The IQ Bell Curve Explained: Distribution & Standard Deviation
IQ scores follow a bell curve — a normal distribution centred on 100. That single shape explains nearly everything about how IQ is read: why most people score near the middle, why very high and very low scores are rare, and where every percentile comes from. Here is how the curve works and what its standard deviation really tells you.
What the bell curve is
A normal distribution is a symmetric, bell-shaped spread in which most values sit near the average and fewer appear as you move toward either extreme. IQ tests are scaled to fit this curve, with the mean set to 100. The width of the curve is set by the standard deviation (SD) — 15 points on most tests — which fixes how far apart the scores spread.
The 68-95-99.7 rule
Every normal distribution obeys the same rule of thumb, and on an SD-15 IQ scale it reads cleanly:
- About 68% of people score within one SD of the mean — between 85 and 115.
- About 95% score within two SDs — between 70 and 130.
- About 99.7% score within three SDs — between 55 and 145.
This is why scores above 130 or below 70 are uncommon — each sits beyond two standard deviations, in the thin tails of the curve. The bands themselves, and the labels attached to them, are laid out in the IQ scale explained.
From curve to percentile
A percentile is just the proportion of the area under the curve that lies to the left of your score. Because the curve is fixed, every IQ maps to a percentile: 100 is the 50th, 115 is roughly the 84th, and 130 is about the 98th. Percentiles are often easier to interpret than the raw number, and they let you compare results across tests that use different scales.
Why the standard deviation matters
The same IQ number can mean different things if the standard deviation differs. Most tests use SD 15, but some (such as the Cattell scale) use 16 or another value, which stretches or compresses the curve — so "top 2%" lands at about 130 on one test and 132 on another. When you compare scores, match the scale or convert to percentiles first. This is exactly why entry thresholds for high-IQ groups are defined by percentile, as we cover in what IQ you need for Mensa.
Reading your place on the curve
The bell curve tells you how rare a score is, but not that it is fixed — any single result carries a margin of error, especially on unsupervised tests (see how accurate online IQ tests are). To see where you fall on this curve, our age-normed free IQ test places your result on the same distribution and shows the matching percentile.
Frequently asked questions
Why do IQ scores follow a bell curve?
IQ tests are deliberately scaled to fit a normal distribution — the bell curve — with the average set to 100. Because reasoning ability in a large population spreads out symmetrically around a middle value, the bell shape is both a natural fit and a design choice built into the scoring.
What is the standard deviation of IQ?
On most modern tests the standard deviation is 15 points. That means one standard deviation spans from 85 to 115, two spans from 70 to 130, and so on. A few scales use 16 or another value, which changes what a given number means.
What is the 68-95-99.7 rule for IQ?
On a normal distribution, about 68% of people fall within one standard deviation of the mean (85–115), about 95% within two (70–130), and about 99.7% within three (55–145). The same rule generates IQ percentiles.
How do percentiles come from the bell curve?
A percentile is the share of the area under the curve to the left of your score. Because the curve is fixed, each IQ maps to a percentile: 100 is the 50th, 115 about the 84th, and 130 about the 98th.
References
- Wechsler, D. (2008). Wechsler Adult Intelligence Scale — Fourth Edition (WAIS-IV): Technical and Interpretive Manual. Pearson.
- Deary, I. J. (2001). Intelligence: A Very Short Introduction. Oxford University Press.
- Neisser, U., et al. (1996). Intelligence: Knowns and Unknowns. American Psychologist, 51(2), 77–101.
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