THIRD EDITION

INDUSTRIAL-OCCUPATIONAL
HYGIENE CALCULATIONS:
A Professional Reference

James H Stewart Ph.D., C.I.H., CSP

Robert F Herrick, Sc.D., C.I.H.
Martin Horowitz, C.I.H., CSP
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Industrial-Occupational Hygiene Calculations:

A Professional Reference

Third Edition, 2017

James H. Stewart, Ph.D, CIH, CSP Editor

Authors

James H. Stewart, Ph.D, CIH, CSP

Robert F Herrick, Sc.D., CIH
Martin Horowitz, CIH, CSP

Copyright, 2017 Millenium Associates

 Industrial-Occupational Hygiene Calculations: A Professional Reference, Third Edition

Copyright © 2017 by Millennium Associates. All rights reserved.

Printed in the United States of America.

Previous editions Copyright © Millennium Associates 1999 and 2005.

Except as permitted under the Copyright Act of 1976, no part of this book may be reproduced or distributed
in any form or by any means, or stored in any database or retrieval system, without prior written permission
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Information contained in this work has been obtained by Millennium Associates from sources believed to
be reliable. However, neither Millennium Associates or its authors guarantee the accuracy or completeness
of any information published herein, and neither Millennium Associates nor its authors shall be responsible
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the understanding that Millennium Associates and its authors are supplying information, but not attempting
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appropriate professional should be sought. Nor will use of this work guarantee passing an industrial or
occupational hygiene professional certification examination.

Library of Congress Cataloging-in-Publication Data

Industrial-Occupational Hygiene and Safety Calculations: A Professional Reference, Third Edition

Stewart, James Henry 2017
p. cm.
Includes bibliographical references and index.
ISBN: 978-0-9671934-6-5

1. Industrial Hygiene 2. Occupational Hygiene 3. Calculations I. Stewart, James H.

 Table of Contents
Section 1: Noise
 p 
SPL or L p = 20log  
Sound Pressure Level......................................................................................1  p0 

Sound Intensity Level.....................................................................................2

 d1 
SPL 2 = SPL 1 + 20 log
 
Distance and Sound Pressure Level.............................................................3 d2

 Ν SPLi 
SPL f = 10 log  ∑ 10 10 
 i=I 
Adding Sound Pressure Levels.....................................................................4  

SPL f  SPLi  10log(n)

Total Sound Pressure Level: n Identical Sources......................................5

L2 − L1
LTotal = L1 + 10 log ( 10 10 + 1)
Total Sound Pressure Level: Two Sources.................................................6
10
10 log 10

Total Sound Pressure Level...........................................................................7

1

 N  Li  
1
Leq = 10log 
T ∑ 10 10 t  
i 

Leq Equivalent Sound Pressure Level..........................................................8  i =1   

Percent (%) Dose (Noise)...............................................................................9

Sound Pressure Level and Sound Power (English).................................10

Sound Pressure Level and Sound Power (metric)....................................11

Directivity Index (DI)..................................................................................12

Allowed Noise Exposure Time...................................................................13

TWAeqCalculated from % Dose (PEL)......................................................14

TWAeqCalculated from % Dose (TLV).....................................................15

Ei
TL  10log
Et
Transmission Loss........................................................................................16
( N )( RPM )
f 
Frequency of Noise Produced by Fan........................................................17 60

c
f 
Frequency and Wavelength.........................................................................18 λ

f 2 = 2 f1
Octave Bands: Upper and Lower Edge.....................................................19
 Total Sound Pressure Level
Category:
Noise
10
10 log 10
Terms and Units 1
L = total sound pressure level generated by
Pt

N sources (dB)
L = individual sound pressure level of ith source (dB)
Pi

N = number of sound pressure levels

Reference:
Berger, E.H., et al., ed., 1986, Noise and Hearing Conservation Manual, American Industrial Hygiene
Association (AIHA), Virginia Page 29.

Theory and Application Example

The sound pressure levels of different noise sources Three machines are going to be situated in close
can be added via the equation above. It is another proximity. Given their individual sound pressure
quantitative version of familiar tables where you levels, L , of 78, 82, and 84 dB, what is the
Pi

will find, e.g. that for a numerical difference of 2 approximate total sound pressure level, L ?
Pt

to 4 dB, you add 2.0 dB to the higher noise level to

determine the total noise level.  78 82 84 
L pt = 10 log 10 +10 +10 
10 10 10
The equation is used at the design stage to estimate 
 
noise levels post construction and to evaluate the
efficacy of purchasing low noise machinery. Adding
noise sources to an existing noise environment is L pt = 86.7dB
another useful application.

Another application of this equation is to octave

band measurements. The separate dB levels at each
octave band can be added:

Octave Band dB level

31.5 88
63 90
125 92
250 92
500 95
1000 96
2000 92
4000 90
8000 88

Using the equation above to add these example

octave band values will yield a noise total sound
pressure level of 101.8 dB.

Copyright©2017 by Millennium Associates

 Adjusting for Unusual Work Schedules(hrs/day)
Category:
General Sciences, Statistics, Standards
8 24 - h
RF = x
h 16
Terms and Units
RF = reduction factor (unitless decimal)
h = number of hours worked in a day
Reference:
Klonne, DR : Occupational Exposure Limits. In AIHA, 2003, The Occupational Environment Its Eval-
uation and Control, and Management, Dinardi, S editor, AIHA, Fairfax, VA , p 67. and Brief, R.S., and
R.A. Scala, Occupational exposure limits for novel work schedules. Am.Ind. Hyg. Assoc. J. 36:467–469
(1975).

Theory and Application Example

Occupational exposure limits like TLVs, PELs and A worker is assigned to job that requires working
RELs are usually developed for an 8-10 hour per 10 hours in a day. The worker is exposed to xylene.
day worker who in one one week would work 40 The TLV for toluene is 188 mg/m3. What is the
hours. The number of hours worked in a day or in adjusted TLV for this worker using the Brief and
a week directly impacts the “recovery” time, i.e., Scala method?
the time away from the exposure. During this time
the worker’s body can detoxify and/or excrete the 8 24-h
RF= x
toxicant. If the occupational exposure limit was de- h 16
8 24-10
veloped with the assumption of 8 hours of exposure RF= x
and 16 hours of recovery time then working more 10 16
14
than 8 hours at the specified occupational exposure RF=0.8 x
16
limit may not provide enough recovery time before RF=0.7
going back into the work environment.
Since the TLV for xylene is 188 mg/m3 and the re-
Brief and Scala, 1975 developed a method of ad- duction factor is 0.7 the worker can only be exposed
justing the occupational exposure limit for unusual to 132 mg/m3 for the 10 hour workday.
work schedules. One equation adjusts for hours
worked in a day, the other adjusts for hours worked
in a week. The calculation is conservative, i.e., it
provides a more protective result than other cur-
rently available methods of accounting for unusual
work schedules. As you can see in the formula as
the number of hours increases the reduction factor
(RF) decreases. The reduction factor is multiplied
by the occupational exposure limit to obtain the
“adusted occupational exposure limit”.
8 24-h
RF= x
h 16

Copyright©2017 by Millennium Associates

 WBGT with Solar Load
Category:
Heat Stress
WBGT = 0.7tnwb + 0.2t g + 0.1tdb
Terms and Units
WBGT = wet bulb globe temperature (⋅F; ⋅C)
tnwb = natural wet bulb temperature (⋅F; ⋅C)
tg = globe temperature (⋅F; ⋅C)
tdb = dry bulb temperature (⋅F; ⋅C)

Reference:
NIOSH, Occupational Exposure to Heat and Hot Enviornments, NIOSH, Cincinnati, OH 2016, p 113;
Larranaga, M.D, Thermal Standards and Measurement Techniques, In The Occupational Environment –
Its Evaluation, Control and Management. 3rd Edition. Anna, D. ed., Fairfax, VA: AIHA, 2013, p. 929.

Theory and Application Example

Heat stress is the environment the worker is in while What was the WBGT reading at on outside con-
heat strain is the physiological response to the heat struction site on a sunny day if the natural wet bulb
stress. Many factors can influence an individual’s measured 83 ºF, the globe temperature was 93 ºF
heat strain. These include age, physical condition, and the dry bulb temperature was 91 ºF?
overall health, medications, ambient conditions
(temperature, humidity, air movement), degree
of acclimatization, and degree of physical exer- WBGT = 0.7 t nwb + 0.2 t g + 0.1 t db
tion. The most effective means of evaluating heat
buildup in the body is to measure deep body (core) ( ) ( )
WBGT = 0.7 83º F + 0.2 93º F + 0.1 91º F( )
temperature. Since this is not usually practical or
acceptable to do in the work environment, exposure WBGT = 86 º F
indices have been developed to asses heat stress.
For workers, the Wet Bulb Globe Temperature In-
dex (WBGT), as described in the ACGIH Threshold
Limit Values publication, is the most commonly
used measure of heat stress. Limits are based on
the work:rest regimen, and on the physical level of
the work. Further adjustments are made for type of
clothing worn

This equation describes the relationship between

the natural wet bulb temperature (tnwb), the globe
temperature (tg), and the dry bulb temperature(tdb)
for computing the Wet Bulb Globe Temperature
(WBGT) Index for work outside on a sunny day
or where there are radiant heat sources such as hot
machinery. All thermometers must have unrestricted
airflow around them and not be shaded from the
sun. The wick of the natural wet bulb must be kept
wet with distilled water, and the globe thermometer
must have a matte black finish.

Copyright©2017 by Millennium Associates

 Hood Flow Rate and Static Pressure (Metric)
Category:
Ventilation

Terms and Units

Q = volumetric flow rate (m3/s)
A = area of the duct (m2)
1.29 = constant based on standard temperature and pressure
SP = hood static pressure (Pa)
Ce = hood entry coefficient (unitless)
df = density factor with reference to standard air((unitless)

Reference:
American Conference of Governmental Industrial Hygienists (ACGIH), Industrial Ventilation: A Manual
of Recommended Practice For Design, 29th Ed. Cincinnati: ACGIH, 2016, p. 3-13

Theory and Application Example

Hood performance can vary over time due to A static pressure tap was installed on an (15.24 cm
obstructions within the duct, or possibly due to diameter duct (A=0.0.0182 m2). The manometer
corroded or dirty fan blades. Therefore, a need read 498 Pa and the air density factor is 0.96. With
exists for calculating the volumetric airflow a hood entry coefficient of 0.85 what was the flow
into a hood opening for comparison to design rate of the hood?
specifications. This equation is sometimes referred
to as the throat-suction equation, and can be used to
determine the volumetric flow rate, Q, of air flowing
into a hood by simply measuring the hood static
pressure, SPh. The hood entry coefficient, Ce , is a
constant for a given hood type, and is a measure of
the overall efficiency of a hood in directing air into
the hood and accelerating it to duct velocity. Since
Ce , 1.29, and the duct area are all constants for a
particular hood type, a simple measurement of the
hood static pressure can quickly and easily yield the
current volumetric flow rate. The density factor (df)
is the ratio of the actual density of air divided by the
density of standard air (1.204 kg/m3) at 21 ºCand
101 kPa).

The hood static pressure is generally measured at

least three duct-diameters down stream from the
hood (throat) opening through the use of a simple
hood static pressure tap connected to an inclined
manometer mounted outside the hood above the
sash.

Copyright©2017 by Millennium Associates

 Shield Thickness
Category:
Ionizing Radiation I1
log( ) HVL
I2
X =
Terms and Units log 2
X = thickness required, any convenient units
HVL = thickness of half-value layer, same units as X
I2 = intensity of attenuated radiation, same units as incident radiation
I1 = intensity of incident radiation. Common units would be photons/cm2-sec, mR/hr, mrad/hr.

Reference:
Shapiro, J., 1990, Radiation Protection: A Guide for Scientists and Physicians, third edition, Harvard
University Press, Cambridge, MA, p115.

Theory and Application Example

This equation gives the thickness of medium re- Calculate the thickness of lead required to reduce
quired to attenuate radiation from intensity I1 to In- the exposure rate of a Cs-137 source at a point 1
tensity I2. The same type of equation can also deal ft from the source from 12 mR/hr to 0.852 mR/hr.
with reductions in dose rate or exposure rate. The The HVL in lead for the 0.6 MeV gamma radiation
basis of the equation is that each half-value layer from Cs-137 is 0.5 cm.
in a medium attenuates the radiation by a factor of
2, so n half-value layers will attenuate the radiation 12.0mR / hr
by a factor of 2n . The number of half-value layers log( )(0.5cm)
X = 0 .852mR / hr
is equal to the thickness of the attenuating medium
log 2
divided by the thickness of a half-value layer, x/
HVL. Thus, the attenuated radiation at thickness I2 log(14.08)(0.5cm)
X =
= I1 / 2x/HVL. This can also be written I1 /I2 = 2x/HVL. log 2
1.149(0.5cm)
The equation is solved for X by taking the log of X =
0.301
both sides. X = 1.9cm

I X (log 2)
log( 1 ) =
I2 ( HVL)

rearranging,

I1 HVL
X = (log )( )
I 2 log 2

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 Acceptable Distance for Laser Barrier
Category: 1
Non-Ionizing Radiation
1  4Φ  2  2
=Ds −a 
Terms and Units
D s = separation for barrier (cm)
φ  π TL  
ø = emergent beam divergence (radians)
Φ = total radiant power output (W)
TL = threshold limit value of barrier (W/cm2)
a = exit beam diameter (cm)

Reference:
ANSI Z136.1, 2000, American National Standard for Safe Use of Lasers, American National Standards
Institute (ANSI), New York, p 120.

Theory and Application Example

This equation allows calculation of the minimum Assuming a TL value of 30 W/cm2 for an 8 hour
distance (Ds) or installation distance for a barrier worst case exposure duration for a 250 W Class 4
to be sufficiently protective for a given laser. At laser with a beam divergence of 2 mrad and an exit
a distance less than Ds, the beam may penetrate beam diameter of 0.5 cm, what is the necessary
the barrier and cause a potential exposure hazard. separation distance, Ds?
Note that it takes the same form as the equation for
nominal hazard zone but substitutes the threshold
1
limit value of the barrier (TL) for the exposure limit
(EL). As the beam diverges, the irradiance (W/ 1  4Φ  2  2
D s =  -a
cm2) decreases. As the emergent beam divergence
(0) increases, the value of Ds, above, decreases
φ  π TL  
since the irradiance of the beam as it reaches the 1
barrier, is lower. In applying this equation to an 1  4 x 250W  2
individual situation, an 8-hour exposure may be Ds =   2 
- 0.52 
assumed in picking the TL value for worst case
2 x 10 rad  π 30 W/cm 
-3

application though 60 sec. is more frequently Ds = 1609cm = 16m
chosen. One type of barrier that is increasingly
available is acrylic plastic windows that allow some
visible wavelengths to penetrate but will have a
significant optical density for the wavelength of the
laser output. For all barriers, the material cannot be
combustible at the worst case conditions present.

In many industrial laser tools, the laser is enclosed

and interlocked so the tool, as a whole, is Class 1.
When the tool is opened for servicing, open beam,
class 3b or 4 conditions may develop. Then, use of
portable barriers may be important. Those people
who work inside the barrier must be trained and
equipped with appropriate personal protection.

Copyright©2017 by Millennium Associates

 References
ACGIH, 2016, Industrial Ventilation: A Manual of Recommended Practice for Design, 29th
Ed., American Conference of Governmental Industrial Hygienists (ACGIH), Cincinnati, Ohio.

ACGIH, 1998, Industrial Ventilation: A Manual of Recommended Practice for Design, 23rd
Ed., American Conference of Governmental Industrial Hygienists (ACGIH), Cincinnati, Ohio.

ACGIH, 2016, TLVs and BEIs , American Conference of Governmental Industrial Hygienists
(ACGIH), Cincinnati, Ohio.

AIHA, 2013 The Occupational Environment – Its Evaluation, Control and Management, Annd, D.,
ed. AIHA, Fairfax, VA

AIHA, 2003 The Occupational Environment – Its Evaluation, Control and Management, DiNardi,SR,
ed. AIHA, Fairfax, VA

AIHA, 1997, The Occupational Environment – Its Evaluation and Control, edited by DiNardi,
SR, Fairfax, VA

AIHA, 2009, Mathematical Exposure Models for Estimating Occupational Exposures to

Chemicals, 2nd Edition, AIHA, Farifax, VA.

AIHA, 2015, A Strategy for Assessing and Managing Occupational Exposures, 4th edition,
AIHA, Fairfax, VA.

ANSI Z136.1, 2000, American National Standard for Safe Use of Lasers, American National Standards
Institute (ANSI), New York, New York.

NSC, 2012, Fundamentals of Industrial Hygiene, Plog, B.A. and Quinlan, P.J., editors Nation-
al Safety Council, Itasca, Illinois

NIOSH, Criteria for a Recommended Standard for Occupational Exposure to Heat and Hot Enviorn-
ments, NIOSH, Cincinnati, OH,

ANSI Z136.1, 2000, American National Standard for Safe Use of Lasers, American National
Standards Institute (ANSI), New York.

Berger, E.H., et al., ed., 1986, Noise and Hearing Conservation Manual, American Industrial
Hygiene Association (AIHA), Virginia.

Brauer, Roger L, 1990, Safety and Health for Engineers, Van Nostrand Reinhold, New York.

Colton, T. 1974, Statistics in Medicine, Little, Brown, Boston, MA.

DiNardi, S.R., 1995, Calculation Methods for Industrial Hygiene, Van Nostrand Reinhold,
New York.

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 Dr. Stewart has served as a Plant, Division and Corporate Director/Manager
of Environmental Health and Safety for several large multinational organi-
zations/companies, and Director of Environmental Health and Safety for
Harvard University and as well as a Compliance Officer (Industrial Hygienist)
with U.S. OSHA. Dr. Stewart is certified in the Comprehensive Practice of
Industrial Hygiene and is also a Certified Safety. Professional. He has many
years of experience as an active member of the environmental health and safety
profession. Dr. Stewart received his Ph.D. in Environmental Health/Toxicology
(minor in Epidemiology) from the University of Massachusetts at Amherst in
1992. He also holds a Master’s degree in Chemistry and a Bachelor’s degree
in Public Health. Dr. Stewart has served on two National Academy of Science
Committees as an industrial hygiene and safety expert Dr. Stewart is a currently
a Visiting Scientist (Instructor Ret.) at the Harvard T.H. Chan School of Public
Health and a Senior Lecturer in Environmental Health

Robert Herrick’s educational background includes a BA degree in Chemistry

from the College of Wooster, an MS in Environmental Health Science from the
University of Michigan, and a Doctor of Science in Industrial Hygiene from the
Harvard School of Public Health. He is certified in the comprehensive practice
of industrial hygiene. His research interests are centered on the assessment
of exposure as a cause of occupational and environmental disease. He has
conducted research on the development of methods to measure the biologically
active characteristics of reactive aerosols, and on studies of work processes in
several industries to develop task-based models to identify and control the
primary sources of worker exposures.

Dr. Herrick is Past Chair of the American Conference of Governmental

Hygienists (ACGIH), and Past President of the International Occupational
Hygiene Association. He is currently a Fellow in the American Industrial Hygiene Association. Prior to joining the
faculty at the Harvard School of Public Health, Dr. Herrick spent 17 years at the National Institute for Occupational
Safety and Health (NIOSH) where he conducted occupational health research. He has served on advisory panels
to the USEPA, the National Academy of Sciences, and NIOSH. Dr. Herrick has authored over 100 peer-reviewed
publications.

Martin is a graduate of the Master’s Program at the Harvard School of Public

Health with a degree in Industrial Hygiene. He spent 14 years at Polaroid Corp.
in the Corporate Industrial Hygiene Office and Divisional Semiconductor
Manufacturing Group. Duties included industrial hygiene monitoring and
control evaluation, radiation and laser safety officer. Martin then worked at the
Micromachined Products Div. of Analog Devices in Cambridge as the Health
and Safety Manager. This included industrial hygiene, safety, and hazardous
waste management at a semiconductor fabrication facility. He assisted in de-
commissioning of the facility before moving to an EHS Engineering position in
the Wilmington production facility. He holds the C.I.H. and CSP certifications.
His special interests/expertise lie in the physical agents such as nonionizing
radiation and noise as well as direct reading instruments.

MA
Millenium Associates

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