IQ bell curve: distribution and standard deviation

The IQ bell curve has a mean of 100 and a standard deviation of 15. About 68% of people score 85 to 115, 95% score 70 to 130 and 99.7% score 55 to 145. Only 2.3% score over 130.

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97.7%
Higher than this share of people: 1 in 44
People who score this high or higher: Gifted
Classification, IQ 130 to 139: +2.00 SD
30 points above the mean

What an IQ of 130 means About the Gifted band IQ range 130 to 139

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What does the IQ bell curve show?

The IQ bell curve shows how scores spread across a population when the average is set to 100. Most people cluster near the middle: about 68% score between 85 and 115 and about 95% between 70 and 130. The further a score sits from 100, the rarer it is.

Each band between two standard-deviation lines holds a fixed share of people. The chart labels them, and they add up the same way on every test that uses a standard deviation of 15.

IQ range	Share of people
55 to 70	2.1%
70 to 85	13.6%
85 to 100	34.1%
100 to 115	34.1%
115 to 130	13.6%
130 to 145	2.1%

So about 68% of people sit within one standard deviation of the mean (85 to 115) and about 95% within two (70 to 130). The shaded area on the interactive chart is everyone who scores below the marker.

Why is IQ a bell curve?

Mostly because it is built that way. Early tests divided mental age by real age. In 1939 David Wechsler replaced that with the deviation IQ: a person's raw score is compared with others of the same age, then converted so the norm group has a mean of 100 and a standard deviation of 15.

That conversion makes the scores fit a normal curve. It is a choice of scale, not a law of nature. Many human traits, such as height, do cluster in a bell shape, and test scores come out close to it. The curve is a useful model, and the tails are where it is weakest.

How many people fall within 1, 2 and 3 standard deviations?

The same three numbers hold for any bell curve, which is why they are worth remembering: about 68%, 95% and 99.7%.

Within	IQ range	Share inside	Share above the range
1 SD	85 to 115	68.3%	15.9%
2 SD	70 to 130	95.4%	2.3%
3 SD	55 to 145	99.7%	0.13%

Read the last column as the tail on one side. Two standard deviations up is IQ 130, and 2.3% of people score above it. Mensa-style societies admit the top 2% on an approved test, which is about 131. The Mensa eligibility checker converts that line for other scales.

From the curve to a number for your score

The curve gives shares of people. To turn a single score into a figure, use one of the tools built for it:

The IQ chart lists the named levels, from average to very superior, and the score range of each.
The IQ percentile calculator gives the exact percentile and z-score, and the percentile to IQ converter reverses it.
How rare is my IQ turns the tail of the curve into "1 in N" and a head count.

What is the standard deviation of IQ?

The standard deviation of IQ is 15 points on almost all modern tests, including the Wechsler scales and the current Stanford-Binet. Older Stanford-Binet editions used 16 and the Cattell III B uses 24, so the same ability can produce different numbers. Always check which scale a score uses.

The same rarity on three scales

Above average by	Top	SD 15 (Wechsler, SB5)	SD 16 (older Stanford-Binet)	SD 24 (Cattell III B)
1 SD	15.9%	115	116	124
2 SD	2.3%	130	132	148
3 SD	0.13%	145	148	172

A "148" on the Cattell III B scale and a "130" on a Wechsler test describe the same position on the curve. This chart uses a standard deviation of 15.

The Flynn effect and renorming

Raw scores rose through most of the 20th century. A meta-analysis of 271 samples by Pietschnig and Voracek (2015) found gains of roughly 2 to 3 IQ points per decade. In some countries the rise has since stalled or reversed.

This is why tests are renormed every 10 to 20 years. Each new norm sample resets the average to 100. An old test scored against old norms gives today's test takers a higher number than a freshly normed one would. The curve stays the same shape. The people on it change.

What the curve can and cannot tell you

It is a model
IQ looks like a bell curve partly by design: publishers convert raw scores so the norm group fits a normal distribution with a mean of 100. Real data has slightly more people at the very low end than the curve predicts, because of medical and developmental conditions.
The tails are thin on evidence
A norm sample of a few thousand people contains only a handful above 145, so rarity figures out there are extrapolated. Most tests stop reporting at 160.
Scales differ
Check whether a score uses a standard deviation of 15, 16 or 24 before comparing it with this chart.
Every score has error
A single result is best read as a range of several points either side. The IQ confidence interval tool shows how wide.
Norms age
Raw scores rose for decades in many countries (the Flynn effect), so a test normed long ago can flatter today's test takers.

Not the book

The Bell Curve (1994) is a book by Richard Herrnstein and Charles Murray. It is a separate and contested topic. This page covers only the statistical curve and what it says about how scores are spread.

Frequently asked questions

What is the IQ bell curve?

A graph of how IQ scores spread across a population. The average is 100, the standard deviation is 15, and most people sit near the middle: about 68% score between 85 and 115.

What is the average IQ?

The average IQ is 100. Test makers set it there by design when they norm a test, so the average is always 100 for the group the test was normed on.

What does a standard deviation of 15 mean?

It is the step size of the scale. One step above average is 115, two is 130, three is 145. About 68% of people fall within one step of 100 and about 95% within two.

What percentage of people have an IQ over 130?

About 2.3%, roughly 1 in 44. 130 is two standard deviations above the mean.

Is IQ really normally distributed?

Mostly by construction. Test makers convert raw scores so the norm group fits a normal curve. Real data has slightly more people at the very low end than the curve predicts, and the far tails are extrapolated rather than counted.

Who invented the IQ bell curve?

No one person. The normal curve comes from 19th century statistics. David Wechsler applied it to intelligence testing in 1939 with the deviation IQ, which replaced the older ratio of mental age to real age.

Why do some tests use a standard deviation of 16 or 24?

Older Stanford-Binet editions used 16 and the Cattell III B uses 24. The position on the curve is the same, only the number changes: 130 on a Wechsler test is about 148 on the Cattell scale.

Is this about the book The Bell Curve?

No. The Bell Curve (1994) is a book by Richard Herrnstein and Charles Murray. This page explains the statistical curve only.

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Sources

Wechsler, D. (1939). The Measurement of Adult Intelligence. Williams & Wilkins.
Pietschnig, J., and Voracek, M. (2015). One century of global IQ gains: a formal meta-analysis of the Flynn effect (1909 to 2013). Perspectives on Psychological Science, 10(3).
Bratsberg, B., and Rogeberg, O. (2018). Flynn effect and its reversal are both environmentally caused. PNAS, 115(26).
Wikipedia, IQ classification
Wikipedia, Flynn effect
Herrnstein, R., and Murray, C. (1994). The Bell Curve. Free Press.
Percentiles and rarity on this page are computed from the normal distribution with a mean of 100 and a standard deviation of 15.