Why does this differ from my official percentile?

Because the real distribution is not exactly normal, particularly in the tails. Use the published table if you have it; this is for scores you have not received a table for.

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GRE and GMAT Percentile Calculator

Percentile from a test score, assuming a normal distribution. Real test score distributions are only approximately normal, so this is an estimate rather than the official table.

Also called: test score percentile, z score to percentile.

Estimated percentile

91.69%

About the 91.69%th percentile, which is 1.38 standard deviations above the mean. That puts you ahead of roughly 91.69% of test takers.

Z score

1.38

Ahead of

91.69%

Behind

8.31%

Score needed for the 90th percentile

318.66

On the normal assumption

This is near the middle of the distribution, where the normal approximation holds reasonably well.

How this is calculated

Method and background

How this is calculated

Convert the score to a z score, the number of standard deviations from the mean, then read the normal cumulative distribution to get the share of test takers below it. The assumption is the weak part: scaled test scores are close to normal in the middle and diverge in the tails, so an estimate near the mean is good and one at the extremes is not. Official percentile tables are published and should be preferred when available.

convert to a z score, then read the normal cumulative distribution

x: Your score
mu: Mean
sigma: Standard deviation

Worked examples

Each of these is asserted on every build. If a change to the engine ever moved one of these answers, the build would fail before the page could print it.

a strong GRE score

Your score: 320
Mean score of test takers: 302
Standard deviation: 13

Estimated percentile91.69%

(320 - 302) / 13, computed independently

Open this example

the mean is the fiftieth percentile

Your score: 302
Mean score of test takers: 302
Standard deviation: 13

Estimated percentile50%

boundary: the definitional case

Open this example

Method and limits

What it assumes

A normal distribution of scores, which is an approximation.

What it deliberately does not model

The tails are where the normal assumption fails most, which is exactly where high scorers care.
Official percentile tables are computed from actual cohorts and supersede this.

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Frequently asked questions

Why does this differ from my official percentile?: Because the real distribution is not exactly normal, particularly in the tails. Use the published table if you have it; this is for scores you have not received a table for.