ASVAB math formulas you should know by heart
Plan on no formula sheet and no calculator, so you need about 20 formulas memorized: perimeter, area and volume, the Pythagorean theorem, slope, simple interest, percent change and the average. This page lists them in one table, shows how each one is used, and gives you practice that uses them by hand.
Which math formulas are on the ASVAB?
The ASVAB math subtests use standard high school formulas, and you should plan to bring them in your head. The official What to Expect page lists no formula sheet among test materials. The official What to Expect page says: "You cannot use a calculator when taking the ASVAB." The official page describes Mathematics Knowledge as "knowledge of high school mathematics principles" and Arithmetic Reasoning as the "ability to solve arithmetic word problems" (What to Expect). In practice that means a short list of formulas comes up again and again.
The table below is the whole list most test takers need. Learn the left column as a sentence ("area of a triangle is half base times height"), not just as letters, because word problems describe the shape in words.
| What you need | Formula | Notes |
|---|---|---|
| Perimeter of a rectangle | P = 2l + 2w | Add all four sides |
| Area of a rectangle | A = l × w | Square units |
| Area of a square | A = s² | Perimeter is 4s |
| Area of a triangle | A = ½ × b × h | Height is perpendicular to the base |
| Area of a parallelogram | A = b × h | Use the slanted side only for perimeter |
| Area of a trapezoid | A = ½ × (b₁ + b₂) × h | Average the two bases, then multiply |
| Circumference of a circle | C = 2πr = πd | π is about 3.14 |
| Area of a circle | A = πr² | Square the radius, not the diameter |
| Volume of a box | V = l × w × h | Cubic units |
| Volume of a cube | V = s³ | Surface area is 6s² |
| Volume of a cylinder | V = πr²h | Circle area times height |
| Pythagorean theorem | a² + b² = c² | Right triangles only; c is the longest side |
| Angles in a triangle | Sum = 180° | A quadrilateral sums to 360° |
| Slope of a line | m = (y₂ − y₁) ÷ (x₂ − x₁) | Rise over run |
| Slope-intercept form | y = mx + b | b is where the line crosses the y-axis |
| Simple interest | I = P × r × t | Rate as a decimal, time in years |
| Percent change | (new − old) ÷ old × 100 | Always divide by the original |
| Distance, rate, time | d = r × t | Keep units matched |
| Average (mean) | sum ÷ count | Total = average × count |
| Probability | favorable ÷ total outcomes | Between 0 and 1 |
You do not need trigonometry, logarithms or calculus. If a practice book drills those for the ASVAB, skip that chapter.
How do you use the area and perimeter formulas?
Perimeter is the distance around a shape, and area is the space inside it. The most common mistake is giving the perimeter when the question asks for area, so circle the word "area" or "fence" or "border" before you start. Fence, border, trim and frame mean perimeter. Carpet, paint, tile and sod mean area.
Example: A patio is 12 feet long and 7.5 feet wide. What are its area and perimeter?
- Area: 12 × 7.5. Split it: 12 × 7 = 84 and 12 × 0.5 = 6, so 84 + 6 = 90.
- Perimeter: 2 × 12 + 2 × 7.5 = 24 + 15 = 39.
- Check units: area in square feet, perimeter in feet.
Answer: area 90 square feet, perimeter 39 feet
Triangles trip people up because of the one half. A triangle is half of a rectangle with the same base and height, which is why the formula has ½ in it. If your answer equals one of the choices doubled, you probably forgot the half.
How do you work with circles without a calculator?
Use 3.14 for π, or leave the answer in terms of π when the choices do. Many MK choices are written like 25π, which saves you the multiplication entirely.
Example: A circular rug has a radius of 5 feet. Find its area and circumference using π ≈ 3.14.
- Area = πr² = 3.14 × 5² = 3.14 × 25.
- 3.14 × 25: 3 × 25 = 75 and 0.14 × 25 = 3.5, so 78.5.
- Circumference = 2πr = 2 × 3.14 × 5 = 3.14 × 10 = 31.4.
Answer: area 78.5 square feet, circumference 31.4 feet
If a problem gives the diameter, halve it before you square it. A circle with diameter 10 has radius 5 and area 25π, not 100π.
When do you use the Pythagorean theorem?
Use it whenever a right triangle has two known sides and you need the third. Ladders against walls, diagonals of rectangles and "how far apart are they" questions are all right triangles in disguise.
Example: The legs of a right triangle are 9 and 12. How long is the hypotenuse?
- a² + b² = c², so 9² + 12² = 81 + 144 = 225.
- c = √225 = 15.
- Shortcut: 9-12-15 is the 3-4-5 triangle multiplied by 3.
Answer: 15
Learn the common whole-number triples: 3-4-5, 5-12-13, 8-15-17 and 7-24-25, plus their multiples (6-8-10, 9-12-15, 10-24-26). When two sides match a triple, you can skip the squaring. The geometry review covers angles and similar triangles in more depth.
How do the volume formulas work?
Volume is area of the base times height. That one idea covers boxes (rectangle base), cubes (square base) and cylinders (circle base), so you only need to remember the base areas.
Example: A storage box is 4 feet long, 5 feet wide and 6 feet tall. What is its volume?
- V = l × w × h.
- 4 × 5 = 20, then 20 × 6 = 120.
Answer: 120 cubic feet
For a cylinder with radius 2 and height 5, the base area is π × 2² = 4π and the volume is 4π × 5 = 20π. If the answers are written with π, stop there.
How do you find the slope of a line?
Slope is the change in y divided by the change in x between two points. Subtract in the same order on top and bottom, or the sign flips.
Example: Find the slope of the line through (2, 3) and (6, 11).
- Change in y: 11 − 3 = 8.
- Change in x: 6 − 2 = 4.
- Slope = 8 ÷ 4 = 2.
Answer: 2
In y = mx + b, the number in front of x is the slope. The line y = 2x − 5 has slope 2 and crosses the y-axis at −5. Equation solving itself is covered in the algebra lesson.
Which money and percent formulas should you know?
Simple interest, percent change and the average cover almost every money word problem on Arithmetic Reasoning. Write the rate as a decimal before you multiply: 5% is 0.05.
Example: You deposit $2,400 at 5% simple interest for 3 years. How much interest do you earn?
- I = P × r × t = 2,400 × 0.05 × 3.
- 2,400 × 0.05 = 120 (5% is half of 10%, and 10% of 2,400 is 240).
- 120 × 3 = 360.
Answer: $360 in interest
Percent change and compound interest have their own page: ASVAB interest and percent change. Averages and probability are on averages and probability.
How do you find surface area and the distance between two points?
Surface area is the total area of every face, and the distance between two points comes from the Pythagorean theorem. Both show up less often than area and volume, but they are easy points once you see the pattern.
A box has three pairs of matching faces: top and bottom, front and back, left and right. Find the area of one face from each pair, add them, and double the sum. A cube has six identical square faces, so its surface area is 6s².
Example: What is the surface area of a box that is 4 by 5 by 6 feet?
- Face areas: 4 × 5 = 20, 5 × 6 = 30, 4 × 6 = 24.
- Add one of each: 20 + 30 + 24 = 74.
- Each face has a twin, so double it: 74 × 2 = 148.
Answer: 148 square feet
For the distance between two points on a graph, draw the right triangle they form. The horizontal leg is the change in x, the vertical leg is the change in y, and the distance is the hypotenuse.
Example: How far apart are the points (1, 2) and (7, 10)?
- Change in x: 7 − 1 = 6. Change in y: 10 − 2 = 8.
- Distance² = 6² + 8² = 36 + 64 = 100.
- Distance = √100 = 10. This is the 3-4-5 triple doubled.
Answer: 10 units
Notice how often the same few ideas repeat. The distance formula is just the Pythagorean theorem, and surface area is just rectangle area six times. Memorizing fewer core ideas and deriving the rest is faster than memorizing a long list of separate formulas.
What is the fastest way to memorize these formulas?
Write the sheet from memory once a day for a week, then check it against the table. The gaps show you exactly which formulas to drill. After a week, switch to using them: do five mixed problems a day where you have to pick the formula yourself.
- Group formulas by idea: "area of base times height" covers three volume formulas.
- Say units out loud. Feet for perimeter, square feet for area, cubic feet for volume.
- Keep a list of the formulas you misused in practice and redo one problem for each before your next session. The mistake review method explains how.
Then test yourself under time on the Mathematics Knowledge practice page or the math workout.
Practice questions
Work each one on paper first, then open the explanation. These are original AptiStep items, not real ASVAB questions.
A triangle has a base of 14 inches and a height of 9 inches. What is its area?
- 126 square inches
- 63 square inches
- 23 square inches
- 46 square inches
Show answer and explanation
Answer: B. 63 square inches
Area of a triangle is one half times base times height. 14 × 9 = 126, and half of 126 is 63. Choosing 126 means the one half was forgotten; 23 comes from adding the two numbers.
A circle has a diameter of 10 cm. Using 3.14 for pi, what is its area?
- 31.4 square cm
- 314 square cm
- 78.5 square cm
- 15.7 square cm
Show answer and explanation
Answer: C. 78.5 square cm
The radius is half the diameter, so r = 5. Area = 3.14 × 5 × 5 = 3.14 × 25 = 78.5. The answer 31.4 is the circumference, and 314 comes from using the diameter as the radius.
What is the volume of a cube with sides of 3 meters?
- 27 cubic meters
- 9 cubic meters
- 54 cubic meters
- 18 cubic meters
Show answer and explanation
Answer: A. 27 cubic meters
Volume of a cube is side cubed: 3 × 3 × 3 = 27. The answer 9 is the area of one face, and 54 is the surface area (6 faces × 9).
A right triangle has a hypotenuse of 13 and one leg of 5. How long is the other leg?
- 8
- 18
- 144
- 12
Show answer and explanation
Answer: D. 12
Use a² + b² = c². 5² + b² = 13², so 25 + b² = 169 and b² = 144. The square root of 144 is 12. This is the 5-12-13 triple. Choosing 144 means you stopped before taking the square root.
What is the slope of the line that passes through (1, 4) and (5, 16)?
- 3
- 4
- 1/3
- 12
Show answer and explanation
Answer: A. 3
Slope is change in y over change in x. 16 − 4 = 12 and 5 − 1 = 4, so the slope is 12 ÷ 4 = 3. Writing 1/3 means the fraction was flipped (run over rise).
A cylinder has a radius of 2 feet and a height of 5 feet. What is its volume?
- 10π cubic feet
- 40π cubic feet
- 20π cubic feet
- 4π cubic feet
Show answer and explanation
Answer: C. 20π cubic feet
Volume of a cylinder is πr²h. The base area is π × 2² = 4π. Multiply by the height: 4π × 5 = 20π. The choice 10π comes from multiplying by r instead of r² (π × 2 × 5), and 4π is only the base area.
You borrow $1,500 at 4% simple interest for 2 years. How much interest do you owe?
- $60
- $120
- $1,620
- $1,200
Show answer and explanation
Answer: B. $120
I = P × r × t = 1,500 × 0.04 × 2. Four percent of 1,500 is 60 (1% is 15, times 4). Over 2 years that is 60 × 2 = 120. The $1,620 choice is the total repaid, not the interest.
Your four test scores are 84, 90, 78 and 88. What is your average?
- 84
- 86
- 85
- 88
Show answer and explanation
Answer: C. 85
Add the scores: 84 + 90 = 174, 174 + 78 = 252, 252 + 88 = 340. Divide by the number of scores: 340 ÷ 4 = 85.
Frequently asked questions
Does the ASVAB give you a formula sheet?
The official What to Expect page does not mention a formula sheet, and it says you cannot use a calculator. Plan to memorize every formula in the table above.
Which formulas show up most often?
Area of rectangles, triangles and circles, the Pythagorean theorem, simple interest and the average. If you are short on time, learn those first.
Should I use 3.14 or 22/7 for pi?
Use whatever the question says. If it says nothing and the choices contain π, leave π in the answer. Otherwise 3.14 is easiest to multiply by hand, and 22/7 is handy when the radius is a multiple of 7.
Where can I practice these formulas?
Use the Mathematics Knowledge practice and Arithmetic Reasoning practice pages, then mixed sets in the math workout.
Sources
Checked November 14, 2026. AptiStep is an independent study site; confirm anything that affects your enlistment with a recruiter.