The IQ bell curve: how scores are spread

Short answer: The IQ bell curve is the normal distribution that IQ scores are placed on. Modern tests set the average at 100 and the standard deviation at 15, the convention given in the APA task force report of 1995. By the normal curve, about 68% of people score between 85 and 115 (NIST/SEMATECH e-Handbook), and the APA report puts about 95% between 70 and 130. The curve is a property of how scores are built: test makers rank each person against a norm group and convert that rank to this scale. Real test data fit it well in the middle and less well at the far ends.

Share of people in each IQ band

These shares come from the normal curve with a mean of 100 and a standard deviation of 15, by our calculation. They describe the ideal curve. A given test's norm table will differ a little, and these figures treat scores as continuous, so a test that reports whole numbers will also differ slightly.

• Below 70: 2.28% of people, about 1 in 44.
• 70 to 85: 13.59%.
• 85 to 100: 34.13%.
• 100 to 115: 34.13%.
• 115 to 130: 13.59%.
• 130 to 145: 2.14%.
• Above 145: 0.13%, about 1 in 741.

Add neighboring bands together and you get the 68-95-99.7 rule. By the same calculation, 68.27% of people fall within one standard deviation of the average (85 to 115), 95.45% within two (70 to 130) and 99.73% within three (55 to 145). These are the figures the NIST/SEMATECH e-Handbook of Statistical Methods gives for any normal distribution, read on 19 October 2026.

What the IQ bell curve shows

A bell curve is a picture of how common each score is. The horizontal axis runs from low scores to high scores, and the height of the curve shows how many people score there. The NIST/SEMATECH e-Handbook describes the normal distribution as "symmetric and unimodal" and notes that it is "called the bell-shaped or Gaussian distribution". Symmetric means the left half mirrors the right half. Unimodal means it has one peak.

On the IQ scale, the peak sits at 100. Two numbers fix the whole shape:

• The mean is the average score, set to 100.
• The standard deviation is the typical distance of a score from the mean, set to 15 on modern tests such as the Wechsler scales and the SB5, the fifth edition of the Stanford-Binet.

The 1995 APA task force report "Intelligence: Knowns and Unknowns" says test scores are by convention converted to a scale "in which the mean is 100 and the standard deviation is 15". The US Supreme Court used the same figures in Hall v. Florida (2014): "The mean IQ test score is 100", and the standard deviation "is approximately 15 points".

Once you know the mean and the standard deviation, you can read any score as a distance from the middle. A score of 115 is one standard deviation above the mean. A score of 70 is two below. An IQ score reports that distance. It does not report the raw number of puzzles solved. Our guide to the average IQ explains how the 100 is set.

Why IQ scores form a bell curve

The short version: because test makers build the scale that way.

The first IQ scores were ratios. The APA task force report explains that the term once meant a quotient "formed by dividing a so-called mental age by a chronological age, but this procedure is no longer used." The formula was mental age divided by age, times 100, so by that formula a 10-year-old who performed like a typical 12-year-old scored 120. The trouble, as Denisova and Lin point out in Autism Research (2022), is that the same ratio does not mean the same thing at different ages.

Modern tests use a deviation IQ instead. Denisova and Wolpert describe deviation IQs in iScience (2024) as "normalized scores with a fixed mean and standard deviation". The steps work like this:

1. A large norm group, chosen to resemble the population, takes the test.
2. Each person's raw score is ranked against people of the same age.
3. That rank is converted to the IQ scale, so the group's average lands on 100 and its spread on 15.

Step 3 is where the bell comes from. Denisova and Lin date the Stanford-Binet's switch from ratio to deviation IQs to its 1960 revision (Terman and Merrill), which set the standard deviation at 16. The Wechsler tests in use today and the SB5 use 15.

So the exact shape of the reported scale is a choice made during norming. The raw scores underneath are often not perfectly normal, as the section on real data below shows. This is also why an IQ score is a rank, not a count of correct answers.

How rare each score is

Because the scale follows the normal curve, you can work out how rare a score is. These figures are by our calculation from the ideal curve with a mean of 100 and a standard deviation of 15:

• 130 or above: 2.28% of people, about 1 in 44.
• 145 or above: 0.13%, about 1 in 741.
• 160 or above: 0.0032%, about 1 in 31,574.
• 90 or below: 25.2%, about 1 in 4.
• 85 or below: 15.9%, about 1 in 6.

The curve also tells you where the cut points sit. By the same calculation, the top 10% starts at 119.2, the top 5% at 124.7, the top 2% at 130.8 and the top 1% at 134.9. That makes 130 itself the 97.7th percentile, a little under the 98th. To turn your own score into a percentile, our IQ percentile guide walks through the arithmetic.

Do real scores fit the bell curve?

The curve fits well in the middle and less well at the edges. There are four reasons.

Raw scores are often skewed. Voncken and colleagues, writing about test norming in the British Journal of Mathematical and Statistical Psychology (2021), say "the assumptions of normality and homoscedasticity are rarely fulfilled in psychometric tests", and that "a floor effect expresses itself in skewness of the test score distribution." Test makers handle this when they convert raw scores, which is why the reported scale is normal even when the raw scores are not.

There are more very low scores than the curve predicts. A perfect curve puts only about 7 in a million people below 35, by our calculation. Reichenberg and colleagues (PNAS, 2016) describe the most severe form of intellectual disability as rare, under 0.5% of people, with IQ scores that "do not exceed 35". Even a small part of that figure would be far more than the curve predicts. Their study of more than a million sibling pairs supported an idea first proposed by Lionel Penrose in 1938: most intellectual disability sits at the low end of the normal distribution, while the most severe cases have distinct causes. A 2021 review of Ed Zigler's work describes his similar 'two-group' approach, which separated people with a clear organic cause from those without one.

Tests stop measuring at the ends. Sansone and colleagues write in the Journal of Neurodevelopmental Disorders (2014) that "Most intelligence tests do not measure IQ below 40". A 2023 study in Toxics gives the children's Wechsler scale (WISC) a full-scale range of 40 to 160. The SB5 has an extended scale for scores beyond those limits, according to a summary from the Texas Statewide Leadership for Autism Training.

Very few people in the norm group sit in the tails. The WAIS-5, the newest adult Wechsler test, was normed on 2,020 people aged 16 to 90, with 180 people in each age band from 16 to 69 (Winter, Trudel and Kaufman, Journal of Intelligence, 2024). By our calculation, the ideal curve puts about 4 of those 180 people at 130 or above and fewer than 1 at 145 or above. Scores far out in the tail are therefore read off a model of the curve, because the ideal curve expects so few people from each age band at those levels. Pearson's WAIS-IV FAQ adds that reliability is often lower in gifted and intellectually disabled samples because of "the restriction in the range of scores obtained by these groups".

None of this makes the bell curve wrong. Our reading of this evidence is that the curve is most trustworthy between about 70 and 130, where most people score, and least trustworthy at the extremes. None of it is a diagnosis either: questions about a person's development belong with a school or clinical psychologist.

Different tests, different standard deviations

Not every test uses 15. A score only makes sense next to the standard deviation of the test that produced it.

• Wechsler scales and the SB5: standard deviation 15.
• Older Stanford-Binet editions: standard deviation 16, for example the fourth edition, as a 2024 study in the Sao Paulo Medical Journal notes.
• Cattell scales: American Mensa's qualifying-score list, read on 19 October 2026, gives 148 for the Cattell and 130 for the Wechsler scales. Exactly two standard deviations above the mean is 130 on a 15-point scale and 148 on a 24-point scale, by our calculation, so the Cattell figure implies a standard deviation of 24.
• Culture Fair Intelligence Test: standard deviation 16, according to a 2025 review in the Orphanet Journal of Rare Diseases.

This is why "my IQ is 130" can mean different things. On a 15-point scale, 130 is the 97.7th percentile. On a 24-point scale, the same number is about the 89th, by our calculation.

Mensa and the top 2%

Mensa sets its bar as a percentile, and each approved test gets its own score. Mensa International says the qualification is "scoring within the upper 2% of the general population on an approved intelligence test." American Mensa's qualifying-score list, read on 19 October 2026, translates that into a score for each approved test. It lists 130 for the Wechsler scales and for the Stanford Binet 5, and 132 for the test it calls simply the Stanford Binet. American Mensa also states: "We do not accept unsupervised testing as proof of eligibility", which includes internet-based tests.

Score labels on the curve

Clinical tests attach words to stretches of the curve. Hwang and colleagues (Psychiatry Investigation, 2019) applied Wechsler's descriptive classification to full-scale IQ scores, running from "Extremely low" at 69 and below through "Average" at 90 to 109 to "Very superior" at 130 and above. A 2020 case report in BMC Psychiatry prints the same bands for WAIS-IV index scores. The WISC-V uses the same numbers with different words, ending at "extremely high" (Medise and colleagues, Frontiers in Pediatrics, 2024). Both sets of labels sit on the same score bands of the same curve.

The curve moves over time

Scores on old norms tend to rise. The APA task force report put the gain at "about three IQ points per decade" in 1995. When a test is re-normed, the new average is set back to 100, "so the increase more or less disappears from view," as the same report says. Pearson's WAIS-IV FAQ notes that the norms of a newer test are "slightly harder due to the Flynn effect". Our guide to the Flynn effect covers what studies found about the rise.

Your score is a range on the curve

A single score is a point on the curve, but your true position is a range around it. In Hall v. Florida (2014), the Supreme Court said an IQ score "is best understood as a range of scores on either side of the recorded score". The width of that range comes from the test's reliability. The WAIS-5 full-scale IQ has a mean reliability of 0.97 (Winter, Trudel and Kaufman, 2024). By our calculation, that gives a standard error of measurement of about 2.6 points and a 90% range of about plus or minus 4 points. Scores can also differ between tests and sittings. Our guide to how accurate IQ tests are explains why.

The bell curve and the book The Bell Curve

Searches for the IQ bell curve sometimes turn up the book The Bell Curve, by Richard J. Herrnstein and Charles Murray, first published in 1994. The term 'bell curve' is older than the book and names the normal distribution in statistics.

Taking a test yourself

WhatIQ's test has 24 timed picture puzzles and takes about 15 minutes (whatiq.com, 19 October 2026). It places your score on the standard scale, with an average of 100 and a standard deviation of 15, and shows the range it most likely sits in. The site says the result is an estimate, not a clinical assessment.

Frequently asked questions

What percentage of people have an IQ of 90 or lower?

About 25%, or 1 in 4, by the normal curve with a mean of 100 and a standard deviation of 15. That is our calculation from the ideal curve; a given test's norm table may differ slightly. In Wechsler's descriptive classification, as given by Hwang and colleagues (Psychiatry Investigation, 2019), scores of 90 to 109 are labeled "Average", so 90 sits at the low end of that band.

Is an IQ of 85 low?

An 85 is one standard deviation below the average, at about the 16th percentile by the normal curve. About 1 in 6 people score at or below it. In Wechsler's descriptive classification, as given by Hwang and colleagues (Psychiatry Investigation, 2019), it falls in the "Low average" band of 80 to 89. Every score has a range, so a reading of 85 on one test could be a few points higher or lower on another.

What IQ is in the top 1%?

On a test with a standard deviation of 15, the top 1% starts at a score of about 134.9 by the normal curve. The top 2% starts at 130.8 and the top 5% at 124.7. On a test with a different standard deviation, the number for the same percentile changes.

What is the standard deviation of IQ?

On modern tests such as the Wechsler scales and the SB5, the fifth edition of the Stanford-Binet, it is 15 points. The APA task force report of 1995 gives the same convention. Older Stanford-Binet editions used 16, and Mensa's Cattell cutoff of 148 implies 24, so always check which scale a score comes from.

Do IQ scores really follow a normal distribution?

The reported scale does, because tests convert raw scores to it. Raw scores are often skewed, according to a 2021 norming paper by Voncken and colleagues, and there are more very low scores than the curve predicts, according to Reichenberg and colleagues in PNAS (2016). On our reading of that evidence, the fit is best between about 70 and 130, where most people score.

Is the IQ bell curve the same as The Bell Curve book?

No. The bell curve is the normal distribution, a statistics term much older than the book. The Bell Curve is a book by Richard J. Herrnstein and Charles Murray, first published in 1994. The IQ bell curve described on this page is the statistical one: the normal distribution that IQ scores are placed on, with an average of 100 and a standard deviation of 15 on modern tests.