Standard IQ scales are built with a mean of 100 and a standard deviation of 15 — this converts a score into its percentile rank on that scale.
How it works
The IQ score is converted to a z-score using the standard mean and deviation, then the area under the standard normal curve up to that point gives the percentile.
What this does not include
This does not include an actual IQ test — this calculator only converts an already-known score to its percentile ranking on the standard scale.
How to use this calculator
- Enter the IQ score.
A worked example
An IQ of 100 (the defined average): z-score = 0, percentile = 50th — exactly the midpoint of the distribution.
An IQ of 130: percentile = 97.72nd — higher than about 97.72% of the population.
What the variables mean
| Variable | Meaning |
|---|---|
| IQ score | Score on a standard IQ scale, where 100 is defined as average |
| Percentile | What fraction of the population the score exceeds |
Edge cases worth knowing
This assumes a standard deviation of 15 — the common convention for most modern IQ tests — but not every test uses the identical scale, so scores from different test publishers aren’t always perfectly comparable.
Very high or low IQ scores fall into distribution tails where percentile estimates become less precise — the normal distribution model this calculator uses is a good approximation near the center, less so at the extremes.
Frequently asked questions
Why do IQ scales use a mean of 100 and SD of 15?
It’s the standard convention across most modern IQ tests (like the Wechsler scales), chosen so that 100 always represents the population average.
What percentile does an IQ of 100 represent?
Exactly the 50th percentile — average, by definition of the scale’s own mean.
Is this percentile exact for any specific test?
It assumes the standard normal-distribution model most IQ tests are built on — actual test norms can vary slightly by the specific test and its own normed sample.
