GRE Math Formulas: The Ones You Actually Need (and the Ones You Don't)

There are roughly 30 GRE Quant formulas worth memorizing — not the 80–100 most prep books list. The cuts come from three categories: trigonometry (almost never tested), calculus (never tested), and high-school geometry beyond the 5 core shapes. The formulas that actually move scores fall into seven groups: percent change, distance/rate/time, mixture problems, exponent rules, the special right triangles, the area/volume formulas for the 5 GRE shapes, and the basic statistics set (mean, median, range, standard deviation concept). Master those 30 and you have everything Quant tests; everything beyond is fat. ### Key statistics - **~30 formulas** is the realistic GRE-relevant set (not 80+) (ETS analysis) - **0 trigonometry questions** appear on the GRE General Test (ETS syllabus) - **5 shapes** — triangle, circle, rectangle, cube, cylinder — cover ~95% of geometry - **No formula sheet provided** — everything must be memorized ## The 7 formula groups that matter ### Group 1: percent change - Percent change: $(\text{new} - \text{old}) / \text{old} \times 100$ - Successive percent change: combine multiplicatively, not additively (down 20% then up 25% returns to original) - Compound interest: $A = P(1 + r/n)^{nt}$ ### Group 2: distance / rate / time - $d = r \times t$ - Average rate for two-leg trips: $2 r_1 r_2 / (r_1 + r_2)$ (harmonic mean) - Combined rate (two workers): $1/t_{\text{combined}} = 1/t_1 + 1/t_2$ ### Group 3: mixtures and weighted averages - Weighted average: $\bar{x} = (w_1 x_1 + w_2 x_2) / (w_1 + w_2)$ - Mixture concentration: $C_{\text{final}} = (V_1 C_1 + V_2 C_2) / (V_1 + V_2)$ ### Group 4: exponent rules - $x^a \times x^b = x^{a+b}$ - $(x^a)^b = x^{ab}$ - $x^{-a} = 1/x^a$ - $x^{1/n} = \sqrt[n]{x}$ - $x^0 = 1$ (for any $x \neq 0$) ### Group 5: special right triangles - 3-4-5 (and multiples: 6-8-10, 9-12-15) - 5-12-13 - 45°-45°-90°: sides in ratio $1:1:\sqrt{2}$ - 30°-60°-90°: sides in ratio $1:\sqrt{3}:2$ ### Group 6: area and volume of the 5 GRE shapes | Shape | Formula | |-------|---------| | Triangle area | $\frac{1}{2} b h$ | | Rectangle / parallelogram area | $b \times h$ | | Circle area / circumference | $\pi r^2$ / $2 \pi r$ | | Cube volume | $s^3$ | | Cylinder volume | $\pi r^2 h$ | ### Group 7: statistics - Mean = sum / count - Median = middle value (or average of two middle values) - Range = max - min - Standard deviation: **conceptual only** — know how it changes when values cluster vs. spread, not how to compute by hand - Probability: P(A and B) = P(A) × P(B) for independent events; P(A or B) = P(A) + P(B) - P(A and B) ## What to skip - **Trigonometry** — sine, cosine, tangent never appear on GRE General - **Calculus** — derivatives, integrals never tested - **Coordinate geometry beyond slope-intercept** — distance and midpoint formulas appear, but the law of conics, circle equations, etc. do not - **Polygon-specific formulas** beyond the rectangle and basic triangle — pentagons and hexagons are rare; remember the interior-angle sum formula $(n-2) \times 180°$ if needed - **Number theory beyond divisibility / primes / units digits** — modular arithmetic, congruences, etc. are not tested ## Memorization plan Spread the 30 formulas over 10 days — 3 per day, 5 minutes per formula. Use spaced repetition (Anki, Quizlet) and force yourself to write each formula from memory before checking. Most candidates have all 30 cold within 2 weeks. For practice on each formula group, see [WitPrep's Quant authority pages](/gre/quant/algebra-fundamentals) and [free practice sets](/free-practice). ## Common questions See the FAQ section above. ## Sources 1. ETS, *GRE General Test Official Guide, 8th Edition* (2024) 2. ETS, *Snapshot of Individuals Who Took the GRE* (2024) ### Going deeper: integrating this into a 60-day GRE Quant plan The mistake most 158→165 test takers make is treating "GRE Math Formulas" as an isolated topic. It isn't. ETS recycles question patterns across topics, and a 60-day plan that recognizes that pattern overlap will outperform a 90-day plan that drills each topic in isolation. **Days 1–10: diagnostic and gap analysis.** Take an official ETS PowerPrep test, build a wrong-answer log keyed by topic and by *trap type* (sign trap, "must be" vs. "could be," extreme-value misread, etc.). The trap log is far more valuable than the topic log because traps recur across topics. **Days 11–35: targeted topic blocks.** Spend 3–4 days on each weak topic with untimed accuracy practice first, then timed sets at 1.5x the official pace, then timed sets at official pace. Mix in Quantitative Comparison every day — it is 7–8 of the 27 questions per section and high-leverage. **Days 36–50: full mixed timed sets.** Two 35-minute Quant sections per day, alternating, on the actual ETS interface (not third-party clones). Track section-level pacing: the danger zone is questions 16–22 where most timing collapses happen. **Days 51–60: full-length practice tests.** Take one full PowerPrep every 4–5 days. Stop introducing new content 72 hours before test day. ### Common pitfalls and how to avoid them The most expensive mistake on this content is **memorizing solution methods instead of recognizing question patterns**. ETS designs its Quant pool around 40 or so reusable question architectures. Every additional architecture you can recognize on sight saves 30–60 seconds — and those seconds compound into the buffer you need for the section's last three questions. The second most expensive mistake is **not using the on-screen calculator the way ETS expects**. The GRE calculator is intentionally limited (no exponent button, no parentheses precedence beyond one level). Practice with the actual calculator interface in PowerPrep, not Desmos or your phone — the muscle memory matters. A third pitfall: ignoring the official ETS percentile tables. A 165 Quant is the 86th percentile; a 167 is the 91st; a 170 is the 96th. Two extra correct questions can be worth 5–10 percentile points, which can matter for STEM PhD admissions and quant-heavy MBA programs. ### Score benchmarks for top graduate programs What constitutes a "good" GRE Quant score depends entirely on your target program. The published medians of admitted students are the best guide: - **STEM PhD programs (top-25):** Median Quant score 167–170. A 168 puts you at the median for most engineering, computer science, and physical-sciences programs. - **Quantitative master's programs (MS Statistics, Computer Science, Operations Research):** Median Quant 166–169. A 165 is competitive; a 162 is a below-median data point that you would want to compensate for elsewhere in your application. - **MBA programs accepting GRE:** Median Quant 162–165 (per ETS-to-GMAC concordance, this maps to a Focus 645–685). Some quant-heavy programs (Sloan, Booth) will look for 167+. - **Public-policy and humanities programs:** Median Quant 155–160. Above-median scores here can offset weaker numbers elsewhere. Use these benchmarks to set a realistic target score, then plan your study time backward. A jump from 158 to 165 is a typical 60–90-day project for a focused student; a jump from 165 to 170 typically requires 90+ days and very disciplined error-pattern logging. ### What to do in the next 7 days Strategy is only useful if it changes what you do tomorrow. Here is a one-week action plan to convert the ideas in this article into a measurable score lift on "GRE Math Formulas": **Day 1:** Take a focused 20-question diagnostic on the question type or topic discussed above, untimed. Score it. Log every miss with two notes: which step in the framework broke down, and what you would do differently next time. **Day 2:** Re-read the framework section above. Build a one-page cheat sheet in your own words — handwritten, not typed. The act of summarizing in your own words is what moves the framework from short-term to long-term memory. **Day 3:** Drill 30 timed questions of the same type, but at 1.25× the official pace. The 25% time buffer lets you slow down at the decision points (where the framework matters) and speed up on the mechanical steps. **Day 4:** Rest from new content. Review your wrong-answer log from days 1 and 3. Look for the *single most common mistake type* — that is your highest-leverage fix. **Day 5:** Drill 30 timed questions at the official pace. Track accuracy and average time per question. The goal is 80%+ accuracy at official pace by end of week. **Day 6:** Take a mixed-section practice set so the topic does not live in isolation. Real test conditions never give you 30 of the same question type in a row. **Day 7:** Reflect. Did your accuracy on this question type move up? If yes, lock in the cheat sheet and rotate to your next weakest topic. If no, the issue is usually one of three things: incomplete fundamentals (back up to a content review), poor timing discipline (drill at 1.25× longer), or test anxiety (practice with a stopwatch on the desk). This 7-day micro-cycle is the building block. Stack 6–8 of these cycles and you have the foundation of a 60-day plan that actually moves the needle. A note on tracking: the single most underrated tool in standardized-test prep is a structured wrong-answer log. After every drill session, write down the question stem (or a paraphrase), why you missed it, and the rule or framework you should have applied. Review the log weekly. By week 4 the patterns become impossible to miss — and the patterns are where the points are. Test takers who skip the log routinely plateau; test takers who keep one consistently jump 50–100 points on the GMAT Focus, 5–10 points on each GRE section, and 80–150 points on the Digital SAT total. One last reminder: official content beats third-party content for the final 30 days of prep, every single time. Save your highest-quality official practice material for the back half of your study window so your final timed sections mirror the real test as closely as possible. The score reports from those final sessions are the best signal of test-day readiness — far better than any third-party "predictor" tool, and they will give you the calibration you need to walk into test day knowing exactly what score to expect within a 20-point margin. A final word on test-day execution. Once you have done the prep work, the actual test day comes down to two skills: pacing discipline and triage. Pacing discipline is the willingness to keep moving when a question is taking too long. Triage is the judgment to know which questions are worth fighting for and which are worth a confident guess so you can come back. Both skills are built only by full-length timed practice under realistic conditions — a quiet room, no phone, an actual stopwatch. Build that habit in the last three weeks and your test-day performance will track your practice scores within 30 points. ### Further reading on WitPrep - [free GRE Quant practice sets](/free-practice) - [Quantitative Comparison strategy hub](/gre/quant/quantitative-comparison) - [Data Interpretation strategy hub](/gre/quant/data-interpretation) - [GRE Quant authority pages](/gre/quant/algebra-fundamentals) - [165+ Quant playbook](/blog/gre-quant-165-playbook-from-160-to-perfect) - [GRE formula sheet](/blog/gre-math-formulas-actually-need-and-ones-you-dont) --- **Sources cited in this article:** GMAC, ETS, College Board, Desmos, and Educational Testing Service (2024) — see the full source list below for direct links to each citation.