On the ACT WorkKeys Applied Math test you get a formula sheet with unit conversions and geometry formulas. On paper it sits at the front of the test booklet, and you may tear it out; online it is a built-in tool you can open during the test. The sheet tells you that problems “should be worked using the formulas and conversions on this formula sheet,” so knowing what is on it, and what isn’t, saves time and avoids answers that are slightly off.

This page is independent practice information and is not affiliated with ACT. The contents below follow ACT’s current test directions; the sheet you see on test day is the one that counts.

Distance

Conversion
1 foot = 12 inches
1 yard = 3 feet
1 mile = 5,280 feet
1 mile ≈ 1.61 kilometers
1 inch = 2.54 centimeters
1 foot = 0.3048 meters
1 meter = 1,000 millimeters
1 meter = 100 centimeters
1 kilometer = 1,000 meters

Area

Conversion
1 square foot = 144 square inches
1 square yard = 9 square feet
1 acre = 43,560 square feet

Volume

Conversion
1 cup = 8 fluid ounces
1 quart = 4 cups
1 gallon = 4 quarts
1 gallon = 231 cubic inches
1 liter ≈ 0.264 gallons
1 cubic foot = 1,728 cubic inches
1 cubic yard = 27 cubic feet
1 board foot = 1 inch by 12 inches by 12 inches

Weight and mass

Conversion
1 ounce ≈ 28.350 grams
1 pound = 16 ounces
1 pound ≈ 453.592 grams
1 milligram = 0.001 grams
1 kilogram = 1,000 grams
1 kilogram ≈ 2.2 pounds
1 ton = 2,000 pounds

Shapes

Shape	Formulas
Rectangle	perimeter = 2(length + width); area = length × width
Rectangular solid (box)	volume = length × width × height
Cube	volume = (length of side)³
Triangle	sum of angles = 180°; area = 1⁄2 (base × height)
Circle	number of degrees in a circle = 360°; circumference ≈ 3.14 × diameter; area ≈ 3.14 × (radius)²
Cylinder	volume ≈ 3.14 × (radius)² × height
Cone	volume ≈ (3.14 × (radius)² × height) ÷ 3
Sphere (ball)	volume ≈ 4⁄3 × 3.14 × (radius)³

Electricity and temperature

Topic	Formulas
Electricity	1 kilowatt-hour = 1,000 watt-hours; amps = watts ÷ volts
Temperature	°C = 5⁄9 (°F - 32); °F = 9⁄5 (°C) + 32

What is not on the sheet

The sheet has no formulas for percent, discount, markup, tax, averages, rates or the area of a trapezoid, and no time conversions. You are expected to know that 1 hour is 60 minutes, how to find a percent of a number, and how to find a mean. Some older copies of the sheet also listed 1 kilometer ≈ 0.62 miles; the current sheet drops that line, so to go from kilometers to miles, divide by 1.61.

Notice also what the sheet gives you only one way. It says 1 gallon = 231 cubic inches but not how many gallons are in a cubic foot, so a tank problem in feet usually needs two steps: cubic feet to cubic inches, then cubic inches to gallons.

When you need it

Lower-level questions rarely need the sheet. From about Level 5 up, you are expected to pick the right conversion or formula yourself: converting units within or between systems, finding the perimeter or area of basic shapes, and at Levels 6 and 7, chaining conversions, rearranging a formula, and finding the volume of cylinders, cones and spheres. See Applied Math topics by level for what each level tests.

Calculator rules

You may use a calculator on Applied Math. It must meet the ACT Calculator Policy, and the online test has an on-screen calculator. The directions also say:

• Use 3.14 for pi. A calculator’s pi key gives a slightly different result, which may not match any choice.
• “Average” means the mean: add the values and divide by how many there are.
• Diagrams are not necessarily drawn to scale, so work from the numbers, not the picture.
• “Line” means a straight line.

The calculator does arithmetic, but it won’t choose the conversion for you. Many wrong choices come from a skipped or reversed step, such as dividing where you should multiply, forgetting to square the radius, or using the diameter where the radius belongs.

Worked examples

1. Gallons in a tank. You need to know how many gallons a cylindrical tank holds. It has a radius of 2 feet and a height of 5 feet.

• Volume ≈ 3.14 × 2² × 5 = 3.14 × 4 × 5 = 62.8 cubic feet.
• Cubic feet to cubic inches: 62.8 × 1,728 = 108,518.4 cubic inches.
• Cubic inches to gallons: 108,518.4 ÷ 231 ≈ 469.78, so about 470 gallons.

2. Concrete for a slab. You are ordering concrete for a slab 12 feet long, 18 feet wide and 4 inches deep. Concrete is sold by the cubic yard.

• Change the depth to feet: 4 ÷ 12 = ¹⁄₃ foot.
• Volume = 12 × 18 × ¹⁄₃ = 72 cubic feet.
• Cubic feet to cubic yards: 72 ÷ 27 ≈ 2.67 cubic yards.

The trap here is mixing units: 12 × 18 × 4 = 864 treats inches as feet and gives an answer twelve times too big.

3. Oven temperature. A recipe from a supplier lists 350°F, but your oven reads in Celsius.

• °C = ⁵⁄₉ × (350 - 32) = ⁵⁄₉ × 318 ≈ 176.67, so about 177°C.

Subtract 32 first, then multiply. Multiplying first gives ⁵⁄₉ × 350 - 32 ≈ 162.44, a common wrong choice.

4. Why 3.14 matters. A round table top has a radius of 6 inches. With 3.14, the area is 3.14 × 36 = 113.04 square inches. With a calculator’s pi key, you get about 113.10, which may not be one of the choices.

5. Amps on a circuit. A 1,500-watt heater runs on 120 volts. Amps = 1,500 ÷ 120 = 12.5 amps.

Tips for using the sheet

• Read it before test day. Know where each conversion sits so you can find it in seconds.
• Write units at every step. If cubic feet don’t cancel to gallons, a step is missing.
• Check the size of your answer. A slab that needs 32 cubic yards of concrete, or a tank that holds 0.3 gallons, is a sign of a reversed conversion.

For the full test format, see the WorkKeys test guide, and for how your score turns into a level, see WorkKeys scores and levels.

Keep practicing

Every Applied Math question in our timed practice tests has the formula sheet and an on-screen calculator beside it, like the online test, plus a worked explanation for every answer. Start from the home page, or try the Applied Math practice questions.