CALCULATING MEDICATION DOSAGES

DOSAGE CALCULATIONS
(INTERPRETING DRUG PRESCRIPTIONS)
Three systems of measurement are used
Ex: Caps. Diphenhydramine (Benadryl) 25 mg
during the calculation, preparation, and
q4h po
administration of medicines.
o Interpretation: “Give the client one 25
METRIC SYSTEM mg capsule by mouth every 4 hours”
Ex: Elixir acetaminophen (Elixir Tylenol) 80 mg
Was invented in France in the late 18th tid pc and at bedtime po
century o Interpretation: “Give 80 mg of elixir
Most widely used system of measure acetaminophen by mouth three times
Based on decimal system, so all units are a day after meals and at bedtime.”
determined as multiples of 10
gram as basic unit of solid(weight) AMOUNT/DOSAGE
liter as basic unit of liquid volume
meter as basic unit of length

Metric Unit most frequently used:

1 g = 1000 mg
1 kg = 1000 g
1 L = 1000 mL
1 mg = 1000 mcg

HOUSEHOLD SYSTEM
TIMING OF ADMINISTRATION
Measuring system that is found in recipe
books
Primarily used by patients who take
medication at home, however they are least
accurate.
Teaspoon as basic unit of fluid measure
Pound as basic unit of solid measure

Common Household Equivalents:

1 quart = 4 cups
1 pint = 2 cups
1 med size glass = 8 ounces
1 teacup = 6 ounces VALUES OF SINGLE ROMAN NUMBERS
1 tablespoon = 3 teaspoons
1 teaspoon = approximately 5 ml

APOTHECARY SYSTEM

Originated in Greece, but eventually it made its

way to England where it was used during the
late 1600s.
Is an ancient system, means “pharmacist” or
“druggist”
Very old system of measure
Uses Roman numerals to denote amount
GENERAL METHODS FOR DRUG
o Ex: 15 grains written as “gr xv”
CALCULATION
Minim as basic unit of liquid volume
Grain as basic unit of solid measure Ratio & Proportion
o Ex: grains – 1/150 Fractional Equation
Basic Formula
Body Weight – Used for pedia patient
Body Surface Area – Used for pedia patient
 TERMS The order has been converted to the same
measurement as the available tablets. Now, solve for
Route: How the medication is entering the
the number of tablets that you will need, letting X be
body. PO? IV? Topical?
the desired dose.
Medications: The actual compound that is
completing the desired effect (25 𝑚𝑔)/(1 𝑡𝑎𝑏𝑙𝑒𝑡) = (50 𝑚𝑔)/𝑋
Dose: How much of this medication is being
administered? 25 (𝑚𝑔)𝑋 = (50 × 1) (𝑚𝑔) (𝑡𝑎𝑏𝑙𝑒𝑡)
Vehicle: The way/size the medication is
available 𝑋 = (50 (𝑚𝑔) (𝑡𝑎𝑏𝑙𝑒𝑡))/(25 (𝑚𝑔))

𝑋 = 𝟐 𝒕𝒂𝒃𝒍𝒆𝒕𝒔
RATIO AND PROPORTION

Ratio – The relationship of two quantities It FRACTION

may be expressed in the form 1:10 or 1: 2,500
Sometimes the desired dose will be a fraction
or it may be expressed as a fraction – 1/10 or
of a tablet or capsule, like ½ or ¼.
1/2,500.
Some tablets come with score markings that
Proportion - Is formed by using two ratios that
allow them to be cut.
are equal.
Pill cutters are readily available in most
pharmacies to help patients cut tablets
EXAMPLE #1 appropriately.
An order is written for 10 grains of aspirin (gr x,
aspirin). The tablets that are available each contain 5 BASIC FORMULA
grains. How many tablets should be given? What will
be your answer? ORAL DRUGS
First, set up the equation: Frequently, tablets or capsules
For solid and liquid preparation
(5 𝑔𝑟)/(1 𝑡𝑎𝑏𝑙𝑒𝑡) = (10 𝑔𝑟)/𝑥
(𝐷 (𝐷𝑒𝑠𝑖𝑟𝑒𝑑 𝐷𝑜𝑠𝑒))/(𝐻 (𝐴𝑚𝑜𝑢𝑛𝑡 𝑜𝑓 𝐷𝑟𝑢𝑔 𝑜𝑛 𝐻𝑎𝑛𝑑))
Cross multiply the ratio: × 𝑉𝑒ℎ𝑖𝑐𝑙𝑒 = 𝐴𝑚𝑜𝑢𝑛𝑡 𝑡𝑜 𝐺𝑖𝑣𝑒

5 (𝑔𝑟) 𝑋 = 10 (𝑔𝑟) (𝑡𝑎𝑏𝑙𝑒𝑡) (𝐷𝑜𝑠𝑒 𝐷𝑒𝑠𝑖𝑟𝑒𝑑)/(𝑆𝑡𝑜𝑐𝑘 𝑜𝑛 𝐻𝑎𝑛𝑑) × . 𝑉

= 𝐴𝑚𝑜𝑢𝑛𝑡 𝑡𝑜 𝐺𝑖𝑣𝑒
Rearrange and cancel the units and numbers:

𝑋 = (10 (𝑔𝑟) (𝑡𝑎𝑏𝑙𝑒𝑡))/(5 (𝑔𝑟)) FOR SOLID

𝑋 = 𝟐 𝒕𝒂𝒃𝒍𝒆𝒕𝒔 A health care provider orders that a patient receive 1g.

of ampicillin. The ampicillin bottle states that each
tablet in the bottle contains 0.5 g
EXAMPLE #2
An order is written for 0.05 g Aldactone to be given (𝐷 = 1.0 𝑔)/(𝑆 = 0.5 𝑔) = 𝟐 𝒕𝒂𝒃𝒍𝒆𝒕𝒔
orally (PO). The Aldactone is available in 25 mg.
NOTE: If the dosage on hand and dosage ordered
tablets. How many tablets would you have to give?
are both in the same system of measurement, but they
First, you will need to convert the grams to milligrams. are not in the same unit of weight within the system,
the units of weight must first be converted.
(1 𝑔)/(1000 𝑚𝑔) = (0.05 𝑔)/𝑋
The health care provider orders 1000 milligrams
Cross multiply: (metric) of ampicillin. On hand is 0.25g (metric) per
tablet.
1 (𝑔)𝑋 = (0.05 × 1000) (𝑔) (𝑚𝑔)
𝑫 𝐷𝑜𝑠𝑒 𝐷𝑒𝑠𝑖𝑟𝑒𝑑
Simplify: × 𝑉𝑒ℎ𝑖𝑐𝑙𝑒 = (1000 𝑚𝑔)/(250 𝑚𝑔)
𝑯 𝐷𝑜𝑠𝑒 𝑜𝑛 𝐻𝑎𝑛𝑑
= 𝟒 𝒕𝒂𝒃𝒍𝒆𝒕𝒔
𝑋 = (50 (𝑔) (𝑚𝑔))/(1 (𝑔))

𝑋 = 𝟓𝟎 𝒎𝒈
 FOR LIQUID PROBLEM #3
The order is for Potassium Chloride (KCl)20 The order is penicillin 50,000 units. The vial
mEq. The bottle is labeled KCl elixir 10 reads penicillin 500,000 units. Add 4.3 mL to
mEq/mL. How many mL. will be given? yield 5mL.

20 𝑚𝐸𝑞 50,000 𝑢𝑛𝑖𝑡𝑠

× 1 𝑚𝐿 = 𝟐 𝒎𝑳 × 5 𝑚𝐿 = 𝟎. 𝟓 𝒎𝑳
10 𝑚𝐸𝑞𝑚𝐿 500,000 𝑢𝑛𝑖𝑡𝑠

Answer: 2 mL Answer: Give 0.5 mL

PREVENTION OF MEDICATION ERRORS

FOR CAPSULE
The order reads: Phentoin sodium capsules The errors that occur when the drug
(Dilantin) gr. v orally. Available is a bottle prescription is misinterpreted. Often, the way
labeled Dilantin 100 mg.per capsule. How the amounts are expressed in the original
many capsules will be given? 1gr. = 60 mg prescription for weights, volumes, and units
cause interpretational errors.
300 𝑚𝑔
× 1 𝑐𝑎𝑝𝑠 = 𝟑 𝒄𝒂𝒑𝒔 In General, the following rules should be followed in
100 𝑚𝑔
transcribing prescriptions:
Answer: 3 caps
Never leave a decimal point naked. Always
place a zero before a decimal expression less
FOR PARENTERAL
than one.
The order reads: Furosemide (Lasix) 35 mg IV. o Ex: 0.2, 0.5
The vial is labeled 40 mg=4 ml. How many mL. Never place a decimal point and zero after a
should be given? whole number, because the decimal may not
be seen and result in a fold overdose.
35 𝑚𝑔
× 4 𝑚𝐿 = 𝟑. 𝟓 𝒎𝑳 o Ex: 2.0 mg read as 20 mg by mistake.
40 𝑚𝑔 The correct way is to write 2 mg.
Avoid using decimals whenever whole
Answer: 3.5 mL
numbers can be used as alternatives.
o Ex: 0.5 g should be expressed as 500
PROBLEM #1 mg, and 0.4 mg should be expressed
An order has been written for 75 mg as 400 mcg
meperidine to be given intramuscularly (IM). Whenever possible, use the metric system
The vial states that it contains meperidine, 1.0 rather than grains.
mL= 50.0 mg. How much should the nurse Consult the facility procedure manual for
administer? abbreviations banned in that facility.
Always spell out the word units. The
75 𝑚𝑔 abbreviation “U” for unit can be mistaken for a
× 1 𝑚𝐿 = 𝟏. 𝟓 𝒎𝑳
50 𝑚𝑔 zero.
o Ex: 10 “U” interpreted as 100 units.
Answer: 1.5 mL The better way is to write out as 10
units.
PROBLEM #2 Avoid drug-drug interactions by assessing
client’s current medication prescription and
For units (some medications such as heparin
medication, OTC, and herbal history.
and penicillin are ordered in units) The ordered
is penicillin 750,000 units. The vial reads
PEDIATRIC DOSAGE CALCULATIONS
300,000 units/2 ml. How many mL will be
given? Pediatric Considerations:
750,000 𝑢𝑛𝑖𝑡𝑠 A child’s body may handle a drug differently in
× 2 𝑚𝐿 = 𝟓 𝒎𝑳
300,000 𝑢𝑛𝑖𝑡𝑠 all areas of pharmacokinetics; absorption,
distribution, metabolism and excretion.
Answer: 5 mL
The responses of the child’s organs to the
effects of the drug also may vary because of
the immaturity of the organs.
Methods of Pediatric Dose: 4 Steps to follow

Clark’s Rule 1. Convert pounds to kg.

Body Surface Area (BSA) 2. Calculate the dose in mg
Dosage based on weight 3. Divide the overall dose by the frequency (BID,
TID, etc.)
CLARK’S RULE 4. Calculate the dose in ml or tablets (follow the
same formula with adults)
Uses the child’s weight to calculate the
appropriate dose and assumes that the adult 𝑆𝑡𝑒𝑝 1 − (22 𝑙𝑏𝑠. )/(2.2 𝑙𝑏𝑠) = 𝟏𝟎 𝒌𝒈
dose is based on a 150-lb person.
Uses Weight in Lbs, NEVER in Kg 𝑆𝑡𝑒𝑝 2 − 10 𝑘𝑔 × 40𝑚𝑔/𝑘𝑔/𝑑𝑎𝑦 = 𝟒𝟎𝟎𝒎𝒈/𝒅𝒂𝒚

Child’s Dose 𝑆𝑡𝑒𝑝 3 − (400 𝑚𝑔 ∕ 𝑑𝑎𝑦)/(2 (𝐵𝐼𝐷) ) = 𝟐𝟎𝟎 𝒎𝒈/𝒅𝒐𝒔𝒆

= (𝐶ℎ𝑖𝑙𝑑^′ 𝑠 𝑊𝑒𝑖𝑔ℎ𝑡 (𝑖𝑛 𝑝𝑜𝑢𝑛𝑑𝑠) 𝑆𝑡𝑒𝑝 4 − (𝐷 × 𝑉)/𝑆 = (200 𝑚𝑔 × 5 𝑚𝑙)/(400 𝑚𝑔)

× 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝐴𝑑𝑢𝑙𝑡 𝐷𝑜𝑠𝑒)/(150 𝑝𝑜𝑢𝑛𝑑𝑠) = 0.5 × 5 𝑚𝑙 = 𝟐. 𝟓 𝒎𝑳

INTRAVENOUS FLUIDS CALCULATIONS

PROBLEM #1
The usual adult dose of Benadryl is 50 mg. What Intravenous (IV) solutions (fluids) consist of a
would be the safe dose for a child weighing 27lb. liquid (solvent) containing one or more
dissolved substances (solutes).
= (27 𝑙𝑏𝑠 × 50 𝑚𝑔)/(150 𝑙𝑏𝑠)
ADMINISTRATION SET
= (1350 𝑚𝑔)/150
Used to deliver a specified volume of solution
= 𝟗 𝒎𝒈 are different, depending on the company
manufacturing the set.
BODY SURFACE AREA (BSA)
MACRODROP
Most accurate method for calculating pediatric
dosages. A chamber that delivers large drops
Adult giving sets and drip chambers are
Child’s Dose calibrated such that 20 drops of fluid = 1 mL
= (𝑆𝑢𝑟𝑓𝑎𝑐𝑒 𝐴𝑟𝑒𝑎 (𝑚2) × 𝐴𝑑𝑢𝑙𝑡 𝐷𝑜𝑠𝑒)/(1.73 𝑚2)
DOSAGE CALCULATIONS FOR IV MEDS

PROBLEM #1 MACRODROP
The adult dose is 100 mg/mL. Demerol. The child More commonly used in adult IVF
weighs 20kg and is 40 inches tall. BSA is 0.77m2 In order to calculate the flow rate, need to
know the drop factor: 10, 15, or 20 gtt/mL
= (0.77 𝑚2 × 100 𝑚𝑔/𝑚𝑙)/(1.73 𝑚2)

= (77 𝑚𝑔/𝑚𝑙)/1.73 MICRODRIP

A chamber that delivers small drops

= 𝟒𝟒. 𝟓 𝒎𝒈/𝒎𝒍
All microdrip chambers deliver 60 drops (gtt)
per mL
DOSAGE BASED ON WEIGHT

Most medications for pediatric clients are done MICRODROP

by child’s weight in order to more accurately
More commonly used for children, elderly or
dose.
critically ill where exact control is required.
Drop factor is always 60 gtt/mL
PROBLEM #1
The manufacturer of the macrodrip administration set
A 1.5-year-old child is prescribed an amoxicillin
has standardized the drops per milliliter called the drop
suspension. The dose prescribed is 40 mg/kg/day
factor (DF) for a specific brand of administration set as
divide into equal BID doses. The suspension is
follows:
available in a 400 mg/5ml suspension. What is the
dose in ml? The child weighs 2.2 pounds.
A specific brand of administration set as follows: DROPS PER MINUTE (GTT/MIN)

Company Name Drop Factor (gtt/mL) 𝑇𝑜𝑡𝑎𝑙 𝑣𝑜𝑙𝑢𝑚𝑒 (𝑚𝐿 )𝑡𝑜 𝑖𝑛𝑓𝑢𝑠𝑒 × 𝑑𝑟𝑜𝑝 𝑓𝑎𝑐𝑡𝑜𝑟
Abbott 15 𝑔𝑡𝑡𝑠 min =
𝑇𝑖𝑚𝑒 (𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑚𝑖𝑛𝑠)
Baxter International 10
B. Braun 15 Directions:
IVAC 20
Use a drop factor of 15 gtt/mL for volumes of
CALCULATION OF FLOW RATES
100 mL or more per hour
Use a microdrip (60gtt/mL) for volumes below
MILLILITERS PER HOUR (ML/HR) 100/hr
𝑚𝐿 𝑡𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑚𝐿 𝑜𝑟𝑑𝑒𝑟𝑒𝑑
= PROBLEM #3
ℎ𝑟 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 ℎ𝑜𝑢𝑟𝑠 𝑡𝑜 𝑟𝑢𝑛
Health Care Providers Order Duration of
Rate (gtt/min) Infusion
MILLILITERS PER MIN (ML/MIN) 125 mL D5W 60 min 31 gtts/min
𝑡𝑜𝑡𝑎𝑙 𝑚𝐿 𝑜𝑟 𝑣𝑜𝑙𝑢𝑚𝑒 100 mL LR 60 min 25 gtts/min
𝑚𝐿/ min = 50 mL 0.9 NaCI 20 min 150 gtts/min
𝑡𝑜𝑡𝑎𝑙 𝑚𝑖𝑛𝑠 𝑡𝑜 𝑟𝑢𝑛

PROBLEM #1 SOLUTIONS

Infuse 1000 mL Lactated Ringer’s (LR) solution over 125 𝑚𝑙 × 15 𝑔𝑡𝑡𝑠/𝑚𝑙 1,875 𝑔𝑡𝑡𝑠
1. =
10 hours. 60 𝑚𝑖𝑛 60 𝑚𝑖𝑛
= 31.2 𝑜𝑟 𝟑𝟏 𝒈𝒕𝒕𝒔/𝒎𝒊𝒏
1000 𝑚𝑙
100 𝑚𝑙 × 15 𝑔𝑡𝑡𝑠/𝑚𝑙 1,500 𝑔𝑡𝑡𝑠
10 ℎ𝑟𝑠 2. = = 𝟐𝟓 𝒈𝒕𝒕𝒔/𝒎𝒊𝒏
60 𝑚𝑖𝑛 60 𝑚𝑖𝑛
= 𝟏𝟎𝟎 𝒎𝒍/𝒉𝒓
50 𝑚𝑙 × 60 𝑔𝑡𝑡𝑠/𝑚𝑙 3,000 𝑔𝑡𝑡𝑠
3. = = 𝟏𝟓𝟎 𝒈𝒕𝒕𝒔/𝒎𝒊𝒏
60 𝑚𝑖𝑛 60 𝑚𝑖𝑛
PROBLEM #2
Health Care Providers Order Duration of
PROBLEM #4
Rate (mL/hr) Infusion
1000 mL 5% dextrose The order is for 1000mL NS over 8 hours; drop factor
12 hrs 83 mL/hr
in water is 10 gtt/mL.
1000 mL Lactated
6 hrs 166 mL/hr
Ringer’s 1000 𝑚𝑙 × 10 𝑔𝑡𝑡𝑠/𝑚𝑙
500 mL 0.9 sodium =
4 hrs 125 mL/hr 480 𝑚𝑖𝑛𝑠 (8 ℎ𝑟𝑠 × 60 𝑚𝑖𝑛𝑠 = 480 𝑚𝑖𝑛𝑠)
chloride
10,000 𝑔𝑡𝑡𝑠
= = 20.83 𝑜𝑟 𝟐𝟏 𝒈𝒕𝒕𝒔/𝒎𝒊𝒏
SOLUTIONS 480 𝑚𝑖𝑛𝑠
1000 𝑚𝑙 The same formula can be used for Ivs
1. = 83.3 𝑜𝑟 𝟖𝟑 𝒎𝒍/𝒉𝒓
12 ℎ𝑟𝑠 requiring microdrip rates or the following
formula can be used.
1000 𝑚𝑙
2. = 166.6 𝑜𝑟 𝟏𝟔𝟔 𝒎𝒍/𝒉𝒓 mL/hr = Microdrops/min
6 ℎ𝑟𝑠
Microdrop – 60 microgtts/ml
500 𝑚𝑙 Hour is 60 mins
3. = 𝟏𝟐𝟓 𝒎𝒍/𝒉𝒓
4 ℎ𝑟𝑠
PROBLEM #5
CALCULATING RATES OF INFUSION FOR
OTHER THAN 1 HOUR Order is for 1000 mL D5S over 24 hours. Drop factor is
60 gtt/ml.
𝑚𝐿/ℎ𝑟
𝑇𝑜𝑡𝑎𝑙 𝑣𝑜𝑙𝑢𝑚𝑒 𝑚𝑖𝑙𝑙𝑖𝑙𝑖𝑡𝑒𝑟𝑠 𝑡𝑜 𝑖𝑛𝑓𝑢𝑠𝑒 × 60 𝑚𝑖𝑛/1 ℎ𝑟 1,000 𝑚𝑙 × 60 𝑔𝑡𝑡𝑠/𝑚𝑙
= =
𝑇𝑖𝑚𝑒 1,440 𝑚𝑖𝑛𝑠 (24 ℎ𝑟𝑠 × 60 𝑚𝑖𝑛𝑠)

Compute: 60,000 𝑔𝑡𝑡𝑠

= = 41.66 𝑜𝑟 𝟒𝟐 𝒈𝒕𝒕𝒔/𝒎𝒊𝒏
1,440 𝑚𝑖𝑛𝑠
1. 50 mL 0.9 NaCI with ampicillin 1 g for 20 mins
2. 150 mL D5W with gentamicin 80 mg to run for
30 mins
 PROBLEM #6
Doctor’s order: Infuse 1200 mL of 0.45% Normal
Saline at 125 mL/hr to run 8 hrs.

Drop factor: 12 gtt/min. How many gtt/min will you

regulate the IV?

1200 𝑚𝐿 1 𝑚𝐿 12 𝑔𝑡𝑡
= × ×
48 ℎ𝑟𝑠 60 𝑚𝑖𝑛𝑠 𝑚𝐿

14400 𝑔𝑡𝑡
= = 𝟑𝟎 𝒈𝒕𝒕/𝒎𝒊𝒏
480 𝑚𝑖𝑛𝑠