IQ Percentile Calculator — Score to Population Rank
Enter an IQ score to see what percentile it falls in, how many standard deviations it is from the population mean, what proportion of people score higher or lower, and its Wechsler classification. Assumes the standard IQ scale: mean = 100, SD = 15.
IQ 115 — High Average — z-score 1
- 1
Z-score
(115 − 100) ÷ 15 = 1Standardises the IQ score relative to the population mean (100) and standard deviation (15). - 2
Percentile (normal CDF)
Φ(1) × 100 = 84.1Φ is the standard normal cumulative distribution function — the shaded area under the bell curve.
How does this calculator work?
IQ scores are standardised to mean 100, SD 15. This calculator converts your score to a percentile using the normal CDF Φ((IQ − 100) / 15). IQ 115 → 84th percentile (top 16%); IQ 130 → 97.7th percentile (top 2.3%); IQ 145 → 99.87th percentile. Includes Wechsler category and 1-in-X frequency.
Formula
How this is calculated
IQ scores on the most widely used scales (Wechsler WAIS/WISC, Stanford–Binet 5th edition, most modern batteries) are standardised so that the population mean is 100 and the standard deviation is 15. This means the scores follow a normal (bell-curve) distribution by construction — the tests are normed against large representative samples and then rescaled to these parameters.
The percentile for an IQ score is computed from the standard normal cumulative distribution function (CDF) Φ: first convert to a z-score by subtracting the mean and dividing by the SD, then evaluate Φ(z) × 100. A z-score of +1.0 (IQ 115) puts you at the 84th percentile; +2.0 (IQ 130) at the 97.7th; +3.0 (IQ 145) at the 99.87th. This calculator uses the Abramowitz & Stegun polynomial approximation of erf, accurate to < 1.5 × 10⁻⁷.
The Wechsler classification labels (Average, High Average, Superior, Very Superior, etc.) are qualitative descriptors used by clinical psychologists — they are defined by IQ ranges, not by specific cognitive outcomes. IQ scores have known limitations: they measure certain types of standardised reasoning and are influenced by test conditions, cultural background, education, and test anxiety. A single score should never be interpreted in isolation.
Frequently asked questions
An IQ at the 84th percentile (IQ ≈ 115, one SD above the mean) means that 84% of the normed population scored at or below that score, and 16% scored higher. Percentiles are population-relative — the same score would be a different percentile if the reference population changed.
IQ scores are designed to be normally distributed — test developers collect large representative samples, then scale and norm the raw scores so that the distribution fits a bell curve with mean 100 and SD 15. The underlying traits being measured may not be perfectly normal, but the published scores are. At extreme ends (IQ < 60 or > 160) the normal approximation is less reliable because very few people are tested at those levels.
The calculator uses the Wechsler/modern standard: mean = 100, SD = 15. The older Stanford–Binet (pre-5th edition) used SD = 16; Cattell used SD = 24. If your score is from a different scale, convert it first: IQ_new = (IQ_old − mean_old) / SD_old × 15 + 100.
Also known as
TG we-Calculate Editorial Team. (2026). IQ Percentile Calculator — Score to Population Rank [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/iq-percentile-calculator
TG we-Calculate Editorial Team. "IQ Percentile Calculator — Score to Population Rank." TG we-Calculate. 2026. https://we-calculate.com/calculator/iq-percentile-calculator.
TG we-Calculate Editorial Team, "IQ Percentile Calculator — Score to Population Rank," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/iq-percentile-calculator
@misc{wecalculate_iq_percentile_calculator, title = {IQ Percentile Calculator — Score to Population Rank}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/iq-percentile-calculator}}, year = {2026}, note = {TG we-Calculate} }
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