached at 3500 Tx/block Bitcoin 37.4 794 47.1 10 4.37×
Best Million

At a single transaction level, Bitcoin today is [36]

η ≈ 0.5 to 3 × more energy ef cient than the [T2] Bitcoin Energy Ef ciency compared to the classical
classical system. The range of ηB ∈ [0.5, 3] System. (Current: Bitcoin current average, Max: Bitcoin at
depends on the number of transactions per block maximum capacity and Best: Bitcoin with newest miner units
for the same PoW)
“Eta" η can be analysed as energy ef ciency or action
ef ciency as per [35]. That is temporal ef ciency BITCOIN LIGHTNING VS INSTANT PAYMENTS
multiplied by work ef ciency or the ratio of action A
per transaction of both systems.
Let’s take into account now Bitcoin Lightning
At its current capacity, Bitcoin PoW can use 412 network compared to Instant Payment (IP) schemes
times more energy per transaction than the electronic that are drastically increasing the nality time of the
system and can nish the same work 413 times faster transaction respectively of both systems. The
with a median block con rmation time of ~7 Lightning Network has an important capability to
minutes/block today. At a block rate of 10 minutes, scale up exponentially the transactions throughput
Bitcoin PoW is at least 288 times faster. above Bitcoin layer 1, yet it does so without growing
in a proportional rate to the energy input.
We can conclude that PoW layer 1 of Bitcoin is
today ηBitcoin at the same energy ef ciency rate It’s important to understand rst how Lightning
or above as the electronic system at single transactions work. Lightning leverages existing
transaction level. Yet this ef ciency is not yet used Bitcoin transaction channels between peer to peer
to its full potential today. If bitcoin adoption lls the payers and payees to group additional Bitcoin
blocks with 3,500 transactions in average, then η = 1 Lightning transactions in a single Bitcoin PoW
and the break even is reached with the classical transaction on the main Blockchain. For example, if
system at a single transaction level. Today at current Alice A wants to pay Georges G, 1000 satoshis44
block size and if the blocks are lled to their Lightning will nd the fastest open channel that’s
maximum capacity ηmax = 3× better energy ef ciency already executing transactions on its path to include
than the classical system per transaction. In the the amount and make the payment instantly on this
future, old miner models will get eventually replaced channel. From A to G the transaction can be direct
between 2 nodes if they have an open prepaid

44 As a reminder 1 bitcoin is divisible into 100 000 000 satoshi so 1 satoshi = 0.00000001 bitcoin about 0.4$ and this date.

Bitcoin: Cryptopayments Energy Ef ciency 23/28 Michel KHAZZAKA — Valuechain

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 channel between them, if not and the transaction depth reaching the core bank main layer (we do not
needs to go to the other end of the globe, it’s account for the noti cations of the payer and the
assumed that ≤ 6 hops are required from A to reach payee of the execution of the transaction since these
G: are sensibly the same also for Lightning). The total
number of hops can be about more than 20 hops
hop hop hop hop hop hop
A B C D E F G between heavy duty servers in data centres and
1 2 3 4 5 6
mainframes in addition to centralised systems at the
central bank linking everyone. For eurozone instant
During the right of this paper, Lightning is in
payments SCTInst scheme, the clearing and
production and live but is still in its early adoption
settlement mechanism CSM can be through an
with 36,852 nodes (14,950 nodes with public IPs) and
intermediary like STET in France, linking banks to
83,601 open channels. Lightning network capacity is
the TIPS system at the European Central Bank. Note
today 141 millions $ with an average node capacity
also that an instant payment transaction is not always
of 8,183$ (0.213 BTC). An instant payment
a nal transaction, it guarantees the nality in
transaction on Bitcoin costs only 1 satoshi as a
advance since it uses mirror accounts at CSM of the
median base fee and takes a fraction of a second to
banks accounts at central banks. The complete
nalise.
nality is usually delayed especially when the central
bank system is not available.
A Bitcoin Lightning node can be modelled using a
Raspberry pi with an SSD par nodes. Such a unit
Note that comparing Bitcoin Lightning to Faster
consumes about 5W if both CPUs are busy which is
Payments or Instant Payment Schemes without
not the case all the time. A transaction is processed in
counting the underlying channel closer on Bitcoin
less than a second roughly in ≈500 milliseconds per
using PoW is a valid approach. The rational is that a
transactions as the duration of actual processing.
Bitcoin Lightning transaction is nal at layer 2 and its
Given the estimation of 6 hops:
an option to write it later on the layer 1 of Bitcoin
with PoW or to close the channel. Also saying that an
EL2 (L i gh t n i n g) ≈ 6 × 5W × 0.5s = 0.00416667W h
instant payment in classical system can take 7
per transaction45 or 7.5W of power, if the
seconds instead of 48 hours is sometimes wrong
transactions are treated in a single mode. This is
because in reality it can takes in certain cases 3 hours
about 172,786 times less energy than a classical
to 24 hours to settle completely with central bank
payments transaction if only L2 is considered (we
money while on Bitcoin Lightning it is nal after a
will include both layers into the benchmark)
fraction of a second and on the worst case it can take
10 minutes (optionally) with a channel closing on the
EL2 ( Lightning ) ≈ 0.000004167 kWh/Tx [35] main Blockchain.

Let’s compare this result to an instant payment Based on the preceding analysis of Lightning and
transaction for instance in the eurozone (SEPA Instant Payments we can consider that instant
SCTInst scheme). A payment transaction is initiated payments energy consumption is equivalent to the
at an online banking account relying on several same old classical system energy consumption since it
banking servers doing compliance, online banking uses the same hardware and banking infrastructure
backend, core banking layer 1 and 2, instant but only prioritises and accelerates certain
payments servers such as Payment as a Service PaaS transactions part of the work ow. In addition the
and the server for instant payments that calls the means of payment by itself as instant payment is still
CSM to reach the central bank instant payment not yet widely adopted in payments globally since it
system to check 1st the reachability of the payee’s is still missing additional complementary services
bank, thus making several calls among at least 5 to 10 such as Request to Pay, link to card payment
hops just for the reachability checks. Then ounce the initiation and PoS acceptance solutions. Finally an
reachability is OK between payer and payees banks, instant payment is today a local payment and is not
the instant payment order is given and the processing available for cross border transactions. On the other
goes through the same hops in addition to more hand Bitcoin Lighting is still also in its beginning of

45This is a minimal energy cost today without counting for smartcontracts added value services above Bitcoin Lightning that will become
possible thanks to new protocols under development such as TARO and Watchtowers.

Bitcoin: Cryptopayments Energy Ef ciency 24/28 Michel KHAZZAKA — Valuechain

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 development with certain issues like stuck and coins, which is not realistic since all central banks
transactions that cancels after a longer time than 1 are promising the opposite. Since IP cannot replace
second. As we see both innovations are competing all electronic payment transactions we are forced to
but still not 100% stable and not deployed to a large maintain the cash servicing energy. We have also
scale. simpli ed the model and considered that additional
energy required to service IP is negligible.
Comparing payments throughput, we saw in [10c]
that the classical system has a capacity of 3.146 Energymin ( IP ) ≈ 2 022 TWh/yr [38a]
Trillion Tx/yr that might seem to correspond to
99,759 Tx/s. But for a large part these transactions Energyavg ( IP ) ≈ 2 252.75 TWh/yr [38]
are bulk payments and not individual peak capacity.
Note from [4d] that the maximum capacity today of Energytx ( IP ) ≈ 71 kWh/Tx [39]
card payments authorisation is limited to ≈48,891
Capacity(IP) ≈ 31.53 Billion Tx/yr [40]
Tx/s. At the same energy input in both systems,
compared to Bitcoin, the Lightning Network can
handle 1,000,000 Tx/s in a single channel that is Note that [38] is only theoretical since today cross
20.45 times more capacity than the classical system border transactions are not instant payment ready
and still 345,600 times faster or at least 14 times and the total number of instant payment Tx is below
faster than Instant Payments46. maximum capacity of [40]. Average energy of a
single IP transaction [39] is between 64 and 71
Lightning is 14 × faster than Instant Payment [37] kWh/Tx based on [38a] and [38] respectively and
the theoretical today’s maximum in [40].

And total Energy consumption of Bitcoin and By applying the same method to a Lightning
Bitcoin Lightning is sensibly the same: transaction, we will not consider the single layer 2
energy and its 0.000004167 kWh/Tx. For Bitcoin we
EL1L2 (B i t c o i n) = EL1 + EL2 = EL1 + ϵL2 ≈ 80.69T W h /y r will also take both layers leading to:

Theoretically if we consider that Instant Payment is

EnergyL1L2 ( Lightning) ≈ 80.69 TWh/yr [41]
fully adopted worldwide even for cross border
payments, the maximum scale up capacity is EnergyL1L2 ( LightningTx) ≈ 0.00256 kWh/Tx [42]
estimated by Swift to be 1000 Tx/s. That is a
maximum throughput of 31.53 Billion Tx/year. This Capacity(IP) ≈ 31.54 Trillion Tx/yr [43]
shows a scalability ceiling for current electronic
centralised payment systems limiting the adoption of
instant payments for about only 1% of current global CONCLUSION
payment transactions. In order to increase this limit
important hardware and architecture changes are Today when we transfer 1 dollar from a payer to a
required from core banking, online banking, payment payee, there is no direct real47 transfer of value done
hubs, Swift GPI to central bank systems. between the two. This is due to the fragmented
nature of electronic monetary system today. What
In order to evaluate the precise total average energy
should take place during the transaction in the
ef ciency of an Instant Payment transaction, we can
electronic system is a change of ownership of the
omit all cash, CIT and ATMs related energy and
asset called money, but in reality it is a conversion of
keep only banking, PSP, and Interbanking energy
commercial bank money supervised by the central
consumption. The 2,252 TWh/yr drops to 2,022
bank. The payment executes a burn of this private
TWh/yr for a maximum capacity of 31.53 Billion
electronic money conserved by the bank of the payer
Tx/year. Note that this lowered total energy
and then a different operation of earn is performed
consumption means that there are no more banknote
for the equivalent amount with a different privately

46 Which is technically sometimes not nal in 7 seconds and require clearing.

47Money in cash form (banknotes and coins) are indeed directly exchanged between Alice and Georges but they are not 100% direct
exchange of money. They are a direct exchange of central promise of the face value on the paper or coin guaranteed by the central bank. So
there’s no intrinsic value being instantly exchanged.

Bitcoin: Cryptopayments Energy Ef ciency 25/28 Michel KHAZZAKA — Valuechain

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 issued electronic money by bank of the payee. The of its value chain and participants, allowing the
settlement of this burn and earn is achieved through a commoditisation of the whole classical payment
distinct transaction48 executed between the bank of system and allowing additional services such as smart
the payer and the bank of the payee using their own contract and programmability. In contrast, Instant
accounts at the central bank. Payments is not, and require additional services such
as Request to Pay scheme and also a link to a card
The payee, although he received the payment, will scheme which are not built into the classical system
never have a direct claim on it. It’s an amount that yet.
he’s is lending to his bank, equivalent to a promise: “I
owe you” (IOU). His bank owes to him this amount of Globally, results prove that Bitcoin uses 28× less
money at the central bank. This is an important energy than the classical system even without
difference between Bitcoin and the classical money the inclusion of Lightning and Instant Payments to
system. A Bitcoin transaction between a payer and a the benchmark and without comparing to any other
payee is a direct transfer of the cryptoasset: bitcoin cryptopayments consensus mechanism using proof
functioning as cryptocurrency without the need of of stake for example.
any trusted third party. The nature of the
cryptocurrency Bitcoin is cryptographically different. Today at a single transaction, level Bitcoin Proof of
It is a token or real value and not money as debt or a Work is in average 0.7× to 3× more energy ef cient
promise, on the contrary it is nal with a direct than a classic electronic payment transaction and can
ownership of the intrinsic value of the asset a feature go up to 4× with more adoption or natural
that the electronic money system does not offer replacement of older mining units with more
consistently except in banknotes and coins. That’s ef cient hardware already available.
why comparing Bitcoin to electronic money and
payment system is not comparing 100% similar When Bitcoin Lightning and Instant Payments are
systems. Yet in this paper we’ve endeavoured to included in the benchmark, and by simulating that
compare their common promise only from an energy they are used to their highest capacity in both
ef ciency point of view, ignoring all additional systems we nd that a Bitcoin Lightning transaction
features of both. For instance Bitcoin is also a is in average 345,000 times faster than classical
programmable form of money with less complexity system and 14 times faster than an instant payment

Total Energy Total Capacity Tx/sec Tx Energy Tx Duration Energy Ef ciency

TWh/yr Tx/yr kWh/Tx Seconds ηEE

Classical System † 2252.75 3 146 616 541 353 99 779 0.7 172 800 1×

Bitcoin PoW 407

80.69 136 043 995 4 409 0.74 ×
Current to 593

Bitcoin PoW
36.7 793 911 131 25 47.1 600 4.37 ×
Theoretic Best

Instant Payment ‡ 2252.75 31 536 000 000 1 000 71 ~7 247 ×

Bitcoin Lightning † 96.7 Million ×

80.69 31 536 000 000 000 1 000 000 0,00282 ~0.5
(L1+L2) ‡ 391,000 ×

[T3] Figures of Instant Payment & Lightning: both systems used to their maximum capacity to demonstrate full potentiel and
scalability. Hypothetically every Tx is switched to its fastest mode in each system

48This transaction groups all the Alice to Georges transaction but bundled with all transaction between these 2 banks after the netting of
their values

Bitcoin: Cryptopayments Energy Ef ciency 26/28 Michel KHAZZAKA — Valuechain

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 transaction. In addition Bitcoin Lightning scales “Banknotes and coins circulation” — ECB, 2022
far higher than Instant Payments with a
“Benchmarking Commercial Building Energy Use Per Square
theoretic capacity of 31 Trillion Tx per year for Foot” — IotaComm, August 20, 2020
Lightning compared to 31 Billion Tx per year for
“Bilan des missions de gaz effet de serre 2017 de la Banque
Instant Payments. This capacity limitation is mostly de France” — Banque de France, Jan 2019
due to the Swift like cross border systems limitation
“Bitcoin, totem & tabou — Que pr sage l’essor des
in throughput at ~1000 transactions per second. In cryptomonnaies ?” Institut Sapiens, Fev 2018
our estimation we’ve used 1000 Tx/s as a global
“Cambridge Bitcoin Electricity Consumption Index” —
maximum for instant payments, but in reality Cambridge (CBECI), 2022
different regional or country systems may be unable
“Circulation velocity and how you can in uence it” — De La
to reach that capacity for instance, European Central Rue, 2018
Bank instant payment scheme (TIPS) is estimated to
process up to a maximum average of 500 “Climat: des emails à l'e-book, l'impact du numérique n'a rien
de virtuel” — Science & Avenir, Mars 2016
transactions per second. As a consequence, if both
systems are used to their maximum capacity, the “Community Banks Get Creative With Unused Branch Space”,
Independentbanker.Org, January 2, 2018
energy cost of a single instant payment transaction
becomes much higher than a classical payment and “Comparing Bitcoin & Lightning energy usage to the real
world” — Co-Authored by Oliver Barratt & Danny Scott, 2021
requires 64 to 71 kWh/Tx. Bitcoin scales better and
manages to decrease drastically down to 0.00256 “Comparing Bitcoin’s Environmental Impact…” — Hass
McCook, April 2021
kWh/Tx on his 2 layers combined (including PoW).
“Con rmed Transactions Per Day” — blockchain.info
In conclusion, Lightning at a single transaction level “Currency and Coin Services” — Board of governors of the Federal
allows Bitcoin to become 96 Million × more Reserve System, April 2022
energy ef cient than a classical payment and “CZ Binance” — twitter.com, March 14, 2022
~ 400,000 × more energy ef cient than an
“Diebold Innovation Leads to World's Greenest, Most Power-
instant payments. Ef cient ATM” — prnewswire.com, March 2014

We can observe that the classical system is over “Electric trucks like the Tesla Semi are 'pointless both
economically and ecologically,' according to a vehicle-tech
optimised to consume less energy per transaction to expert” — Johannes Kaufmann and Qayyah Moynihan, Business
operate trillions of transaction per year in relative Insider Deutschland , Apr 3, 2019
slow speed between 2 to 7 days to complete. This “En moyenne, en France, un trader gagne 1 million d'euros par
over optimisation and specialisation causes it to be an” — lepoint.fr, 2014
fragmented, fragile and less capable of scaling up “Energy hogs: Servers vs. desktops vs. set-top boxes” — Patrick
today into instant payments. While Bitcoin has a Thibodeau, JUL 6, 2011
higher power output ratio and is capable to scale very “Energy Losses Due to Imperfect Payment Infrastructure and
ef ciently using Lightning Network, thanks to the Payment Instruments” — Oleksandr Melnychenko, Oct 9, 2021
PoW layer of its main Blockchain. “Everything you need to know about cross-border payments” —
emerchantpay, 2021

“Fourteen Facts about the US Penny” — Design Life-Cycle, 2014

“From Home to Work, the Average Commute is 26.4 Minutes”

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Bitcoin: Cryptopayments Energy Ef ciency 27/28 Michel KHAZZAKA — Valuechain

Electronic copy available at: https://ssrn.com/abstract=4125499

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“Number of employees at banking institutions in China from (*) Michel KHAZZAKA (@kneisseh), founder of Valuechain a
2009 to 2017 (in million persons)” — Statistica Cryptopayments consulting enterprise and YouTube channel.
Electronic Telecom and Computer Engineer specialised for 17
“Number of individuals employed by credit institutions in
Europe (EU28) from 2009 to 2019” — Statista years+ in payments security and innovation. Lead of
Cryptopayments workgroups at several french payments and inter-
“Real-Time Lightning Network Statistics” — 1ML.com, banking entities. An international speaker and trainer, has given
lectures and courses in 5 continents on payments, blockchain and
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Paribas dans le monde de 2017 à 2020” — Statista cryptocurrencies, some of which at Sorbonne and Paris Dauphine
universities in Paris and the American University of Beirut.
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Free” — The Scholarly Kitchen, 2022

Bitcoin: Cryptopayments Energy Ef ciency 28/28 Michel KHAZZAKA — Valuechain

Electronic copy available at: https://ssrn.com/abstract=4125499

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