About the IQ Percentile Calculator
Most modern intelligence tests are deliberately scaled so that scores form a normal (bell curve) distribution with a mean of 100. This calculator takes a raw IQ score and reports where it falls on that curve: the percentile rank, the z-score, how rare the score is, and a common descriptive classification band.
How the calculation works
The calculator first converts the IQ score to a z-score, the number of standard deviations the score sits from the mean of 100: z = (IQ − 100) / SD. Most current tests, including the Wechsler scales (WAIS, WISC) and the Stanford-Binet Fifth Edition, use SD = 15; some older tests used SD = 16, which is offered as an alternate scale. The z-score is then converted to a percentile using the cumulative standard normal distribution (evaluated here with the Abramowitz-Stegun approximation to the error function), which gives the share of the population expected to score at or below that value. Rarity is the inverse of the appropriate tail probability, expressed as "1 in N," and the group-size result multiplies the upper-tail probability by the comparison group you enter.
Reading standard deviation and classification
Because IQ is normally distributed, about 68% of people fall within one SD of 100 (85-115 on the SD 15 scale), about 95% within two SD (70-130), and about 99.7% within three SD (55-145). Scores are commonly grouped into bands: 130 and above is Very Superior, 120-129 Superior, 110-119 High Average, 90-109 Average, 80-89 Low Average, 70-79 Borderline, and below 70 Extremely Low. These bands describe a score's position in the population, not a person's worth or potential.
When to consult a professional
This tool performs the standard percentile arithmetic behind a reported score; it does not administer or score an IQ test. Formal IQ testing, and any decisions about educational placement, support services, or clinical diagnosis, should be handled by a licensed psychologist or qualified professional using a validated test instrument.