Percentile to IQ Calculator

Convert a percentile rank into the IQ score that matches it. Enter a percentile between 0.01 and 99.99 and choose the scale. Example: the 98th percentile corresponds to z = 2.054 and an IQ of about 131 on an SD 15 scale. The result uses the normal distribution with mean 100, so it is a statistical conversion rather than a test result.

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Percentile rank

Percent of people who score lower, 0.01 to 99.99.

Test scale (standard deviation)

How to use the Percentile to IQ Calculator

Enter the percentile rank, such as 90 for the 90th percentile.
Choose the scale: 15 for most modern tests.
Press Calculate to get the IQ, the z-score and the descriptive band.
Check the reference table for common percentiles on all three scales.

Formula and method

The percentile is turned into a z-score with the inverse of the standard normal cumulative distribution, z = Phi^-1(p / 100). The IQ is then IQ = 100 + SD x z. For the 90th percentile z = 1.2816, so IQ = 100 + 15 x 1.2816 = 119.2 on SD 15.

Reference table: common percentiles and IQ scores

Percentile	IQ (SD 15)	IQ (SD 16)	IQ (SD 24)
50	100.0	100.0	100.0
75	110.1	110.8	116.2
90	119.2	120.5	130.8
95	124.7	126.3	139.5
98	130.8	132.9	149.3
99	135.0	137.2	156.0

Why one percentile gives different IQ numbers

The percentile is the same everywhere because it is a rank. The IQ number depends on the standard deviation chosen by the test publisher, so the 98th percentile is about 131 on SD 15 but about 149 on SD 24. That is why comparing raw IQ numbers across different tests can mislead. The IQ score converter handles the translation both ways.

Where percentiles come from in testing

Test publishers give a test to a large, representative norming sample and record how raw scores are distributed. Each raw score is mapped to a standard score with mean 100 and a fixed standard deviation. The normal model used here is the usual smooth approximation of that mapping.

Percentile ranks near the extremes

Because the bell curve tapers, each extra IQ point at the top covers fewer people. Going from the 90th to the 99th percentile takes about 16 points on SD 15, while the next step from the 99th to the 99.9th takes about 10 more. Measurement error is also larger relative to the spacing of rare scores.

Limits and responsible use

Important: this is a statistics tool, not an IQ test. It converts a score you already have into a percentile and a descriptive band using a normal (bell-curve) model. Clinical IQ scores come only from a standardized test given and interpreted by a qualified psychologist, and online quizzes give estimates at best.

Frequently asked questions

What IQ is the 90th percentile?

About 119 on an SD 15 scale.

What IQ is the 95th percentile?

About 125 on SD 15.

What IQ is the 99th percentile?

About 135 on SD 15, 137 on SD 16 and 156 on SD 24.

What IQ is the 50th percentile?

Exactly 100, the mean on every standard scale.

Why is the maximum percentile 99.99?

The 100th percentile is not defined for a normal curve, because the distribution has no upper limit.

Is a percentile the same as a percent score?

No. A percentile is a rank within a group, not the share of questions answered correctly.

Sources

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Effortless Math Team

9 minutes ago