GRE Math Formula Sheet

Every core GRE Quant formula, grouped by topic and searchable, with a free downloadable PDF. The GRE gives you no formula sheet on test day, so these are the ones to know cold. Filter, search, or grab the PDF and drill.

marks the highest-yield formulas, know these cold.

grezıGRE Math Formula Sheet

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Geometry at a glance

a² + b² = c²

45-45-90

30-60-90

A = πr²
C = 2πr

slope = rise / run

V = l · w · h

Percents & Ratios

Percent change
(new − old) / old × 100
Percent of a number
part = (percent / 100) × whole
x is what percent of y
(x / y) × 100
Increase by p%
multiply by (1 + p/100)
Decrease by p%
multiply by (1 − p/100)
Successive % changes
multiply the factors; they do NOT add
Simple interest
I = P × r × t
Compound interest
A = P(1 + r/n)^(nt)
Ratio to fraction
in a : b, part a = a / (a + b) of the whole

Averages & Statistics

Average (mean)
sum of terms / number of terms
Sum from average
sum = average × number of terms
Weighted average
Σ(value × weight) / Σ(weights)
Average speed
total distance / total time
Median
middle value of an ordered set (mean of the two middle if even count)
Range
greatest value − least value
Interquartile range
IQR = Q₃ − Q₁
Standard deviation
spread from the mean; +constant to all is unchanged, ×constant scales it
Normal distribution
≈68% within 1 SD, ≈95% within 2, ≈99.7% within 3

Number Properties & Sequences

Even / odd (add)
even ± even = even; odd ± odd = even; even ± odd = odd
Even / odd (multiply)
even × anything = even; odd × odd = odd
Number of factors
for p^a · q^b · …, count = (a + 1)(b + 1)…
GCF and LCM
GCF × LCM = product of the two numbers
Sum of consecutive integers
count × (first + last) / 2
Arithmetic sequence (nth term)
aₙ = a₁ + (n − 1)d
Arithmetic sequence (sum)
n × (a₁ + aₙ) / 2

Arithmetic & Rates

Distance
distance = rate × time
Work rate
rate = 1 / time
Combined work rate
1/t = 1/t₁ + 1/t₂

Exponents & Roots

Multiply same base
xᵃ · xᵇ = xᵃ⁺ᵇ
Divide same base
xᵃ / xᵇ = xᵃ⁻ᵇ
Power of a power
(xᵃ)ᵇ = xᵃᵇ
Power of a product
(xy)ᵃ = xᵃ · yᵃ
Zero exponent
x⁰ = 1 (x ≠ 0)
Negative exponent
x⁻ᵃ = 1 / xᵃ
Fractional exponent
x^(1/n) = ⁿ√x
Root of a product
√(ab) = √a · √b

Algebra

Quadratic formula
x = (−b ± √(b² − 4ac)) / 2a
Difference of squares
a² − b² = (a + b)(a − b)
Square of a sum
(a + b)² = a² + 2ab + b²
Square of a difference
(a − b)² = a² − 2ab + b²
Inequalities
flip the sign when you × or ÷ by a negative
Overlapping sets
Total = A + B − both + neither

Coordinate Geometry

Slope
m = (y₂ − y₁) / (x₂ − x₁)
Slope-intercept form
y = mx + b
Parallel / perpendicular
parallel: equal slopes; perpendicular: slopes multiply to −1
Distance between points
√((x₂ − x₁)² + (y₂ − y₁)²)
Midpoint
((x₁ + x₂)/2, (y₁ + y₂)/2)

Angles & Triangles

Angles on a line
sum to 180°
Angles around a point
sum to 360°
Triangle angle sum
the three angles sum to 180°
Triangle area
½ × base × height
Equilateral triangle
area = (s²√3)/4; height = (s√3)/2
Pythagorean theorem
a² + b² = c²
Pythagorean triples
3-4-5, 5-12-13, 8-15-17, 7-24-25 (× any factor)
45-45-90 triangle
sides in ratio x : x : x√2
30-60-90 triangle
sides in ratio x : x√3 : 2x
Similar triangles
sides proportional; area ratio = (side ratio)²
Triangle side rule
|a − b| < third side < a + b

Circles

Area
πr²
Circumference
2πr = πd
Arc length
(central angle / 360) × 2πr
Sector area
(central angle / 360) × πr²

Polygons & Solids

Rectangle
area = l × w; perimeter = 2(l + w)
Square
area = s²; diagonal = s√2
Parallelogram area
base × height
Trapezoid area
½ × (b₁ + b₂) × height
Interior angles of n-gon
sum = (n − 2) × 180°
Rectangular box volume
l × w × h
Rectangular box surface area
2(lw + lh + wh)
Box diagonal
√(l² + w² + h²)
Cube
volume = s³; diagonal = s√3
Cylinder volume
πr²h
Cylinder surface area
2πr² + 2πrh

Probability & Counting

Probability
favorable outcomes / total outcomes
Not A
P(not A) = 1 − P(A)
At least one
P(at least one) = 1 − P(none)
A or B
P(A) + P(B) − P(A and B)
Independent A and B
P(A) × P(B)
Fundamental counting
n₁ × n₂ × n₃ × …
Permutations (order matters)
nPr = n! / (n − r)!
Combinations (order does not)
nCr = n! / (r!(n − r)!)

Common traps that cost points

Successive percent changes multiply, they never add: +20% then −20% is −4%, not 0.
Flip the inequality sign whenever you multiply or divide by a negative.
An unanswered question counts as wrong, so guess before the clock runs out.
Adding the same value to every number leaves the standard deviation unchanged.
Read carefully: "percent of" and "percent greater than" are not the same thing.

The GRE gives you no formula sheet on test day. Download the PDF, print it, and drill these until they are automatic.

Frequently asked questions

Does the GRE give you a formula sheet?

No. Unlike some tests, the GRE provides no formula sheet or reference sheet on the Quantitative section. You are expected to know the core arithmetic, algebra, and geometry formulas from memory, which is exactly why a cheat sheet like this is worth drilling before test day.

What math formulas do I need for the GRE?

The GRE tests arithmetic and number properties, percents and ratios, exponents and roots, basic algebra, coordinate and plane geometry, solids, statistics (mean, median, range, standard deviation), and probability and counting. All of them are on this sheet, grouped by topic.

Is there a GRE math formulas PDF I can download?

Yes. Use the Download PDF button above to save the full formula sheet as a clean, printable PDF for offline review.

How much math do I really need to memorize?

Less than most people fear. GRE Quant rewards reasoning and number sense more than obscure formulas. Master this one-page set, then spend your time on strategy and practice rather than memorizing rare identities.

Knowing the formula is step one

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