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Essential ASVAB Math Formulas for an Easier Exam

Sarah Nguyen

Created at June 9, 2025

Struggling to remember key ASVAB math formulas under pressure? You’re not alone. Many test-takers blank when confronted with fractions, percentages, and geometry during the ASVAB. That’s why we’ve crafted this ultimate ASVAB math formulas guide. In the next few minutes, you’ll gain clarity on essential formulas, organized by topic group, so you can confidently crack every question, without scrambling mid-test. We’ll go beyond regurgitated lists and show you how and when to apply each formula. By the end, you’ll have an actionable formula toolbox and the confidence to maximize your ASVAB score.

ASVAB math formulas

$ASVAB math formulas$

ASVAB math formulas

Divisibility, prime numbers, GCF & LCM

Understanding divisibility rules, prime numbers, GCF (Greatest Common Factor), and LCM (Least Common Multiple) is essential for solving many arithmetic problems. To help you quickly recall and apply these concepts, refer to the summary table of key ASVAB formulas below.

Divisibility rules:

Divisibility Rule	Condition
Divisible by 2	The number ends in an even digit (0, 2, 4, 6, 8)
Divisible by 3	The sum of its digits is divisible by 3
Divisible by 5	The number ends in 0 or 5
Divisible by 9	The sum of its digits is divisible by 9

Greatest common factor (GCF)

$\text{GCF}(a, b) = \text{GCF}(b, \ a \bmod b)$

Least common multiple (LCM):

$\text{LCM}(a, b) = \frac{|a \times b|}{\text{GCF}(a, b)}$

Fractions, decimals & ratios

Mastering conversions between fractions, decimals, and ratios is crucial for understanding relationships and solving comparison problems. Use the formula table below to refresh your skills quickly.

Concept	Formula	Notes
Add/subtract fractions	$frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}$	Find a common denominator and combine numerators
Multiply fractions	$\frac{a}{b} \times \frac{c}{d} = \frac{ac}{bd}$	Multiply across numerators and denominators
Divide fractions	$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} = \frac{ad}{bc}$	Invert the second fraction and multiply
Fraction-to-decimal conversion	$\frac{1}{2} = 0.5,\quad \frac{3}{4} = 0.75,\quad \frac{2}{5} = 0.4$	Convert common fractions into decimals
Ratios and proportions	$\frac{a}{b} = \frac{c}{d} \Rightarrow ad = bc$	Cross-multiplication shows two ratios are equivalent
Part-whole relationship	$\text{Part} = \frac{\%}{100} \times \text{Whole}$	Use the percent to find a portion of a whole
Percent change	$\text{Percent Change} = \frac{\text{New} - \text{Old}}{\text{Old}} \times 100\%$	Measures increase or decrease as a percentage
Simplifying fractions	$\quad \frac{a}{b} = \frac{a \div \text{GCF}(a,b)}{b \div\text{GCF}(a,b)}$
Mixed numbers ↔ Improper fractions	$\text{Mixed number to improper fraction:} \quad a \frac{b}{c} = \frac{ac + b}{c}$
Percent change formula	$\text{Percent Change} = \frac{\text{New} - \text{Original}}{\text{Original}} \times 100\%$

Arithmetic reasoning & word problems

These problems test your ability to apply math in real-world scenarios. Use the key ASVAB formulas in the table to break down and solve complex word problems more efficiently.

Concept	Formula	Meaning
Distance, rate, time	$d = r \times t$	d: distance, r: rate (speed), t: time
Simple interest	$I = Prt$	I: interest, P: principal (starting amount), r: rate (annual interest rate), t: time (years)
Compound interest	$A = P \left(1 + \frac{r}{n}\right)^{nt}$	A: final amount, P: principal, r: annual rate, n: compounding periods per year, t: years
Work together	$\frac{1}{T} = \frac{1}{A} + \frac{1}{B}\quad \text{where } T = \text{total time working together}$	T: total time working together, A: time for person A alone, B: time for person B alone
Mixture value	$\text{Total Value} = (\text{Quantity}_1 \times \text{Value}_1) + (\text{Quantity}_2 \times \text{Value}_2)$	$\text{Quantity}_1$ , $\text{Quantity}_2$ : amounts of each item; $\text{Value}_1$ , $\text{Value}_2$ : cost per unit
Age problems	$\text{Present Age} + \text{Years Passed} = \text{Future Age}$	Simple relationship between present, past, and future age

Algebra essentials

Algebra involves working with variables, expressions, and equations. Refer to the formula table below for quick access to foundational rules and techniques.

Concept	Formula	Meaning
Distributive property	$a(b + c) = ab + ac$
Slope and line equations	$y - y_1 = m(x - x_1)$	Line through point $x_1, y_1$ with slope m
	$m = \frac{y_2 - y_1}{x_2 - x_1}$	m: slope between two points $x_1, y_1$ and $x_2, y_2$
	$y = mx + b$	A slope-intercept form where m is the slope and b is the y-intercept
Quadratics & factoring	$ax^2 + bx + c = 0$	Standard quadratic form
	$(x + a)(x + b) = x^2 + (a + b)x + ab$	FOIL method (First, Outer, Inner, Last) for factoring quadratics
	$a^2 - b^2 = (a + b)(a - b)$	Special product identity: difference of squares
Quadratic formula	$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$	Solves any quadratic equation
Completing the square	$x^2 + bx = \left(x + \frac{b}{2}\right)^2 - \left(\frac{b}{2}\right)^2$	Rewriting quadratic expressions to factor easily
Absolute value equations	$\|x\| = a \Rightarrow x = a \text{ or } x = -a$
Inequality rule	$\text{If } a < b \text{ and you multiply both sides by } -1, \text{ then: } -a > -b$	Flip the inequality sign when multiplying/dividing by a negative number
Exponent rules	$a^m \cdot a^n = a^{m+n}$	Add exponents when multiplying the same base
	$(a^m)^n = a^{mn}$	Multiply exponents when raising a power to another power
	$a^{-n} = \frac{1}{a^n}$	A negative exponent means reciprocal
	$\sqrt{a^2} = \|a\|$
Scientific notation	$a \times 10^n$	Used to express large/small numbers in powers of 10, $1\le a<10$ , n is an integer

Systems of equations

Systems of equations involve finding values that satisfy multiple equations at once.

Elimination: Add or subtract to eliminate one variable.
Substitution: Solve one equation for a variable, and plug it into the other.

Geometry & measurement

Geometry covers shapes, sizes, angles, and measurement concepts. Use the summary table to recall essential formulas for area, perimeter, volume, and more.

Shape	Perimeter / Area	Volume	Surface Area	Meaning
Rectangle	$P = 2(l + w)$ $A = lw$			l: length, w: width
Triangle	$P = a + b + c$ $A = \frac{1}{2} \times b \times h$			a,b,c: sides, b: base, h: height
Circle	$C = \pi d = 2 \pi r$ $A = \pi r^2$			d: diameter, r: radius
Trapezoid	$P = a + b + c + d$ $A = \frac{1}{2} (b_1 + b_2) h$			a,b,c,d: sides; $b_1, b_2$ : parallel sides, h: height
Cube		$V = s^3$	$A = 6 s^2$	s: side length
Rectangular prism (cuboid)		$V = l \times w \times h$	$A = 2(lw + lh + wh)$	l, w, h: length, width, height
Cylinder		$V = \pi r^2 h$	$SA = 2 \pi r^2 + 2 \pi r h$	r: radius, h: height
Cone		$V = \frac{1}{3} \pi r^2 h$	$SA = \pi r^2 + \pi r l$	r: radius, h: height, l: slant height
Sphere		$V = \frac{4}{3} \pi r^3$	$SA = 4 \pi r^2$	r: radius

Other important ASVAB math formulas for geometry areas:

Distance between 2D points:
$\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$
Distance between 3D points:
$\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2}$
Sum of angles in triangle: Sum of
$\text{Sum of angles} = 180^\circ$
Volume of prism (general):
$\text{Base Area} \times \text{Height}$

Exponents, scientific notation & factorials

These topics help simplify large or small numbers and repeated multiplication. Check the table for key rules and shortcuts to handle them quickly and accurately.

Concept	Formula	Meaning / Explanation
Powers rules	$x^a \times x^b = x^{a+b}$	Powers with the same base have to add exponents
	$\left(x^a\right)^b = x^{ab}$	The power of a power has to multiply exponents
	$x^0 = 1$	Zero power
Negative exponent	$x^{-n} = \frac{1}{x^n}$	Reciprocal
Scientific notation	$a \times 10^n$	1 ≤ a <10
Factorial	$n! = n \times (n-1) \times (n-2) \times \dots \times 2 \times 1$	A way to express very large or very small numbers compactly
Exponentials with roots	$x^{\frac{m}{n}} = \sqrt[n]{x^m} = \left(\sqrt[n]{x}\right)^m$	Fractional exponents express roots and powers
Logarithm relations	$\log_b(xy) = \log_b x + \log_b y$ $\log_b \left(\frac{x}{y}\right) = \log_b x - \log_b y$ $\log_b \left(x^a\right) = a \log_b x$	Logarithm properties that convert multiplication, division, and exponents into sums, differences, and products respectively

Ratios & proportions

Ratios and proportions are used to compare quantities and solve scaling problems. Use the formulas in the table to solve them confidently and correctly.

Concept	Formula	Notes
Ratio	$\frac{a}{b}$ or a : b	Comparison between two quantities
Proportion	$\frac{a}{b} = \frac{c}{d} \Rightarrow ad = bc$	Cross multiplication
Part-to-whole ratio	$\frac{\text{Part}}{\text{Total}}$	Fraction of total
Scale ratio	$\frac{\text{Model}}{\text{Real}}$ or vice versa	Used in maps, blueprints
Similar figures (length)	$\frac{L_1}{L_2} = \frac{W_1}{W_2}$	Length/width scaling
Similar figures (area)	$\frac{A_1}{A_2} = \left( \frac{L_1}{L_2} \right)^2$	Area scales with the square of length ratio
Similar figures (volume)	$\frac{V_1}{V_2} = \left( \frac{L_1}{L_2} \right)^3$	Volume scales with the cube of length ratio
Unit rate (speed)	$\text{Speed} = \frac{\text{Distance}}{\text{Time}}$	Common unit rate
Unit rate (price)	$\text{Unit Price} = \frac{\text{Total Price}}{\text{Quantity}}$	Cost per unit

Statistics & probability

This section deals with data interpretation and chance. Refer to the table for important formulas on mean, median, mode, range, and basic probability calculations.

Concept	Formula	Meaning
Mean (average)	$\text{Mean} = \frac{\text{Sum of terms}}{\text{Number of terms}}$	Average value
Median	Middle number in sorted list	Middle value
Mode	Most frequent number	Most common value
Range	$\text{Range} = \text{Max} - \text{Min}$	Difference between max & min
Probability	$P(E) = \frac{\text{Favorable outcomes}}{\text{Total outcomes}}$	Likelihood of event E
Addition rule (for mutually exclusive events)	$P(A \text{ or } B) = P(A) + P(B)$	The probability of either event A or B
Multiplication rule (for independent events)	$P(A \text{ and } B) = P(A) \times P(B)$	The probability of both A and B occurring

Final thoughts

Mastering the ASVAB math formulas is essential for boosting your confidence and scoring high on the test. This formula guide is designed to give you quick access to the most important equations across topics like algebra, geometry, ratios, and probability. By understanding these key formulas and applying them through regular practice, you’ll be able to tackle a wide range of math problems more efficiently. Remember, success on the ASVAB isn’t just about memorization; it’s about knowing when and how to use the right formula. Stay focused, keep practicing, and let this guide support your journey to a better score.