Enter the IQ score, mean IQ score, and standard deviation into the calculator to determine the IQ percentile.

IQ Percentile Calculator

Enter any 3 values to calculate the missing variable

IQ Percentile Formula

The IQ percentile tells you the percentage of people in the reference group who score at or below a given IQ score. When IQ scores are modeled with a normal distribution, the percentile is found from the z-score and the standard normal cumulative distribution function.

z = \frac{IQ - M}{SD}
IQP = \Phi(z)\times 100
IQP = \Phi\!\left(\frac{IQ - M}{SD}\right)\times 100
  • IQ = the individual score
  • M = the population mean (average) IQ
  • SD = the standard deviation of IQ scores
  • IQP = IQ percentile
  • Φ = the cumulative distribution function of the standard normal distribution

Reverse Formulas

Because this calculator can solve for the missing value when you enter any 3 variables, these rearrangements are useful:

z = \Phi^{-1}\!\left(\frac{IQP}{100}\right)
IQ = M + SD\cdot \Phi^{-1}\!\left(\frac{IQP}{100}\right)
M = IQ - SD\cdot \Phi^{-1}\!\left(\frac{IQP}{100}\right)
SD = \frac{IQ - M}{\Phi^{-1}\!\left(\frac{IQP}{100}\right)}

If the percentile is exactly 50, then the z-score is 0 and the IQ score equals the mean.

How to Use the IQ Percentile Calculator

  1. Enter the IQ score you want to evaluate.
  2. Enter the mean IQ for the norm group.
  3. Enter the standard deviation used by that IQ scale.
  4. Click calculate to get the percentile rank.

If you already know the percentile and want to estimate the corresponding IQ score, enter the percentile, mean, and standard deviation instead. Enter percentile as a percent value such as 90, not a decimal like 0.90.

What the Result Means

  • 50th percentile means the score is exactly average for that reference group.
  • 84th percentile is about 1 standard deviation above the mean.
  • 16th percentile is about 1 standard deviation below the mean.
  • 97.7th percentile is about 2 standard deviations above the mean.

A percentile is a rank, not a raw score. An IQ percentile of 90 does not mean 90% correct on a test. It means the score is higher than about 90% of the comparison group.

Common IQ Scores and Approximate Percentiles

The table below assumes a common IQ scale with mean 100 and standard deviation 15.

IQ Score z-Score Approx. Percentile Plain-English Meaning
70 -2.00 2.28% Higher than about 2% of the population
85 -1.00 15.87% Higher than about 16% of the population
100 0.00 50.00% Exactly average
115 1.00 84.13% Higher than about 84% of the population
120 1.33 90.88% Higher than about 91% of the population
130 2.00 97.72% Higher than about 98% of the population
145 3.00 99.87% Higher than nearly all of the population

Example

Suppose an IQ score is 120, the mean is 100, and the standard deviation is 15.

z = \frac{120 - 100}{15} = 1.3333
IQP = \Phi(1.3333)\times 100 \approx 90.88

This means a score of 120 is at about the 90.9th percentile, or higher than roughly 9 out of 10 people in that norm group.

Why the Mean and Standard Deviation Matter

The same percentile can map to different IQ scores if the test uses different norms. For that reason, the calculator asks for the mean and standard deviation rather than assuming one fixed scale. While 100 for the mean and 15 for the standard deviation are common values, some tests use different standard deviations.

Important Notes and Limitations

  • The percentile is an approximation based on a normal-distribution model.
  • Rounding can cause small differences, especially in the extreme high and low tails.
  • Percentile changes are not linear. A 15-point increase near the center of the distribution does not produce the same percentile jump as a 15-point increase far into the tails.
  • Very high percentiles and very low percentiles are sensitive to small score changes because the distribution is compressed at the extremes.

Quick FAQ

Is IQ the same as percentile?
No. IQ is the score itself; percentile is the relative standing of that score within a comparison group.
What percentile is an average IQ?
An average IQ is the mean of the distribution, which corresponds to the 50th percentile.
Can two tests give the same percentile but different IQ scores?
Yes. If the tests use different norms or different standard deviations, the score tied to a given percentile can differ.
Why does percentile matter?
Percentile makes interpretation easier because it expresses where a score stands relative to the reference population rather than only showing the raw IQ value.