IQ Percentile Calculator (score → percentile, rarity, z-score)

Understanding the IQ percentile calculator — concept and principle

This calculator converts an IQ score into a percentile, the share of people expected to score lower, using the normal model on which modern IQ scales are built. It also gives the z-score, the share scoring higher, how rare a score this far out is, and the score range of the middle 95 %. Use it to understand a reported score, not to diagnose anything.

Two standard deviations above the mean leaves about 2.3 % higher.

How it is calculated

z = (IQ − 100) ÷ SD

Percentile = Φ(z), the standard normal cumulative probability

Share scoring higher = 1 − Φ(z)

Rarity (1 in N) = 1 ÷ (share this far out or further)

Middle 95 % = 100 ± 1.96 × SD

Wechsler tests (WAIS, WISC) use mean 100 and SD 15; some other tests use a different SD, which you can enter.

The principle

Modern IQ scores are standard scores: the test is normed so that the reference group averages 100 with a standard deviation of 15. Assuming scores are normally distributed, a score's distance from 100 in SD units fixes its percentile: 115 (z = 1) is about the 84th percentile, 130 (z = 2) about the 97.7th, and 145 (z = 3) about the 99.87th. Norm tables come from finite samples, so the extreme tails are the least precise.

Worked example

Default inputs: IQ 130, SD 15.

z = (130 − 100) ÷ 15 = 2.
Percentile = Φ(2) = 97.725 %; share scoring higher = 2.275 %.
Rarity: 1 ÷ 0.02275 = 43.96, about 1 in 44.
Out of 1,000 people, about 22.8 would score higher.
Score range of the middle 95 % = 100 ± 1.96 × 15 = 70.6 – 129.4.

Each point is the calculator re-run with only “IQ score” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

IQ score	Percentile (share scoring lower)
32.5	0.000339767%
65	0.981533%
97.5	43.3816%
130	97.725%
162	99.9985%
195	100%
260	100%

How to read the result

A percentile describes rank within the norm group, not an amount of ability. Any single score has measurement error, usually reported as a confidence band of several points, so 128 and 132 are not meaningfully different. Scores from tests with different SDs must be converted before comparing.

Common mistakes

Comparing scores from tests with SD 15 and SD 16 or 24 directly.
Reading a percentile as the percentage of questions answered correctly.
Treating a single score as exact.
Assuming the normal model is precise in the far tails.

Keep in mind: IQ scores do not capture everything about a person and are not a diagnosis. Interpretation of an individual test result belongs to a qualified psychologist.

Frequently asked questions

What percentile is an IQ of 130?

About the 97.7th percentile on a scale with SD 15.

What is an average IQ?

100 by definition; about 68 % of people score between 85 and 115.

How rare is an IQ of 145?

About 1 in 740 score that high or higher on an SD-15 scale.

Sources: Illinois State University, "WISC-IV (2003)" summary (mean 100, SD 15) · OpenStax, Introductory Business Statistics 2e, §6.1 The Standard Normal Distribution

Checked 9 Nov 2026. Illinois State University, “WISC-IV (2003)” summary (Full Scale IQ and composite scores: mean 100, SD 15; subtest scaled scores: mean 10, SD 3); OpenStax, Introductory Business Statistics 2e, §6.1 The Standard Normal Distribution (z-scores).

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