ASVAB Math Formulas Cheat Sheet
Updated July 2026 · AFQT · 6 min read
The essential ASVAB math formulas cover area, perimeter, volume, percentages, basic algebra, and geometry — the same high-school math tested on the two math subtests, Arithmetic Reasoning (AR) and Mathematics Knowledge (MK). Both subtests feed your AFQT score, which decides whether you can enlist, so memorizing this cheat sheet is one of the fastest ways to raise your number. Because there is no calculator and no formula sheet on the ASVAB, the goal is simple: lock these formulas into memory and practice them by hand until they are automatic.
Use the Arithmetic Reasoning practice test and Mathematics Knowledge practice test to see which formulas you actually need to drill.
Arithmetic and percentage formulas
Most Arithmetic Reasoning questions are word problems that hide one of these formulas inside a real-world scenario — money, distance, mixtures, or discounts. Learn to spot which one the problem is really asking for.
| Concept | Formula | Quick example |
|---|---|---|
| Percent | part ÷ whole × 100 | 15 of 60 = 15 ÷ 60 × 100 = 25% |
| Percent of a number | percent × whole | 20% of 80 = 0.20 × 80 = 16 |
| Percent change | (new − old) ÷ old × 100 | 40 → 50 = 10 ÷ 40 = 25% increase |
| Distance | rate × time | 60 mph × 3 h = 180 miles |
| Simple interest | principal × rate × time | $1,000 × 0.05 × 2 = $100 |
| Average (mean) | sum ÷ number of items | (4 + 8 + 6) ÷ 3 = 6 |
| Ratio/proportion | a/b = c/d → cross-multiply | 2/5 = x/20 → x = 8 |
Tip: Convert percents to decimals before you multiply (25% = 0.25). It is faster and prevents place-value slips when you are working without a calculator.
Area and perimeter formulas
Geometry is heavy on the Mathematics Knowledge subtest, and nearly all of it is straight formula recall. Keep these on a flashcard until they are instant.
| Shape | Area | Perimeter / Circumference |
|---|---|---|
| Square | s² | 4s |
| Rectangle | length × width | 2(l + w) |
| Triangle | ½ × base × height | side + side + side |
| Circle | πr² | 2πr (circumference) |
| Parallelogram | base × height | 2(a + b) |
| Trapezoid | ½(b₁ + b₂) × height | sum of all sides |
Use π ≈ 3.14 unless the problem tells you otherwise. For a circle with radius 5, area = πr² = 3.14 × 25 ≈ 78.5 square units.
Volume formulas
Volume problems ask how much space a solid holds. The pattern is usually “area of the base × height.”
- Cube: s³ (side cubed)
- Rectangular box (prism): length × width × height
- Cylinder: πr² × height
- Sphere: ⁴⁄₃ πr³
- Cone: ⅓ πr² × height
Example: A box 4 × 3 × 2 feet holds 4 × 3 × 2 = 24 cubic feet.
Algebra and exponent rules
Mathematics Knowledge leans on clean algebra. Master these and you can solve most equations in two or three steps.
- Solve for a variable: do the same operation to both sides until it stands alone. 3x + 7 = 22 → 3x = 15 → x = 5.
- FOIL (multiply binomials): (x + 2)(x + 3) = x² + 5x + 6.
- Multiply like bases: add exponents — x³ · x² = x⁵.
- Divide like bases: subtract exponents — x⁵ ÷ x² = x³.
- Power of a power: multiply — (x²)³ = x⁶.
- Negative exponent: flip it — x⁻² = 1 ÷ x².
- Slope of a line: (y₂ − y₁) ÷ (x₂ − x₁).
Memorize the perfect squares up to 15² = 225 and the order of operations (PEMDAS: parentheses, exponents, multiply/divide, add/subtract). Both save time and prevent the careless errors that cost easy points.
The Pythagorean theorem
For any right triangle, the square of the longest side (the hypotenuse) equals the sum of the squares of the other two sides:
a² + b² = c²
If the legs are 3 and 4, then c² = 9 + 16 = 25, so c = 5. Watch for the common triples — 3-4-5, 5-12-13, and 8-15-17 — because recognizing them lets you skip the arithmetic entirely. For a fuller walkthrough of these topics, see the Mathematics Knowledge study guide.
Mental-math tips for a no-calculator test
Because you cannot use a calculator on the ASVAB, the formulas only help if you can compute quickly by hand.
- Estimate first. Round numbers to check whether an answer choice is even reasonable before doing exact math.
- Simplify fractions early. Cancel common factors so you multiply small numbers, not large ones.
- Break percents apart. 15% = 10% + 5%; find 10% by moving the decimal, then halve it for 5%.
- Plug in the answers. When solving directly stalls, test each choice in the equation — one has to work.
- Never leave a blank. There is no penalty for guessing, so eliminate the obvious wrong choices and pick the best remaining option.
Put the formulas to work
Reading a cheat sheet is not the same as recalling it under a clock. Turn these into flashcards, drill them daily, and then run full timed sets from the main ASVAB study guide. When you want to see how a stronger math score moves your qualifying number, feed your practice results into the ASVAB score calculator. Consistent, hands-on repetition is what turns a formula list into real points on test day.
