What this calculator does
IQ percentile works out where an IQ score ranks against the population, from the normal distribution. Enter your own figures above and the answer updates as you type: nothing is fixed in the code, so the result reflects exactly the numbers you supply.
The formula this calculator evaluates is printed under the tool and explained below, so you can check the working by hand or reuse it in a spreadsheet.
The formula
Formulaz = (IQ − mean) ÷ SD; percentile = Φ(z) × 100, using the standard normal CDF Φ
The inputs explained
| Field | What to enter |
|---|---|
| IQ score | A number. Starts at 115. |
| Population mean | A number. Starts at 100. |
| Standard deviation | Choose from 15 (Wechsler, Stanford-Binet 5), 16 (older Stanford-Binet), 24 (Cattell). |
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How the answer changes with iq score
Every other input is held at the calculator’s starting values while iq score varies. Select any row to load that scenario into the calculator.