IQ Percentile Calculator

How the calculation works

Most familiar IQ scales, including the Wechsler tests, place the average at 100 and set one standard deviation at 15 points. The calculator treats the population as a normal (bell-shaped) distribution with those two numbers and works out the area of the curve that falls below the score you entered. That area, expressed as a percentage, is the percentile: a score at the 84th percentile sits above 84 percent of the reference group and below the other 16 percent. This is a statistical conversion only. It does not measure anything about a person, and feeding in a result from a casual online quiz does not make that result clinical.

One detail that trips people up: a few older tests, and the Cattell scale used in some Mensa materials, use a standard deviation of 16 or even 24 rather than 15. The same raw standing produces a different-looking number on each scale, which is why an IQ figure is only meaningful when you know which scale it came from. This tool assumes the 15-point scale throughout.

Reference points on the 15-point scale

These conversions follow directly from the normal-distribution model and are useful for sanity-checking any percentile you are quoted:

• IQ 85 is roughly the 16th percentile; IQ 115 is roughly the 84th. About two thirds of people fall between those two scores.
• IQ 100 is the 50th percentile by definition, the exact middle of the distribution.
• IQ 120 is near the 91st percentile, and IQ 130 near the 98th, the threshold often cited for the top 2 percent.
• IQ 70 and IQ 130 sit about two standard deviations either side of the mean, so each tail beyond them holds only about 2 percent of people.

Notice how the gaps compress as you move outward: adding 10 points near the average moves you many percentile places, while adding 10 points near 140 barely changes the percentile, because there are so few people out there to pass.

Use the result carefully

A percentile is a ranking against a reference group, not a judgment of worth, character, or potential, and not a fixed property of a person. Formal assessments compare a test-taker only against others of the same age, combine several subtests, are administered under standard conditions, and are interpreted by a professional who accounts for context. A single number stripped of all that carries a wide margin of error. Sleep, stress, first-language, practice with the item formats, motivation on the day, and any uncorrected sensory or attention difficulty all shift performance, sometimes by 10 points or more.

If you are converting a score from the free test on this site, treat the output as an illustration of where that score would fall on a conventional scale, not as a personal statistic to record or act on. It should never be used for school placement, hiring, clinical, or legal decisions.

Read the full IQ percentile guide, see the standard score ranges and labels, or read how IQPF describes the limits of its own tests.