CIH Equation Sheet Explained: How to Use Every Formula on Exam Day

📋 Table of Contents

Understanding the Equation Sheet
The On-Screen Calculator
Ventilation Formulas
Noise & Acoustics Formulas
Heat Stress Formulas
Statistics Formulas
Radiation Formulas
Gas Laws & Conversions
Exposure Assessment Formulas
Common Calculation Mistakes
Practice Strategy
Frequently Asked Questions

One of the most anxiety-inducing aspects of the CIH exam is the calculation component. The good news: BGC provides an equation sheet during the exam. The challenging news: the equation sheet contains formulas without any explanation of when or how to use them.

This guide bridges that gap. For each major formula category, you'll learn not just what the formula is, but—more importantly—how to recognize when to apply it and how to avoid common mistakes. By the time you finish this guide, you'll be able to look at a problem and immediately know which equation to reach for.

💡 The Real Challenge

The CIH equation sheet gives you all the formulas you need. The exam doesn't test whether you've memorized equations—it tests whether you can recognize which equation applies to each problem and execute the calculation correctly. This guide focuses on pattern recognition: learning to identify problem types and match them to the right formula.

Understanding the Equation Sheet

The BGC-provided equation sheet appears on your computer screen during the exam. You can reference it at any time, but you cannot bring your own materials or notes. Here's what you need to know:

What's on the Equation Sheet

The equation sheet includes formulas for:

Ventilation: Flow rate, velocity, capture velocity, hood design, fan laws, pressure relationships
Noise: Decibel addition, OSHA dose calculations, TWA, sound pressure relationships
Heat Stress: WBGT calculations for indoor and outdoor environments
Statistics: Mean, standard deviation, confidence intervals, coefficient of variation
Radiation: Inverse square law, dose calculations, half-life
Gas Laws: Ideal gas law, unit conversions (ppm to mg/m³)
Exposure Assessment: TWA calculations, mixture formulas

What's NOT on the Equation Sheet

The equation sheet does not include:

Explanations of when to use each formula
Variable definitions (you must know what each symbol means)
Step-by-step problem-solving procedures
Unit conversion factors (some are provided, many are not)
Regulatory limits (OELs, action levels, etc.)

⚠️ Critical Point

Having the formulas doesn't help if you don't know which one to use. Many candidates mistakenly think "I don't need to learn the formulas—they're provided." Wrong approach. You need to recognize problem types instantly and know exactly which formula applies. This requires extensive practice before exam day.

The On-Screen Calculator

You cannot bring your own calculator to the CIH exam. Instead, you'll use the embedded Pearson VUE on-screen calculator.

Calculator Characteristics

Type: Basic scientific calculator with standard functions
Functions Available: Basic operations, square root, exponents, logarithms, trigonometric functions
Interface: Click-based (mouse or touchscreen)
Limitation: Slower than a physical calculator—factor this into your time management

Calculator Practice Tips

Practice with on-screen calculators before exam day—the Windows calculator in scientific mode is similar
Double-check entries—it's easy to mis-click on a touchscreen
Write intermediate steps on your whiteboard to avoid losing your place
Budget extra time for calculation questions due to slower input

Ventilation Formulas

💨

Ventilation

Critical Priority

Ventilation is consistently identified as one of the most important—and most heavily tested—topics on the CIH exam. Master these formulas thoroughly.

Basic Flow Equation (Q = VA)

Fundamental

Q = V × A

Q: = Volumetric flow rate (cfm or m³/s)
V: = Velocity (fpm or m/s)
A: = Cross-sectional area (ft² or m²)

🎯 When to Use This Formula

Calculate airflow through a duct given velocity and duct dimensions
Determine required duct velocity given flow rate and area
Size ducts for a given flow rate and target velocity
Any problem relating flow, velocity, and area

📝 Example Problem

A 12-inch diameter round duct has an average velocity of 3,500 fpm. What is the volumetric flow rate?

Step 1: Calculate duct area
A = π × r² = π × (0.5 ft)² = 0.785 ft²

Step 2: Apply Q = VA
Q = 3,500 fpm × 0.785 ft² = 2,748 cfm

Capture Velocity

Hood Design

Q = V_x × (10x² + A)

Q: = Required flow rate (cfm)
V_x: = Capture velocity at distance x (fpm)
x: = Distance from hood face to source (ft)
A: = Hood face area (ft²)

🎯 When to Use This Formula

Designing a hood to capture contaminants at a specific distance
Determining required flow rate for an exterior hood
Problems mentioning "capture velocity" or contaminant capture at a distance
Unflanged or plain opening hood calculations

📝 Example Problem

A plain rectangular hood opening (2 ft × 1 ft) needs to capture contaminants at a distance of 1 foot with a capture velocity of 100 fpm. What flow rate is required?

Step 1: Identify variables
V_x = 100 fpm, x = 1 ft, A = 2 ft²

Step 2: Apply formula
Q = 100 × (10(1)² + 2) = 100 × 12 = 1,200 cfm

Fan Laws

System Design

Q₁/Q₂ = RPM₁/RPM₂

SP₁/SP₂ = (RPM₁/RPM₂)²

HP₁/HP₂ = (RPM₁/RPM₂)³

Q: = Volumetric flow rate (cfm)
RPM: = Fan speed (revolutions per minute)
SP: = Static pressure (inches w.g.)
HP: = Horsepower (brake horsepower)

🎯 When to Use These Formulas

Predicting effect of changing fan speed on flow, pressure, or power
Determining new RPM needed to achieve target flow rate
Calculating power increase when increasing system capacity
Problems involving fan speed changes and their effects

💡 Memory Aid

Fan Law Exponents: 1-2-3
Flow is proportional to RPM¹ (linear)
Pressure is proportional to RPM² (squared)
Power is proportional to RPM³ (cubed)

Doubling fan speed: Flow doubles, pressure quadruples, power increases 8×!

📝 Example Problem

A fan operating at 1,200 RPM delivers 5,000 cfm. If fan speed is increased to 1,500 RPM, what is the new flow rate?

Apply Fan Law 1:
Q₁/Q₂ = RPM₁/RPM₂
5,000/Q₂ = 1,200/1,500
Q₂ = 5,000 × (1,500/1,200) = 6,250 cfm

Duct Velocity Pressure

Measurements

VP = (V/4,005)² or V = 4,005 × √VP

VP: = Velocity pressure (inches w.g.)
V: = Velocity (fpm)
4,005: = Constant for standard air density

🎯 When to Use This Formula

Converting pitot tube readings (VP) to velocity
Problems involving duct traverse measurements
Calculating velocity from manometer readings

Noise & Acoustics Formulas

🔊

Noise & Acoustics

Critical Priority

Noise calculations appear frequently on the CIH exam. The logarithmic nature of decibels makes these calculations tricky—practice extensively.

Decibel Addition

Fundamental

L_total = 10 × log₁₀(10^L₁/10 + 10^L₂/10 + ... + 10^Lₙ/10)

L_total: = Combined sound level (dB)
L₁, L₂, Lₙ: = Individual sound levels (dB)

🎯 When to Use This Formula

Combining sound levels from multiple sources
Calculating total noise exposure from multiple machines
Adding noise contributions in an area assessment

💡 Quick Rules for dB Addition

Equal sources: Two equal dB levels add 3 dB (e.g., 90 + 90 = 93 dB)
10 dB difference: The higher level dominates (e.g., 90 + 80 ≈ 90.4 dB)
3 dB difference: Add 1.8 dB to higher (e.g., 90 + 87 ≈ 91.8 dB)

These shortcuts can help verify your calculations or estimate answers quickly.

📝 Example Problem

Three machines produce sound levels of 85 dB, 88 dB, and 90 dB. What is the combined sound level?

Apply dB addition formula:
L_total = 10 × log₁₀(10^85/10 + 10^88/10 + 10^90/10)
L_total = 10 × log₁₀(3.16×10⁸ + 6.31×10⁸ + 1.0×10⁹)
L_total = 10 × log₁₀(1.95×10⁹) = 10 × 9.29 = 92.9 dB

OSHA Noise Dose

Compliance

D = 100 × (C₁/T₁ + C₂/T₂ + ... + Cₙ/Tₙ)

D: = Dose (percent)
C: = Actual exposure time at each level (hours)
T: = Allowed exposure time at each level (hours)

OSHA Permissible Exposure Times:

Sound Level (dBA)	Permitted Time (hours)
85	16
90	8
95	4
100	2
105	1
110	0.5
115	0.25

🎯 When to Use This Formula

Calculating OSHA compliance for varying noise exposures
Determining if a worker exceeds 100% dose (the PEL)
Problems involving multiple noise levels throughout a shift

📝 Example Problem

A worker is exposed to 95 dBA for 3 hours and 90 dBA for 5 hours. Calculate the OSHA noise dose.

Step 1: Find permitted times
At 95 dBA: T = 4 hours
At 90 dBA: T = 8 hours

Step 2: Calculate dose
D = 100 × (3/4 + 5/8) = 100 × (0.75 + 0.625) = 137.5%

Interpretation: Exceeds 100% dose, worker is overexposed.

TWA from Dose

Exposure Assessment

TWA = 16.61 × log₁₀(D/100) + 90

TWA: = Time-weighted average (dBA)
D: = Dose (percent)
16.61: = Constant based on OSHA 5 dB exchange rate
90: = OSHA PEL in dBA

🎯 When to Use This Formula

Converting dosimeter percent reading to TWA
Expressing noise exposure as an 8-hour equivalent
Comparing exposures across different shift lengths

Heat Stress Formulas

🌡️

Heat Stress

High Priority

WBGT (Wet Bulb Globe Temperature) calculations are commonly tested. Know the difference between indoor and outdoor formulas.

WBGT - Outdoor (with solar load)

Heat Index

WBGT_outdoor = 0.7 × NWB + 0.2 × GT + 0.1 × DB

NWB: = Natural wet bulb temperature
GT: = Globe temperature (black globe)
DB: = Dry bulb temperature

🎯 When to Use This Formula

Outdoor work environments with solar radiation
Any situation mentioning sun exposure or outdoor conditions
Construction, roofing, agriculture, or other outdoor work assessments

WBGT - Indoor (no solar load)

Heat Index

WBGT_indoor = 0.7 × NWB + 0.3 × GT

NWB: = Natural wet bulb temperature
GT: = Globe temperature

🎯 When to Use This Formula

Indoor work environments without solar radiation
Foundries, kitchens, laundries, manufacturing facilities
Any indoor hot environment assessment

💡 Memory Aid: Indoor vs Outdoor

Indoor: No sun = No dry bulb = 0.7/0.3 formula
Outdoor: Has sun = Has dry bulb = 0.7/0.2/0.1 formula

The natural wet bulb always has the highest weighting (0.7) because humidity is the most important factor in heat stress.

📝 Example Problem

In an outdoor environment, measurements show: NWB = 78°F, GT = 95°F, DB = 88°F. Calculate the WBGT.

Use outdoor formula:
WBGT = 0.7(78) + 0.2(95) + 0.1(88)
WBGT = 54.6 + 19 + 8.8 = 82.4°F

Time-Weighted Average WBGT

Multiple Locations

WBGT_TWA = (WBGT₁ × t₁ + WBGT₂ × t₂ + ...) / (t₁ + t₂ + ...)

🎯 When to Use This Formula

Worker moves between different thermal environments
Calculating average exposure across work/rest cycles
Multiple exposure periods at different WBGT values

Statistics Formulas

📊

Statistics & Data Analysis

High Priority

Statistics questions test your ability to analyze sampling data and draw valid conclusions about exposures.

Arithmetic Mean

Central Tendency

x̄ = (x₁ + x₂ + ... + xₙ) / n = Σx / n

x̄: = Arithmetic mean (average)
x₁, x₂, xₙ: = Individual sample values
n: = Number of samples

🎯 When to Use This Formula

Finding the average of a data set
Calculating mean exposure from multiple samples
When data is normally distributed

Geometric Mean

Central Tendency

GM = (x₁ × x₂ × ... × xₙ)^1/n = exp[(Σln x) / n]

GM: = Geometric mean
x₁, x₂, xₙ: = Individual sample values
n: = Number of samples

🎯 When to Use This Formula

When data is lognormally distributed (common for exposure data)
Industrial hygiene exposure data sets
When problem mentions "lognormal" distribution

Standard Deviation (Sample)

Variability

s = √[Σ(xᵢ - x̄)² / (n - 1)]

s: = Sample standard deviation
xᵢ: = Individual sample values
x̄: = Sample mean
n: = Number of samples
n-1: = Degrees of freedom (Bessel's correction)

🎯 When to Use This Formula

Measuring variability/spread in sample data
Calculating confidence intervals
Assessing sampling precision

Coefficient of Variation

Relative Variability

CV = (s / x̄) × 100%

CV: = Coefficient of variation (%)
s: = Standard deviation
x̄: = Mean

🎯 When to Use This Formula

Comparing variability between data sets with different means
Expressing variability as a percentage
Assessing analytical method precision

95% Confidence Interval

Inference

CI = x̄ ± t × (s / √n)

CI: = Confidence interval bounds
x̄: = Sample mean
t: = t-value for desired confidence level and df
s: = Sample standard deviation
n: = Sample size

🎯 When to Use This Formula

Estimating true population mean from sample data
Determining range where true exposure likely falls
Making compliance decisions with statistical confidence

Radiation Formulas

☢️

Radiation

High Priority

Radiation calculations test your understanding of exposure relationships. The inverse square law is particularly important.

Inverse Square Law

Distance Effects

I₁/I₂ = d₂²/d₁² or I₁ × d₁² = I₂ × d₂²

I₁: = Intensity at distance 1
I₂: = Intensity at distance 2
d₁: = Distance 1 from source
d₂: = Distance 2 from source

🎯 When to Use This Formula

Calculating radiation intensity change with distance
Determining safe working distance from a source
Point source radiation problems
Also applies to noise from point sources

💡 Quick Mental Math

Distance doubles → Intensity drops to 1/4
Distance triples → Intensity drops to 1/9
Distance halves → Intensity increases 4×

This is because intensity is proportional to 1/d². Use this for quick verification of your calculations.

📝 Example Problem

A radiation source produces 100 mR/hr at 2 feet. What is the intensity at 5 feet?

Apply inverse square law:
I₁ × d₁² = I₂ × d₂²
100 × 2² = I₂ × 5²
100 × 4 = I₂ × 25
I₂ = 400/25 = 16 mR/hr

Radioactive Decay / Half-Life

Time Effects

A = A₀ × (1/2)^t/t½ or A = A₀ × e^-λt

A: = Activity at time t
A₀: = Initial activity
t: = Elapsed time
t½: = Half-life
λ: = Decay constant (λ = 0.693/t½)

🎯 When to Use This Formula

Calculating remaining activity after a time period
Determining how long until activity drops to a specific level
Waste decay calculations

Gas Laws & Conversions

🧪

Gas Laws & Unit Conversions

Medium Priority

Unit conversions and gas law calculations appear throughout the exam. Master these fundamental relationships.

ppm to mg/m³ Conversion

Unit Conversion

mg/m³ = (ppm × MW) / 24.45

mg/m³: = Concentration in milligrams per cubic meter
ppm: = Concentration in parts per million
MW: = Molecular weight (g/mol)
24.45: = Molar volume at 25°C and 1 atm

🎯 When to Use This Formula

Converting between concentration units
Comparing measurements to OELs in different units
Any gas/vapor concentration conversion

📝 Example Problem

Convert 50 ppm of toluene (MW = 92) to mg/m³.

mg/m³ = (50 × 92) / 24.45 = 4,600 / 24.45 = 188 mg/m³

Ideal Gas Law

Fundamentals

PV = nRT

P: = Pressure
V: = Volume
n: = Number of moles
R: = Gas constant
T: = Temperature (absolute)

🎯 When to Use This Formula

Adjusting concentrations for non-standard conditions
Calculating gas volumes at different temperatures/pressures
Understanding gas behavior fundamentals

Exposure Assessment Formulas

📋

Exposure Assessment

High Priority

Time-Weighted Average (TWA)

Exposure Calculation

TWA = (C₁T₁ + C₂T₂ + ... + CₙTₙ) / 8

TWA: = 8-hour time-weighted average
C: = Concentration for each period
T: = Time at each concentration (hours)
8: = Standard work shift (hours)

🎯 When to Use This Formula

Calculating average exposure from varying concentration data
Comparing exposure to 8-hour OELs
Multiple sampling periods during a shift

Mixture Formula (Additive Effects)

Multiple Substances

E_m = C₁/OEL₁ + C₂/OEL₂ + ... + Cₙ/OELₙ

E_m: = Equivalent exposure (unitless)
C: = Concentration of each substance
OEL: = Occupational exposure limit of each substance

🎯 When to Use This Formula

Evaluating exposure to multiple substances with similar health effects
If E_m > 1, mixture exposure exceeds acceptable level
Additive health effects (same target organ)

📝 Example Problem

A worker is exposed to toluene at 30 ppm (OEL = 50 ppm) and xylene at 40 ppm (OEL = 100 ppm). Both affect the CNS. Is the combined exposure acceptable?

Apply mixture formula:
E_m = 30/50 + 40/100 = 0.6 + 0.4 = 1.0

Interpretation: E_m = 1.0 means exposure is exactly at the limit. Any increase would exceed acceptable exposure.

Common Calculation Mistakes

Avoid these frequent errors that cause candidates to lose points on calculation questions:

❌

Unit Confusion

Mixing feet and inches, cfm and m³/s, or forgetting to convert units before calculating. Always check that your units are consistent and match the formula requirements.

❌

Wrong WBGT Formula

Using the outdoor formula (with dry bulb) for indoor environments or vice versa. Read the problem carefully to determine if solar load is present.

❌

Adding Decibels Directly

Treating dB as linear values (e.g., thinking 80 dB + 80 dB = 160 dB). Decibels are logarithmic—use the dB addition formula. Two equal sources add only 3 dB.

❌

Forgetting Duct Area Calculation

Using diameter instead of area in Q=VA problems. Remember: Area = π × r² for round ducts. A 12" duct has r = 0.5 ft, so A = 0.785 ft².

❌

Inverse Square Law Direction

Setting up the ratio incorrectly. Remember: intensity DECREASES as distance INCREASES. If you're moving away from the source, the intensity should be lower.

❌

Calculator Entry Errors

Mis-clicking on the on-screen calculator. Write intermediate results on your whiteboard so you can verify and recover from errors.

❌

Fan Law Exponent Errors

Confusing which fan law uses which exponent. Remember: Flow is linear (¹), pressure is squared (²), power is cubed (³). The sequence 1-2-3 matches the increasing impact.

Practice Strategy

Mastering the equation sheet requires systematic practice. Here's a proven approach:

Phase 1: Learn the Formulas (Weeks 1-2)

Download the official BGC equation sheet
For each formula, understand what it calculates and what each variable represents
Create flashcards linking problem types to formulas
Don't try to memorize—focus on understanding

Phase 2: Pattern Recognition (Weeks 3-6)

Work through practice problems by category (all ventilation, then all noise, etc.)
Before calculating, identify which formula you need and why
Check your reasoning: "I'm using Q=VA because this problem asks about flow rate given velocity and area"
Build automatic recognition of problem types

Phase 3: Mixed Practice (Weeks 7-12)

Work through random/mixed calculation sets
Practice identifying formula without category hints
Time yourself—aim for 2-3 minutes per calculation question
Review every error: was it formula selection or execution?

Phase 4: Exam Simulation (Weeks 13+)

Take full-length practice exams with calculation questions included
Use only the on-screen calculator and equation sheet
Practice time management across the full exam
Build stamina for 5 hours of focused work

✅ Daily Calculation Practice

Dedicate 15-30 minutes daily to calculation practice. Like learning a musical instrument, frequent short sessions build fluency better than occasional long sessions. Aim to work through 5-10 calculation problems daily during your preparation. By exam day, you should have completed several hundred calculation problems across all categories.

Frequently Asked Questions

What formulas are on the CIH equation sheet?

The CIH equation sheet includes formulas for ventilation (Q=VA, capture velocity, fan laws), noise (dB addition, OSHA dose, TWA), heat stress (WBGT indoor and outdoor), statistics (mean, standard deviation, confidence intervals, coefficient of variation), radiation (inverse square law, half-life), gas laws (ideal gas law, ppm to mg/m³ conversion), and exposure assessment (TWA, mixture formula). The sheet provides the formulas but not explanations of when to use them—that's what you must learn through practice.

Can I bring my own calculator to the CIH exam?

No, you cannot bring your own calculator to the CIH exam. You must use the embedded on-screen calculator provided by Pearson VUE. This is a basic scientific calculator with standard functions including logarithms, exponents, and trigonometric functions. It's essential to practice with an on-screen calculator format before exam day, as the click-based interface is slower than a physical calculator. The Windows calculator in scientific mode provides a similar experience for practice.

How do I prepare for CIH exam calculations?

To prepare for CIH calculations: (1) Download the official BGC equation sheet and study it thoroughly, (2) Learn to recognize which formula applies to each problem type—this is the key skill, (3) Work through hundreds of practice calculation problems across all categories, (4) Practice with an on-screen calculator to build familiarity with the interface, (5) Focus extra time on high-frequency topics like ventilation, noise, and statistics, (6) Take timed practice exams to build speed and stamina. Aim to complete 5-10 calculation problems daily during your preparation period.

Which calculations appear most frequently on the CIH exam?

Based on exam analysis and candidate feedback, the most frequently tested calculation topics are: (1) Ventilation—Q=VA, capture velocity, fan laws; (2) Noise—dB addition, OSHA dose, TWA from dose; (3) Statistics—mean, standard deviation, confidence intervals; (4) Heat stress—WBGT calculations; (5) Unit conversions—ppm to mg/m³. Ventilation calculations are particularly important and appear throughout the exam. Ensure you're comfortable with all these categories before exam day.

Do I need to memorize the CIH formulas?

No, you don't need to memorize the formulas—they're provided on the equation sheet during the exam. However, you absolutely must be able to recognize which formula to use for each problem type. The equation sheet lists formulas without context or explanations. Your job is to: (1) Read the problem and identify what's being asked, (2) Recognize which formula applies, (3) Know what each variable means, (4) Execute the calculation correctly. This requires extensive practice, not memorization.

Master the Equations, Master the Exam

The calculation portion of the CIH exam doesn't have to be intimidating. Yes, the formulas are complex. Yes, there are many of them. But with systematic preparation and consistent practice, you can approach calculation questions with confidence.

Remember: the equation sheet gives you the formulas. Your job is to develop the pattern recognition skills to know which formula applies and the execution skills to calculate accurately under time pressure. Both skills come from practice—lots of it.

Download the BGC equation sheet today. Work through problems in each category until the formula selection becomes automatic. Then mix it up with random practice until you can identify the right approach for any problem type. That's how you turn the calculation section from a weakness into a strength.

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