ASVAB guideSkills
ASVAB Math Formulas: A Study Reference With Examples
A short lookup for percent, rate, algebra, and geometry, with the units and the trap next to each relationship. This is not an official formula list and not a test-day sheet.
Short answer
Use this page to recall a relationship while you study. It is not an official list of tested formulas, and you cannot bring it into the ASVAB. A calculator is not allowed. For a full lesson, use Arithmetic Reasoning for word problems and Mathematics Knowledge for algebra and geometry.
Which relationship do I need?
| The sentence gives you | Use | Do not use |
|---|---|---|
| A discount, a tax, or “percent of” | Percent of a whole, then add or subtract if the question asks for a final amount | The percent number alone |
| “For every” or a mixture that stays in proportion | A ratio scaled by one factor | Addition of the two parts |
| Price per hour, miles per hour, or liters per hour | Rate × time, with the time unit converted first | A rate multiplied by the wrong unit |
| “Average” or “mean” of a list | Sum divided by how many numbers | The middle number, unless you have checked the mean |
| An equation already written | Inverse steps, then a substitution check | A guess plugged in once without the check |
| A fence, a border, or “around” | Perimeter | Area |
| Carpet, paint, or “cover” | Area | Perimeter |
| A circle’s width through the center | Diameter, then radius = diameter / 2 if the formula needs radius | The diameter left inside a radius formula |
There is no PDF of this page. Print from the browser if you want paper at your desk. Leave it at home on test day.
Percent, ratio, and rate
| Relationship | Meaning of the letters | A compact example | Trap |
|---|---|---|---|
| Percent of a whole: part = rate × base | Rate is the decimal. 25 percent is 0.25. | 0.25 × $48 = $12 of discount | Reporting $12 when the question asked for the sale price, $36 |
| Percent increase: increase = rate × original | The increase is not the final amount. | A $20 item up 10 percent increases by $2 and costs $22 | Answering $2, or multiplying 20 × 10 |
| Ratio scale: new = old × factor | The factor has to hit every part. | 3:2 scaled by 5 becomes 15:10 | Scaling only one side |
| Distance = rate × time | Rate and time share a unit. | 40 miles per hour × 1.5 hours = 60 miles | Using 90 minutes as if it were 90 hours |
| Mean = sum / count | Count is how many addends. | (8 + 11 + 14) / 3 = 11 | Dividing by an extra number you did not add |
The lessons behind the first three rows are on Arithmetic Reasoning.
Algebra and geometry
| Relationship | When it fits | Example | Assumption |
|---|---|---|---|
| a(x + b) = c, then x + b = c / a | A number multiplies a parenthesis | 3(x − 2) = 15 gives x − 2 = 5 and x = 7 | a is not zero |
| x^2 means x × x | The exponent is 2 | 9^2 = 81 | It does not mean 9 × 2 |
| Rectangle area = length × width | You need the inside | 6 × 4 = 24 square units | Right angle, opposite sides equal |
| Rectangle perimeter = 2 × (length + width) | You need the outside | 2 × (6 + 4) = 20 units | Same rectangle |
| Circle area = π × radius^2 | You need the disk | Radius 3 gives about 3.14 × 9 = 28.26 | Use the π value the question gives. If it leaves π, keep π. |
| Radius = diameter / 2 | The given length crosses the center | Diameter 10 means radius 5 | Do not square the diameter by mistake |
Mathematics Knowledge walks the sign errors and the area mix-up. This table does not.
A three-line recall
- A $60 item rises by 15 percent. The increase is 0.15 × 60 = 9, so the new price is 69. The answer 9 is only the increase.
- A radius is 4. The diameter is 8. Area uses 4, not 8: π × 16.
- 20 minutes at 3 liters per hour is 1/3 hour, so 1 liter, not 60 liters.
Use a new practice item when the recall is clean. Do not treat this sheet as the list of formulas the ASVAB must ask.
Trust the source
Official sources
Exam policies can change. Use these primary sources for the most current details.