GRE Math Formulas Cheat Sheet 2026: Every Quant Formula You Need
Every GRE Quant formula in one place — arithmetic, percentages, number properties, algebra, geometry, data analysis and probability — with worked notes and the traps that cost points. Unlike the GMAT, the GRE tests geometry and gives you a calculator.
▶ Free College Predictor & study-abroad toolsWhat GRE Quant tests in 2026
On the shortened GRE General Test, Quantitative Reasoning is two sections, 27 questions total, about 47 minutes, mixing Quantitative Comparison, multiple choice and Numeric Entry. Two things make it different from the GMAT: the GRE gives you an on-screen calculator, and it does test geometry. Content spans four areas — arithmetic, algebra, geometry and data analysis — and each Quant section is scored on the 130–170 scale.
Arithmetic, fractions and percentages
Percentages and ratios dominate GRE arithmetic. The calculator does the multiplication; you supply the right relationship.
| Concept | Formula |
|---|---|
| x percent of y | (x / 100) × y |
| What percent a is of b | (a / b) × 100 |
| Percent change | (New − Old) / Old × 100 |
| Successive % change (p then q) | Net = (1 + p/100)(1 + q/100) − 1 |
| Increase then decrease by same x% | Net change = −x² / 100 (a net loss) |
| Part of a total from ratio a : b | Part = Total × a / (a + b) |
Averages, ratios and proportions
| Concept | Formula |
|---|---|
| Average (arithmetic mean) | Sum ÷ Count |
| Sum from average | Average × Count |
| Weighted average | Σ(weight × value) ÷ Σ(weights) |
| Proportion (cross-multiply) | a/b = c/d ⟶ a·d = b·c |
Number properties
Even/odd behaviour, factors, multiples and divisibility appear constantly in Quantitative Comparison questions.
- Even ± Even = Even, Odd ± Odd = Even, Even ± Odd = Odd
- Even × anything = Even; Odd × Odd = Odd
- Number of factors of N = p^a · q^b · r^c is (a+1)(b+1)(c+1)
- The product of any n consecutive integers is divisible by n!
- For two numbers, LCM × HCF = product of the two numbers
- Divisibility: by 3 or 9 if the digit sum is; by 4 if last two digits are; by 8 if last three are; by 6 if divisible by 2 and 3
Algebra: identities, quadratics and exponents
| Identity / rule | Formula |
|---|---|
| Square of a sum / difference | (a ± b)² = a² ± 2ab + b² |
| Difference of squares | a² − b² = (a + b)(a − b) |
| Sum / difference of cubes | a³ ± b³ = (a ± b)(a² ∓ ab + b²) |
| Quadratic roots | x = [ −b ± √(b² − 4ac) ] / (2a) |
| Sum & product of roots | Sum = −b/a , Product = c/a |
| Exponent rules | aᵐ·aⁿ = aᵐ⁺ⁿ ; aᵐ/aⁿ = aᵐ⁻ⁿ ; (aᵐ)ⁿ = aᵐⁿ ; a⁻ⁿ = 1/aⁿ ; a⁰ = 1 |
| Roots | √(ab) = √a · √b ; ⁿ√a = a^(1/n) |
Word problems: rate, work, interest, mixtures
| Type | Formula |
|---|---|
| Distance | Distance = Speed × Time |
| Average speed | Total distance ÷ Total time (NOT the average of the speeds) |
| Equal distance at speeds x, y | Average speed = 2xy / (x + y) |
| Combined work | Time together = ab / (a + b) |
| Simple interest | SI = P · R · T / 100 |
| Compound interest (amount) | A = P (1 + R/100)ᵀ ; CI = A − P |
| Profit / loss percent | (SP − CP) / CP × 100 |
Geometry (the GRE tests this — the GMAT no longer does)
Geometry is a big GRE differentiator. Memorise these; figures are not always drawn to scale, so reason from the formulas, not the picture.
| Shape / concept | Formula |
|---|---|
| Triangle area | ½ × base × height |
| Pythagoras | a² + b² = c² (right triangles) |
| Special right triangles | 45-45-90 → 1 : 1 : √2 ; 30-60-90 → 1 : √3 : 2 |
| Sum of interior angles of an n-gon | (n − 2) × 180° |
| Rectangle | Area = l × w ; Perimeter = 2(l + w) |
| Square | Area = s² ; Perimeter = 4s |
| Circle | Area = π r² ; Circumference = 2π r |
| Arc length / sector area | Arc = (θ/360) · 2π r ; Sector = (θ/360) · π r² |
| Box (rectangular solid) | Volume = l × w × h ; Surface = 2(lw + lh + wh) |
| Cylinder | Volume = π r² h ; Surface = 2π r² + 2π r h |
| Coordinate geometry | Distance = √[(x₂−x₁)² + (y₂−y₁)²] ; Slope = (y₂−y₁)/(x₂−x₁) ; Line: y = mx + b |
Data analysis and statistics
GRE Data Analysis goes a step beyond the GMAT: expect quartiles, percentiles and the normal distribution alongside the basics.
| Measure | Formula / rule |
|---|---|
| Mean / Median / Mode | Mean = Sum ÷ n ; Median = middle value ; Mode = most frequent |
| Range | Maximum − Minimum |
| Quartiles & IQR | Q1 = 25th percentile, Q3 = 75th ; Interquartile range = Q3 − Q1 |
| Percentile | % of values at or below a given value |
| Standard deviation | Measures spread; SD = 0 only when all values are equal |
| Normal distribution (68-95-99.7) | ≈68% within 1 SD, ≈95% within 2 SD, ≈99.7% within 3 SD of the mean |
Counting, probability and sequences
| Concept | Formula |
|---|---|
| Permutations (order matters) | nPr = n! / (n − r)! |
| Combinations (order doesn't) | nCr = n! / [ r! (n − r)! ] |
| Probability of an event | Favourable outcomes ÷ Total outcomes |
| P(A or B) | P(A) + P(B) − P(A and B) |
| P(not A) | 1 − P(A) |
| Independent events | P(A and B) = P(A) × P(B) |
| Arithmetic progression | aₙ = a + (n−1)d ; Sum = n/2 · (First + Last) |
| Sum of first n integers | n(n + 1) / 2 |
The formula traps that cost the most GRE points
- Quantitative Comparison + variables. When a quantity has variables, test negatives, zero and fractions — not just positive integers — before choosing.
- Averaging speeds. Average speed is total distance ÷ total time, never (x + y)/2 unless the times are equal.
- Figures not to scale. GRE geometry figures can mislead; solve from the given numbers and formulas.
- Successive percentages. A 20% rise then a 20% fall is a net 4% loss, not break-even.
- Integers from a to b inclusive is b − a + 1, not b − a.
Lock it in — free GRE practice
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Frequently asked questions
- Does the GRE give you a calculator?
- Yes. The GRE provides an on-screen four-function calculator (with a square-root key) for the Quantitative Reasoning section, so the formulas matter more for setting up the problem than for the arithmetic itself. The GMAT, by contrast, gives no calculator on its Quant section.
- Does the GRE test geometry?
- Yes. Unlike the GMAT Focus Edition, which removed geometry from its Quant section, the GRE still tests geometry — triangles, circles, polygons, coordinate geometry and 3-D solids — so keep those formulas sharp.
- Is there a formula sheet provided in the GRE?
- No. The GRE does not provide a formula sheet, so every formula on this page must be memorised. The on-screen calculator helps with computation but will not give you the relationships.
- How is GRE Quant scored?
- Each measure — Verbal Reasoning and Quantitative Reasoning — is scored from 130 to 170 in 1-point increments. Quant is two sections totalling 27 questions in about 47 minutes on the shortened GRE.
- How many formulas do I need for the GRE?
- The core set on this page covers the large majority of GRE Quant: percentages and ratios, number properties, the main algebra identities, the full geometry list, and the data-analysis rules (quartiles, percentiles, normal distribution). Master these and practise under timing.