🧩 IQ Percentile Calculator

IQ tests are standardized to a bell curve with a mean of 100 and a standard deviation of 15. That standardization is what makes percentiles exact: a score of 115 is one standard deviation above the mean, which always lands at the 84th percentile, on any properly normed test. This calculator converts any score to its percentile, z-score, and rarity.

Percentiles are the honest way to read an IQ score because the point gaps mean different things in different places. The gap from 100 to 115 moves you past 34% of people, while the gap from 130 to 145 moves you past barely 2%. Points are not created equal on a bell curve.

How to Use This Calculator

Enter the full-scale IQ score from a professionally administered test such as the WAIS or WISC. Online quizzes are not normed the same way and their numbers do not convert meaningfully. Read the percentile, the z-score, and how rare the score is.

The Bell Curve Math

Subtracting the mean and dividing by the standard deviation converts any IQ into a z-score: how many standard deviations from average. The cumulative normal distribution then gives the share of the population below that point. A z of 1.0 always yields about 84.1%, z of 2.0 about 97.7%, and z of 0 exactly 50%. The calculator evaluates the normal CDF with the Abramowitz-Stegun approximation, accurate to about seven decimal places, far beyond what the input precision needs.

Worked Example

An IQ of 120 sits 90.9th percentile, meaning about 90.9% of people score at that level or below and only 9.1% score higher. That is roughly 1 in 11. An IQ of 100 is exactly the 50th percentile by definition, and 130 marks the 97.7th percentile, the usual cutoff researchers call gifted range.

What the Bands Mean

The standard descriptive bands: below 70 extremely low, 70 to 84 below average, 85 to 115 average (about 68% of people), 116 to 129 above average, 130 and up very high. Two cautions keep this honest. First, every score carries a confidence interval of roughly plus or minus 3 to 5 points from measurement error, so 118 and 122 are effectively the same result. Second, IQ measures specific cognitive abilities, not worth, creativity, or life outcomes; it predicts academic-style performance modestly and everything else weakly.

Scores Are Tools, Not Verdicts

A low score that affects school or work deserves a full neuropsychological evaluation, not an internet conversion. A high score changes nothing about what you should do next. If testing was done for a diagnosis like intellectual disability or gifted placement, the psychologist's report and confidence intervals matter far more than the single number. For informational purposes only, not medical advice. Consult a healthcare professional.

Related tools: Morse fall scale and BMI calculator.

For informational purposes only, not medical advice. Consult a healthcare professional.