Do I need to be good at math to pass the CIH exam?

No. The CIH exam's calculation questions reuse a small, repeating set of math moves — rearranging a formula, converting units, exponents, roots, logarithms, scientific notation, ratios, and weighted averages. Recognizing those moves and executing them confidently on a calculator matters far more than raw math ability.

What calculator is allowed on the CIH exam, and does it matter which one I practice with?

Candidates are provided a basic scientific calculator (TI-30XS MultiView or equivalent) at the test center — you cannot bring your own. Practicing on the exact key layout beforehand, including the 2nd-key shifted functions, removes the fumbling that costs time on exam day.

Why do I need logarithms for an industrial hygiene exam?

Several CIH calculations deal with quantities that span many orders of magnitude — sound intensity, radioactive decay, and similar exponential relationships. Logarithms convert those enormous ranges into manageable numbers, so several exam formulas are built directly on log or ln.

What's the difference between a square root and an nth root?

A square root undoes a square: √(x²) = x. An nth root generalizes that idea to any power and is mathematically the same as raising a number to a fractional exponent, 1/n — for example, a 5th root equals raising a number to the power 1/5.

Why does scientific notation matter for the CIH exam?

Several CIH calculations involve values that are either extremely large or extremely small (radioactive activity, particle counts). Scientific notation — a number times a power of ten — lets those values be entered on a calculator accurately without miscounting zeros, which is a common source of exam errors.

What's a common mistake candidates make with the calculator's negative-entry key?

The (−) key is a prefix operator you press before typing a number, not a sign-flip you apply afterward — pressing it in the wrong order produces a calculator error or, worse, a silently wrong answer instead of the intended negative value.

Do I need a separate study resource just for calculator practice, or is this covered elsewhere?

This math-basics refresher and its built-in practice calculator are free and cover the underlying skills in isolation. The CIH Equation Master then applies those same skills to all 98 real CIH equations with worked practice problems, using this exact calculator.

Updated August 28, 2026·Reference — Math Refresher·By Kevin L., CRSP & CRST

CIH Calculator & Math Basics

Every CIH equation eventually comes down to the same handful of math moves — logs, exponents, roots, ratios — done on a scientific calculator. If it's been a few years since you've touched any of this, or you've just never thought of yourself as a "math person," this page is the refresher: what each skill actually means, a worked example, and the exact calculator keys to press.

Why this page exists

You don't need to be good at math to pass the CIH exam — you need to recognize a small, repeating set of calculator moves and be able to execute them without hesitating under time pressure. This page covers every one of those moves in plain language, with a real practice example for each, and a working calculator below so you can try them yourself before you ever open a real CIH equation.

What's covered

Ten skills, each showing up over and over across the actual CIH formulas:

Rearranging a formula
Keeping units consistent
Exponents & powers
Square roots & nth roots
Logarithms & antilogs
Scientific notation
Ratios & proportions
Squares, sums of squares & reciprocals
Weighted averages & signed numbers
Basic areas

Open the practice calculator now and keep it open while you work through the examples below — it's the same simulated calculator used throughout the CIH Equation Master app.

The Math, One Skill at a Time

1. Rearranging a Formula

Most exam questions don't hand you the exact formula you need — they give you the answer and ask for one of the inputs. Whatever you do to one side of an equation, you must do to the other: multiply to move a divisor, divide to move a multiplier.

Example

From $a = bc$: to solve for $c$, divide both sides by $b$, giving $c = a/b$.

Harder example

From $y = \frac{x}{2} + 5$: subtract 5 from both sides first, then multiply both sides by 2 — giving $x = 2(y-5)$. Check it: if $y=9$, then $x=2(9-5)=8$, and $8/2+5=9$. ✓

Do the rearrangement on paper first, then type once: 2 × ( 9 - 5 ) enter

2. Keeping Units Consistent

A formula only works if every value going into it is in the same unit system — mixing inches with feet, or seconds with minutes, silently wrecks the answer without ever throwing an error.

Example

An 8-inch measurement must become $8/12 = 0.667$ ft before it can combine with a value already in feet.

Harder example

A rate quoted as "90 seconds per cycle" needs converting to minutes before it can combine with a flow rate in cfm (cubic feet per minute): $90 \div 60 = 1.5$ minutes.

90 ÷ 60 enter

3. Exponents & Powers

$x^n$ means $x$ multiplied by itself $n$ times. Small numbers raised to a power can grow — or shrink — much faster than intuition suggests, especially once the exponent gets past 2 or 3.

Example

Repeated halving: $0.5^4 = 0.0625$ — four halvings leaves just 6.25% of the original amount.

.5 ^ 4 enter

Harder example

A small percentage change raised to a higher power creates a much bigger swing: $1.1^5 \approx 1.61$ — a 10% increase becomes a 61% increase once raised to the 5th power. Also try $2^{10}=1{,}024$ — ten doublings takes you from 1 to over a thousand.

1.1 ^ 5 enter | 2 ^ 10 enter

4. Square Roots & nth Roots

A square root undoes a square: $\sqrt{x^2}=x$. An nth root is the same idea generalized — it's really just a fractional power: $\sqrt[n]{x}=x^{1/n}$.

Example

$\sqrt{0.04+25}=\sqrt{25.04}\approx5.004$. When a formula adds two squared quantities before rooting, both must already be in the same unit.

2nd x² types sqrt(

Harder example

$\sqrt[5]{3125} = 3125^{1/5} = 5$. And roots aren't always positive-only: $\sqrt[3]{-27}=-3$, since $(-3)^3=-27$ — odd-numbered roots can take a negative input, unlike square roots.

3125 2nd ^ 5 ) enter

5. Logarithms & Antilogs

Read $\log(x)$ as "what power of 10 gives me $x$?" — it converts a ratio into an order of magnitude. Antilog reverses it: $10^{\log(x)}=x$. Natural log ($\ln$) and $e^x$ are the same relationship using the natural base $e\approx2.71828$ instead of 10.

Example

$\log(1000)=3$, because $10^3=1000$. And $e^{-1.5525}\approx0.2117$ — a negative exponent always means decay toward zero.

log 1000 ) enter | 2nd ln types e^(

Harder example

Log-scale quantities never add directly. Two values that are each $10^9$ don't combine to "$10^{18}$" — add the actual numbers first, then take the log: $10^9+10^9=2\times10^9$, and $\log(2\times10^9)\approx9.3$, not 18.

log 2 × 2nd log 9 ) enter — this calculator has no "implied multiplication," so open with log first and use × to combine the 2 with the 10⁹, rather than typing the 2 before 2nd log (which would be read as the single number "210", not "2 times 10").

6. Scientific Notation

Numbers that span an enormous range are written as a number times a power of ten, so you're never stuck counting zeros by hand.

Example

1 Curie $= 3.7 \times 10^{10}$ Becquerels — 37 billion, written compactly.

3.7 ×10ⁿ 10

Harder example

Small numbers work the same way, with a negative exponent: $0.000045 = 4.5\times10^{-5}$. Count how many places the decimal point moves — 5 places right to reach 4.5, so the exponent is $-5$.

4.5 ×10ⁿ (−) 5 enter — press the single (−) key (bottom row, next to enter) before the 5, not after. It's one "make the next number negative" key — don't build it out of the separate (, −, ) keys elsewhere on the pad, which type literal parentheses and a subtraction sign instead and will error.

7. Ratios & Proportions

When a formula is built from a ratio, the actual units cancel out — only consistency between the two sides matters. Squaring a ratio means small changes get amplified, not just doubled.

Example

$\left(\frac{2}{4}\right)^2=0.25$ — a ratio of one-half becomes one-quarter once squared.

( 2 ÷ 4 ) x²

Harder example

If two quantities are inversely proportional (their product stays constant) and one doubles, the other must halve to compensate: with $a \times b = 12$, if $a$ goes from 3 to 6, $b$ must go from 4 down to 2 — $6\times2=12$, same as $3\times4=12$.

12 ÷ 6 enter

8. Squares, Sums of Squares & Reciprocals

Squaring makes every deviation positive so they can't cancel each other out. Summing reciprocals (then inverting the sum) is how you combine rates or parallel contributions — never just average them.

Example

Deviations of $+2$ and $-2$ sum to zero, but their squares sum to 8 — squaring is what keeps variability formulas from cancelling to nothing.

x² after each value, then add

Harder example

Classic "two pipes" problem: one pipe alone fills a tank in 100 minutes, another alone in 50 minutes. Combined, they don't average to 75 minutes — sum the reciprocals (rates), then invert: $\frac{1}{\frac{1}{100}+\frac{1}{50}} = 33.3$ minutes.

( 1 ÷ 100 + 1 ÷ 50 ) x⁻¹ enter

9. Weighted Averages & Signed Numbers

A weighted average multiplies each value by its own weight (the weights always sum to 1.0) before adding — it is not the same as a plain average. Some formula terms can be positive or negative depending on the situation, so track signs deliberately rather than assuming everything adds.

Example

Three grades weighted 50% / 30% / 20%: $0.5(80)+0.3(90)+0.2(70) = 81$. A plain average of 80, 90, and 70 would give 80 — a meaningfully different number.

.5 × 80 + .3 × 90 + .2 × 70 enter

Harder example

A running total with a gain and two losses: net $=500-200-150=150$. When a term's sign can flip depending on conditions (a gain in one scenario, a loss in another), use the calculator's (−) key to enter it as negative rather than trying to track the sign in your head.

500 - 200 - 150 enter

10. Basic Areas

A rectangular area is width × height; a circular area is $\pi r^2$. Keep every length in the same unit before multiplying — area formulas amplify a unit mistake instead of just carrying it through.

Example

A 2 ft × 3 ft rectangle is 6 ft².

2 × 3 enter

Harder example

A circular opening with radius 1.5 ft: $\pi(1.5)^2 \approx 7.07$ ft².

π × 1.5 x² enter

Ready for the Real Equations?

Everything above is the math skill on its own — the CIH Equation Master puts it to work on all 98 real CIH equations across Radiation, Ventilation, Noise, Science & Statistics, Hood Airflow, and Heat Stress, with worked practice problems and this exact calculator built in.

Try the CIH Equation Master →

Radiation equations are free to try — no sign-up required