ASVAB Math Cheat Sheet: Every Formula You Need to Know

The ASVAB has two math subtests, Arithmetic Reasoning (AR) and Math Knowledge (MK), and your scores on these directly affect which military jobs you qualify for. Here’s the complete cheat sheet plus a smart prep plan.

Arithmetic & number sense

• \(a % text{ of } b = dfrac{a}{100} times b\)
• Percent change = \(dfrac{text{new}-text{old}}{text{old}} times 100%\)
• Simple interest: (I = Prt)
• Distance, rate, time: (d = rt)
• Average: \(dfrac{text{sum}}{text{count}}\)
• Mean × count = sum (useful for “average” word problems)

Algebra

• Slope: \(m = dfrac{y_2 – y_1}{x_2 – x_1}\)
• Slope-intercept: (y = mx + b)
• Quadratic formula: \(x = dfrac{-b pm sqrt{b^2 – 4ac}}{2a}\)
• Distance between two points: \(d = sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)
• Midpoint: \(left(dfrac{x_1+x_2}{2}, dfrac{y_1+y_2}{2}right)\)

Geometry

• Pythagorean theorem: (a^2 + b^2 = c^2)
• Area of a rectangle: (A = lw)
• Area of a triangle: \(A = tfrac{1}{2}bh\)
• Area of a circle: \(A = pi r^2\)
• Circumference of a circle: \(C = 2pi r\)
• Volume of a rectangular prism: (V = lwh)
• Volume of a cylinder: \(V = pi r^2 h\)
• Volume of a sphere: \(V = tfrac{4}{3}pi r^3\)
• Volume of a cone: \(V = tfrac{1}{3}pi r^2 h\)
• Sum of angles in a triangle: 180°
• Sum of angles in a quadrilateral: 360°

Probability & statistics

• \(P(text{event}) = dfrac{text{favorable outcomes}}{text{total outcomes}}\)
• Independent events: \(P(A text{ and } B) = P(A) cdot P(B)\)
• Mutually exclusive: \(P(A text{ or } B) = P(A) + P(B)\)

Common Pythagorean triples (memorize)

3-4-5, 5-12-13, 8-15-17, 7-24-25.

Pacing tips

• AR: 15 scored questions in 55 minutes on the CAT-ASVAB, so you have over 3 minutes per question. Slow down on word problems.
• MK: 15 scored questions in 31 minutes, about 2 minutes per question. These are formula-driven, so the formulas above save time.

Arithmetic Reasoning vs. Mathematics Knowledge at a glance

Both math subtests count toward your AFQT score, along with Word Knowledge and Paragraph Comprehension. Here is how they compare on the computer version (CAT-ASVAB), based on officialasvab.com.

You may see up to 15 extra tryout questions on a subtest. They do not count, but you will not know which ones they are, so treat every question as scored.

Four quick worked examples

1. Percent change (AR): A $40 jacket is on sale for $30. Change = 40 − 30 = 10, and 10 ÷ 40 = 0.25, so it is a 25% discount.
2. Distance (AR): A truck drives 150 miles at 50 mph. Time = distance ÷ rate = 150 ÷ 50 = 3 hours.
3. Work rate (AR): Pipe A fills a tank in 3 hours and Pipe B in 6 hours. Together they fill 1/3 + 1/6 = 1/2 of the tank per hour, so the job takes 2 hours.
4. Equation (MK): Solve 3x − 7 = 11. Add 7: 3x = 18. Divide by 3: x = 6.

FAQ

Is a calculator allowed on the ASVAB?

No, all math is done by hand or in your head.

What’s a good ASVAB math score?

Each military branch sets its own minimum AFQT score (which depends partly on AR and MK). Most jobs require AFQT 50+; technical jobs often need 65+.

How is the ASVAB scored?

The AFQT composite score combines AR, MK, Paragraph Comprehension, and Word Knowledge into a percentile (1 to 99).

How long should I prep?

4 to 8 weeks of consistent practice is typical for a 10+ point AFQT increase.

Where can I get more practice?

Our ASVAB Math Practice Workbook (resource currently unavailable) has hundreds of practice problems with full solutions.

What’s the difference between AR and MK?

AR (Arithmetic Reasoning) is word problems. You have to set up the math from a story. MK (Math Knowledge) is direct math, plug into formulas, solve equations, manipulate algebraic expressions. Most students find MK faster but AR more brain-intensive.

Can I retake the ASVAB?

Yes. After your first attempt, you can retake after 1 month. After your second attempt, another month. After that, you must wait 6 months before retaking.

What is the AFQT, exactly?

The Armed Forces Qualification Test (AFQT) is a percentile composed from your AR, MK, Paragraph Comprehension, and Word Knowledge scores. It ranges 1 to 99 and is the most important number for enlistment eligibility.

Is the ASVAB computer-adaptive?

Yes, the CAT-ASVAB is the version taken at most MEPS (Military Entrance Processing Stations). The paper version (PiCAT, P&P) is sometimes given at Mobile Examination Test (MET) sites and is not adaptive.

How is the CAT-ASVAB different from a paper test?

On the CAT, you can’t skip a question or go back. Each question gets harder or easier based on your previous answer. This means early questions matter more. They set the difficulty curve.

Can you use a calculator on the ASVAB?

No. The official ASVAB site states that calculators are not allowed. You will do all the math by hand on scratch paper or in your head. That is why practicing mental math, fractions, and long division matters as much as knowing the formulas.

How many math questions are on the CAT-ASVAB?

On the computer version, Arithmetic Reasoning has 15 scored questions with a 55-minute limit, and Mathematics Knowledge has 15 scored questions with a 31-minute limit. Some test takers also get unscored tryout questions, which raises the time limits to 113 and 65 minutes.

What is the easiest way to pass the ASVAB math sections?

Learn the core formulas until you can write them from memory, then do timed practice without a calculator. Spend extra time on word problems, since Arithmetic Reasoning has more reading. Review every mistake and redo similar problems. Short daily practice usually works better than one long session.

How soon can you retake the ASVAB?

Under the official retest policy, you can take your first retest one month after your initial test and a second retest one month after that. After the second retest, you must wait six months between tests. Your recruiter can tell you how your most recent score will be used.

Smart strategies for AR (the word-problem subtest)

AR is where most students lose points. Three habits that help:

1. Read twice. Read once for the story, once for the math.
2. Underline the question. Literally underline what you’re being asked to find.
3. Write your variable on the page. “Let \(x =\) number of pounds of coffee.” Defining the variable forces you to commit to a structure.

Most AR questions reduce to: distance/rate/time, work rate, percent, mixture, or simple algebra word problems. Drill these 5 templates and you’ll see them everywhere.

Smart strategies for MK (the formula subtest)

MK rewards speed. Three habits:

1. Memorize the cheat sheet above. No calculator means every formula has to be in your head.
2. Master signed arithmetic. Almost every MK miss traces back to a sign error.
3. Practice mental math. Get fast at doubling, halving, percent of, and common squares (up to 20² = 400).

A week of focused mental-math drills can add 5 to 10 AFQT points by itself.

A realistic 6-week ASVAB study plan

• Week 1: Diagnostic + weakness map.
• Week 2 to 3: Drill arithmetic, fractions, decimals, percents, and basic algebra.
• Week 4: Geometry, ratios, and probability formulas.
• Week 5: Two full-length timed practice tests.
• Week 6: Light review, last-minute formulas, sleep.

If you don’t have 6 weeks, prioritize Weeks 2 and 5. They give the highest score-per-hour return.

The geometry shortcuts you must memorize

Without a calculator, every second counts. These mental shortcuts pay off:

• Common right triangles: 3-4-5, 5-12-13, 8-15-17, 7-24-25. If you see two of the sides, you know the third.
• 45-45-90 triangle: legs equal, hypotenuse = leg × \(sqrt{2}\).
• 30-60-90 triangle: sides in ratio 1: \(sqrt{3}\): 2.
• Common Pythagorean triples make many “find the diagonal” problems instant.

Need more practice? ASVAB Math for Beginners 2027 covers ASVAB math step by step, with practice problems and answers. Look inside · $17.99

Percent shortcuts

• 10% of a number: move the decimal one place left.
• 5% of a number: 10% then halve.
• 15%: 10% + 5%.
• 20%: double 10%.
• 25%: divide by 4.
• Percent change: (new − old) ÷ old × 100%.

Master these and you can do most ASVAB percent questions in under 15 seconds.

Common types of AR word problems

From our data, these 7 patterns cover ~80% of AR questions:

1. Cost/quantity, “How much does \(x\) pounds cost at $y per pound?”
2. Sale price, “Original $A\(, discounted \)p%$, what’s the sale price?”
3. Mixture / averages, “Mix $a\( gallons at \)x%\( with \)b\( at \)y%\(..”
4. Rate, distance, time, (d = rt) variations.
5. Work, “A can do it in \)a\( hours, B in \)b$ hours, together?”
6. Simple interest, (I = Prt).
7. Ratio, “Boys to girls is 3:2; 25 total students; how many boys?”

Drill these and AR becomes pattern recognition.

MK, quick-recall topics

For Math Knowledge, you have to recognize the situation in under 5 seconds. Memorize:

• Exponent rules: \(x^a cdot x^b = x^{a+b}\); \((x^a)^b = x^{ab}\); \(x^{-a} = tfrac{1}{x^a}\).
• Simplifying radicals: \(sqrt{ab} = sqrt{a}sqrt{b}\).
• FOIL: ((a+b)(c+d) = ac + ad + bc + bd).
• Factoring difference of squares: (a^2 – b^2 = (a+b)(a-b)).
• Slope formula and slope-intercept form.
• Pythagorean theorem.

If any of these feel slow, drill them 20 minutes a day until they’re automatic.

A final word on test-day mindset

The ASVAB rewards calm pattern recognition more than raw mathematical talent. Students who treat it like a familiar pattern-matching exercise outperform students who treat it as a test of math genius. Take a deep breath, read each question once for the picture and once for the math, and trust your prep.

Extra study tips that move the needle

Most students don’t fail because the math is too hard. They fail because their practice habits are inefficient. Here are the habits that separate the students who improve fast from those who stall.

Practice with a timer. Untimed practice teaches you to eventually get the right answer; timed practice teaches you to get it in test conditions. Set a stopwatch every time you sit down. Aim for 90 seconds per question on most standardized tests.

Keep an error log. A simple spreadsheet with three columns, Problem, My answer, Correct answer, Why I missed it, is the single most powerful study tool ever invented. Review your error log weekly. The same mistakes show up again and again until you name them.

Mix topics every session. Doing 20 problems on the same topic feels productive, but spaced and interleaved practice, mixing topics, builds retrieval skills, which is what the test actually measures. Spend 70% of your time on mixed sets and only 30% on isolated drills.

Sleep on it. Memory consolidation happens during sleep. A 30-minute session the night before a quiz, followed by 7+ hours of sleep, beats a 3-hour cram session that ends at midnight. This is settled cognitive science.

Teach the topic out loud. If you can’t explain it, you don’t fully know it. Either record yourself, write a one-paragraph “how I’d teach this” explanation, or grab a friend to listen. Teaching exposes the gaps your problem sets hid.

When to ask for help

Spinning your wheels for more than 15 minutes on a single problem is a signal, not of failure, but of a missing piece of background. Stop, mark the problem, and either ask a teacher, post in our community, or watch a video on the relevant subtopic. Resuming after gaining the missing piece is much more efficient than guessing your way forward.

A quick self-assessment

Before you close this tab, answer these three questions honestly:

1. What’s the one topic in this article you understood best?
2. What’s the one topic that still feels fuzzy?
3. What concrete next step (a worksheet, a practice test, a video) will you take in the next 48 hours?

Writing those answers down, even just in a notes app, has been shown to roughly double the chance you actually follow through. Treat the next 48 hours as a small, doable experiment, not a marathon. Your future test-day self will thank you.

The military uses a separate score from your sub-tests (called line scores or composite scores) to determine job (MOS, AFSC, Rate) eligibility. The math subtests (AR, MK) feed into many of these composites. A higher score doesn’t just help you qualify. It lets you choose among more jobs. So even after you pass, every additional point matters for picking the career you actually want.

Recommended EffortlessMath Books

For a workbook that pairs with this cheat sheet, the ASVAB Math for Beginners (resource currently unavailable) walks through every AR and MK topic with worked examples. For complete enlistment-test prep with multiple full-length practice tests, see the ASVAB Math Test Prep Bundle.

ASVAB Math for Beginners 2027 The Ultimate Step by Step Guide to Preparing for the ASVAB Math Test

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Frequently Asked Questions

Do you get a formula sheet on the ASVAB?

No. The ASVAB does not give you a formula sheet, and calculators are not allowed on any subtest, so every formula has to come from memory. Before test day, practice writing the essentials on blank paper: percent change, d = rt, I = Prt, slope, A = πr² and a² + b² = c². If you can write the whole list from memory in a few minutes, you are well prepared.

What kind of math is on the ASVAB?

The ASVAB has two math subtests. Arithmetic Reasoning is word problems built on everyday arithmetic, such as percents, ratios, rates, averages and simple interest. Mathematics Knowledge tests algebra and geometry directly, including exponents, solving equations, slope, area, volume and the Pythagorean theorem. Both count toward your AFQT score, which affects enlistment eligibility, so neither one is safe to skip.

How many math questions are on the ASVAB?

On the computer-based CAT-ASVAB, Arithmetic Reasoning has 15 scored questions with a 55-minute limit, and Mathematics Knowledge has 15 scored questions with a 31-minute limit, so 30 scored math questions in all. Some test takers also see unscored tryout questions. The paper version has more questions per subtest, so ask your recruiter which format you will take.

Is ASVAB math hard?

ASVAB math stays around high school level, so most of it is familiar, but having no calculator and a time limit makes it feel harder. Arithmetic Reasoning trips people up through the reading more than the math. For example, a jacket marked down from $80 to $60 is a 25% decrease, because (80 − 60) ÷ 80 × 100 = 25. Practicing setups like that by hand makes the test far more manageable.

How do you pass the ASVAB math section?

Memorize the core formulas first, then do timed practice with no calculator. For Arithmetic Reasoning, underline what the question actually asks and estimate before calculating so you can rule out choices. For Mathematics Knowledge, drill exponent rules, factoring and geometry formulas until they are automatic. Review every missed problem and redo it a few days later. Your recruiter can tell you the score your target branch requires.

What formulas do you need to know for the ASVAB?

For Arithmetic Reasoning, know percent = part ÷ whole × 100, percent change, distance = rate × time, simple interest I = Prt, and average = sum ÷ count. For Mathematics Knowledge, add slope, y = mx + b, the quadratic formula, exponent rules, area and perimeter of rectangles, triangles and circles, volume of a box and cylinder, and a² + b² = c². Memorizing triples like 3-4-5 and 5-12-13 saves time too.

Related EffortlessMath Lessons

If a topic on this page feels rusty, these short lessons go deeper:

• Free ASVAB Math practice test
• How to find the slope of a line
• How to use the quadratic formula
• How to use the Pythagorean theorem
• Rules of exponents

Official source: the content of each ASVAB subtest is described on the official ASVAB Enlistment Testing Program site at officialasvab.com.

Related: AFOQT math topics · How the ASTB is scored