Quick answer: Below is a compact, high-impact GRE Quant formula list plus practical strategies for memorizing and using these formulas during study and on test day. Learn the formulas by category, practice with targeted problems, and focus on deriving or checking formulas when possible rather than rote memorization. With steady practice you can reduce calculation time and avoid common formula errors.
Why these formulas matter for the GRE Quantitative Reasoning section
The GRE Quant section tests reasoning with arithmetic, algebra, geometry, basic statistics, and probability. ETS does not provide a comprehensive formula sheet during the test. That means you need quick access to the most frequently used formulas in your head. Knowing these formulas well helps you:
- Set up problems correctly so you solve fewer wrong paths.
- Estimate and check answer choices faster.
- Use algebraic manipulation to simplify work and avoid heavy arithmetic.
Common challenges students face with formulas
- Too many formulas at once: Trying to memorize rare formulas wastes time. Prioritize high-frequency ones.
- Memory without understanding: Memorizing syntactically without understanding derivation makes recall unreliable under pressure.
- Application errors: Confusing similar formulas, such as circumference vs. area, or mean vs. median usage.
- Arithmetic mistakes: Correct formula use can still fail because of careless arithmetic or misreading the question.
Quick, categorized GRE quant formula list
The table below groups the formulas you should know. Learn the ones in bold first, then add the rest. After the table you’ll find short notes and example uses.
| Category | Formula | When to use |
|---|---|---|
| Arithmetic & Ratios | Percent change: (new − original) / original × 100% | Percent increase/decrease, comparing values |
| Arithmetic & Ratios | Ratio scaling: If A:B = m:n then A = km, B = kn | Mixtures, proportional allocation |
| Algebra | Quadratic formula: x = (−b ± sqrt(b² − 4ac)) / (2a) | Solving ax² + bx + c = 0 when factoring not obvious |
| Algebra | Difference of squares: a² − b² = (a − b)(a + b) | Quick factoring, simplifying expressions |
| Algebra | Sum/difference of cubes: a³ ± b³ = (a ± b)(a² ∓ ab + b²) | Factoring cubic expressions |
| Exponents & Logs | Product rule: a^m · a^n = a^(m+n) | Combining powers |
| Exponents & Logs | Power rule: (a^m)^n = a^(mn) | Nested exponents |
| Exponents & Logs | Log rule: log_b(xy) = log_b x + log_b y; log_b(x^k) = k log_b x | Simplifying log expressions |
| Number theory | GCD/LCM basics and prime factorization | Divisibility, least common multiple problems |
| Geometry — lines & coordinates | Slope: m = (y2 − y1) / (x2 − x1) | Line problems, parallel/perpendicular checks |
| Geometry — lines & coordinates | Distance: sqrt[(x2 − x1)² + (y2 − y1)²] | Distance between points in coordinate plane |
| Geometry — lines & coordinates | Midpoint: ((x1 + x2)/2, (y1 + y2)/2) | Segment bisector, coordinate geometry |
| Geometry — triangles | Pythagorean theorem: a² + b² = c² | Right triangle side lengths |
| Geometry — triangles | Area: (1/2)·base·height | Triangle area problems |
| Geometry — triangles | 30-60-90: sides in ratio 1 : sqrt(3) : 2 | Fast triangle side inference |
| Geometry — triangles | 45-45-90: sides in ratio 1 : 1 : sqrt(2) | Isosceles right triangle quick values |
| Geometry — circles | Circumference: 2πr or πd | Perimeter of circle |
| Geometry — circles | Area: πr² | Area and sector problems |
| Geometry — polygons | Area rectangle = lw, area parallelogram = base·height, area trapezoid = (1/2)(b1 + b2)h | Basic polygon areas |
| Geometry — 3D | Volume prism = base area · height; volume cylinder = πr²h | 3D volume problems |
| Statistics | Mean: (sum of values) / n | Average problems |
| Statistics | Median: middle value when data sorted | Robust central tendency |
| Statistics | Range = max − min; Mode = most frequent value | Descriptive stats |
| Probability & Counting | Probability = favorable outcomes / total outcomes | Basic probability |
| Probability & Counting | Permutation P(n, k) = n! / (n − k)!; Combination C(n, k) = n! / [k!(n − k)!] | Ordered vs unordered selection |
| Misc useful | Sum of first n integers = n(n + 1)/2; sum of arithmetic series | Sequence problems |
Which formulas to prioritize
- First priority: Percent change, ratio/scaling logic, Pythagorean theorem, area/volume basics, mean/median, basic probability, slope/distance, basic exponent rules.
- Second priority: Quadratic formula, combinations/permutations, circle formulas, coordinate midpoint/distance formulas, special right triangle ratios.
- Lower priority: Sum/difference of cubes, rare trig identities (GRE rarely tests advanced trig), obscure series formulas. Learn these only if you encounter them frequently in practice.
Step-by-step strategy for learning and using the formula list
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Create a compact reference sheet.
Write one page with the prioritized formulas grouped by category. Use this page when you study and shrink it to a pocket-sized version for quick review.
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Learn by derivation and example.
For each formula, work through one simple derivation or understand why it holds. For example, derive area of triangle as half base times height or derive quadratic formula once. Understanding reduces memory load.
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Use spaced repetition flashcards.
Create flashcards with the formula on one side and a short solved example on the other. Use an SRS app or a daily review schedule to reinforce recall.
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Practice targeted question sets.
After you learn a formula, solve a cluster of 10 to 15 focused problems that require that formula. This trains retrieval and helps you spot common misuses.
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Practice deriving under time pressure.
On the GRE you may not need to memorize every constant. Practice quickly reconstructing formulas from first principles when possible. For example, if you forget area of trapezoid, average the bases and multiply by height.
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Learn quick checks and estimation.
Always estimate an answer to check plausibility. Use rounding to verify magnitudes before finalizing your choice.
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Simulate test conditions.
Do full sections under timed conditions with only the on-screen calculator ETS provides. This builds speed and reduces formula-fumble anxiety.
Common mistakes to avoid
- Mixing up area and perimeter. Pause and ask whether the question asks for area (square units) or perimeter (linear units).
- Applying percent change formulas incorrectly when going from A to B versus B to A. Remember the denominator matters.
- Using combination when permutation is required or vice versa. Ask whether order matters.
- Forgetting to check domain restrictions like negative square roots, zero denominators, or integer constraints.
- Relying on complex formulas when a simpler ratio or elimination approach will solve the problem faster.
Practice and implementation: worked examples
Example 1 — Percent change and fast checking
Question: A number increases by 20% and then decreases by 20%. What is the net percent change?
- Start with 100 for easy arithmetic. After a 20% increase: 100 × 1.20 = 120.
- Then a 20% decrease of 120: 120 × 0.80 = 96.
- Net change: 96 − 100 = −4, that is a 4% decrease.
Key idea: Percent changes are multiplicative, not additive. Learning that keeps you from the common error that +20% then −20% is zero change.
Example 2 — Geometry with Pythagorean and special triangles
Question: In a right triangle the hypotenuse is 10 and one leg is 5. What are the other leg’s length and the area?
- Use Pythagorean theorem: a² + b² = c². Let a = 5, c = 10. Then b² = 10² − 5² = 100 − 25 = 75. So b = sqrt(75) = 5·sqrt(3).
- Area = (1/2)·(leg1)·(leg2) = 0.5 × 5 × 5·sqrt(3) = 12.5·sqrt(3).
Note: Recognizing 5, 5·sqrt(3), 10 fits a scaled 30-60-90 triangle helps you double-check.
Example 3 — Probability and combinations
Question: From 8 students, how many 3-student committees can you form?
- Order does not matter, so use combinations: C(8,3) = 8! / (3!·5!) = (8·7·6) / (3·2·1) = 56.
Example 4 — Quadratic formula and quick factoring check
Question: Solve x² − 5x + 6 = 0.
- Try factoring first: factors of 6 that add to 5 are 2 and 3 so (x − 2)(x − 3) = 0. Solutions x = 2 or 3.
- If factoring not obvious, quadratic formula: x = [5 ± sqrt(25 − 24)] / 2 = [5 ± 1] / 2 = 3 or 2.
Tip: Always try simple factoring before the quadratic formula to save time.
How to practice formulas efficiently
- Use short, focused daily drills: 15–30 minutes on one formula family.
- Alternate formats: include numeric-answer, multiple-choice and data-interpretation problems using the same formulas.
- Keep a mistake log. For each error note whether it was a formula recall issue, setup error, or arithmetic slip.
- Time yourself on clusters of problems to build fluency with formula application under pressure.
- Periodically create mini-tests where you cannot access your reference; this simulates test recall demands.
Frequently asked questions
Q: Does ETS give a formula sheet on the GRE?
A: ETS does not provide a complete formula sheet for every topic. You will have an on-screen basic calculator during the Quant section, but you should plan to remember the common formulas listed above. Practice reconstructing formulas from fundamentals if you forget one.
Q: How many formulas do I need to memorize?
A: Focus on a core set of 20 to 30 high-frequency formulas listed in the prioritized categories. Many problems require reasoning and algebra more than obscure formulas. Quality of understanding matters more than quantity.
Q: Is it better to memorize or derive formulas on the fly?
A: Use both approaches. Memorize the most-used formulas for speed. For less common formulas, practice quick derivations so you can reconstruct them reliably during the test.
Q: Should I use the on-screen calculator for all calculations?
A: Use the calculator selectively. It helps with arithmetic and checking, but excessive reliance slows you down. Practice doing some calculations mentally or with scratchwork to improve speed.
Q: Any tips for international students who learned different notation?
A: Translate notation into terms you are comfortable with. For example, understand that “mean” equals average, “s.d.” or “standard deviation” is spread, and decimal commas may be formatted differently in source materials. Practice ETS-style questions to get used to their phrasing.
Q: Where should I get practice problems that reinforce these formulas?
A: Use official ETS practice sets and reputable GRE prep materials. When you work practice problems, tag them by the formulas used so you can target weak areas efficiently.
Final thoughts
Memorizing a compact GRE quant formula list is necessary but not sufficient. The highest-return approach is a balanced one: memorize the most common formulas, understand derivations for quick reconstruction, and repeatedly apply formulas in timed practice. Keep a focused one-page formula sheet, run daily drills on priority formulas, and practice estimating answers to catch careless errors. Over time this combination of memory, comprehension, and timed practice will reduce errors and speed up your problem solving on test day.
