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.
Percents & Ratios
- Percent change(new − old) / old × 100
- Percent of a numberpart = (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)
- Ratio to fractionin a : b, part a = a / (a + b) of the whole
Averages & Statistics
- Average (mean)sum of terms / number of terms
- Sum from averagesum = average × number of terms
- Weighted averageΣ(value × weight) / Σ(weights)
- Average speedtotal distance / total time
- Medianmiddle value of an ordered set (mean of the two middle if even count)
- Rangegreatest value − least value
- Standard deviationa measure of spread from the mean (GRE rarely asks you to compute it)
Arithmetic & Rates
- Distancedistance = rate × time
- Work raterate = 1 / time
- Combined work rate1/t = 1/t₁ + 1/t₂
- Even / odd (add)even ± even = even; odd ± odd = even; even ± odd = odd
- Even / odd (multiply)even × anything = even; odd × odd = odd
- Sum of consecutive integerscount × (first + last) / 2
Exponents & Roots
- Multiply same basexᵃ · xᵇ = xᵃ⁺ᵇ
- Divide same basexᵃ / xᵇ = xᵃ⁻ᵇ
- Power of a power(xᵃ)ᵇ = xᵃᵇ
- Power of a product(xy)ᵃ = xᵃ · yᵃ
- Zero exponentx⁰ = 1 (x ≠ 0)
- Negative exponentx⁻ᵃ = 1 / xᵃ
- Fractional exponentx^(1/n) = ⁿ√x
- Root of a product√(ab) = √a · √b
Algebra
- Quadratic formulax = (−b ± √(b² − 4ac)) / 2a
- Difference of squaresa² − 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
Coordinate Geometry
- Slopem = (y₂ − y₁) / (x₂ − x₁)
- Slope-intercept formy = mx + b
- Distance between points√((x₂ − x₁)² + (y₂ − y₁)²)
- Midpoint((x₁ + x₂)/2, (y₁ + y₂)/2)
Angles & Triangles
- Angles on a linesum to 180°
- Angles around a pointsum to 360°
- Triangle angle sumthe three angles sum to 180°
- Triangle area½ × base × height
- Pythagorean theorema² + b² = c²
- 45-45-90 trianglesides in ratio x : x : x√2
- 30-60-90 trianglesides in ratio x : x√3 : 2x
- Triangle side rule|a − b| < third side < a + b
Circles
- Areaπr²
- Circumference2πr = πd
- Arc length(central angle / 360) × 2πr
- Sector area(central angle / 360) × πr²
Polygons & Solids
- Rectanglearea = l × w; perimeter = 2(l + w)
- Squarearea = s²
- Parallelogram areabase × height
- Trapezoid area½ × (b₁ + b₂) × height
- Interior angles of n-gon(n − 2) × 180°
- Rectangular box volumel × w × h
- Rectangular box surface area2(lw + lh + wh)
- Cube volumes³
- Cylinder volumeπr²h
- Cylinder surface area2πr² + 2πrh
Probability & Counting
- Probabilityfavorable outcomes / total outcomes
- Not AP(not A) = 1 − P(A)
- A or BP(A) + P(B) − P(A and B)
- Independent A and BP(A) × P(B)
- Fundamental countingn₁ × n₂ × n₃ × …
- Permutations (order matters)nPr = n! / (n − r)!
- Combinations (order does not)nCr = n! / (r!(n − r)!)
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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