Test Percentile Calculator

Standardized test scores get reported with both raw scores and percentiles, and translating between them — or comparing two students' scores — is a common task without an obvious answer.

Given a raw score, the test's mean, and standard deviation, the calculator returns the percentile rank (assuming a normal distribution) and the z-score. Or work in reverse: enter a target percentile and get the raw score that corresponds to it.

The normal-distribution assumption is good for SAT, GRE, IQ tests, and most large-population standardized exams, since they're typically scaled to be normal. Smaller or non-normalized tests (a class quiz, an AP exam with a hard ceiling) won't follow a normal curve as cleanly, and the percentile estimate will be approximate.

The core formula is the cumulative distribution function of the normal distribution. Given a z-score (your distance from the mean in standard deviation units), the CDF returns the percentile. z = (raw − mean) / SD. A z of 0 is the 50th percentile (right at the mean). z=1 is the 84th percentile. z=2 is the 97.7th. z=3 is the 99.87th. Going the other way: enter a percentile, the tool inverts the CDF to get the z-score, then converts back to raw using the supplied mean and SD.

The pain this addresses: a parent looking at a kid's standardized test report sees 'raw score 1240, percentile 73' and wants to compare to a sibling's 1260 from a different test year (different mean and SD). Or a graduate program reports 'mean GRE Q is 156' and you want to know what percentile that is. The arithmetic is trivial; the formula is opaque. The tool wraps it.

Worked example: SAT mean is around 1050 with SD of 210. You scored 1300. z-score: (1300 − 1050)/210 = 1.19. The CDF at z=1.19 returns roughly 0.883, meaning 88.3rd percentile. So you scored better than 88.3% of test-takers. Going backwards: to be in the top 1%, you need z=2.33, which translates to a raw score of 1050 + 2.33×210 ≈ 1539. The math is consistent with what test-prep sites report, because the tests are designed to follow the normal distribution.

Where the normal assumption fails: tests with hard ceilings or floors. The SAT max is 1600. If too many people score 1600, the upper tail of the distribution gets squashed against the ceiling — z-scores beyond a certain point all map to the same raw score. The 99.5th percentile and the 99.9th percentile both happen to be 1600, even though they should be different. For tests that genuinely have hard caps (AP exams scored 1-5, IB exams 1-7), the normal model breaks down completely and you need actual percentile tables from the test publisher.