The IQ Bell Curve Explained: How IQ Is Distributed and What a Standard Deviation Means

An IQ score is just a number until you put it on a curve. The IQ bell curve is what tells you that 115 beats about 84% of people, that 130 is a 1-in-44 result and that a claimed IQ of 190 deserves a raised eyebrow. This guide explains how IQ is distributed and what a standard deviation actually is, with real numbers: the 68-95-99.7 rule, z-scores, how rarity grows along the curve, the three different IQ “rulers” and the fine print most charts leave out.

What is the IQ bell curve? The IQ distribution in one picture

The IQ bell curve is the shape you get when you plot how many people earn each IQ score. Most people cluster in the middle, fewer and fewer appear as you move away from it, and the two sides mirror each other. Statisticians call this a normal (or Gaussian) distribution. As the NIST/SEMATECH e-Handbook of Statistical Methods explains, a normal curve is fully described by two numbers: its center (the mean) and its spread (the standard deviation). In a perfect normal curve, the mean, the median and the most common value are the same point.

For modern IQ tests, both numbers are fixed by design. The free psychology textbook from OpenStax puts it plainly: “The results of intelligence tests follow the bell curve,” and “In modern IQ testing, one standard deviation is 15 points” (OpenStax Psychology 2e).

That fixed scale is what makes the curve useful. Because the center and the spread are known, every IQ score maps to an exact position on the curve, and that position is a percentile.

How the IQ test curve is built: norming

Nobody answers questions “in IQ points.” You earn a raw score, and the test converts it using a norm sample: a large group of people, chosen to mirror the population, who took the same test under the same conditions. OpenStax describes norming as giving a test “to a large population so data can be collected comparing groups, such as age groups.”

Two examples of what that looks like for the most widely used clinical tests:

• The WAIS-5, the newest Wechsler adult scale, was normed on 2,020 examinees, according to Pearson’s WAIS-5 fact sheet.
• The children’s WISC-V was normed on 2,200 children, per Pearson’s WISC-V Technical Report #6.

Raw scores are then placed on the 100-and-15 scale, and Pearson describes even its special extended norms as “consistent with the normal curve.” So the IQ test curve is partly a fact about people and partly a deliberate choice by test makers. Each age group gets its own curve, which is why the average is 100 at every age (our guide to average IQ by age explains what does change as you get older). For the history of how this “deviation IQ” replaced the old mental-age formula, see what IQ is and how it’s calculated.

What a standard deviation of 15 means: the 68-95-99.7 rule

A standard deviation is the typical distance between a score and the average. On the IQ scale it is 15 points, so 115 is one standard deviation above the mean and 70 is two below. The fastest way to read the IQ distribution is the 68-95-99.7 rule, which holds for any normal curve. With a mean of 100 and a standard deviation of 15, it says:

• 68.3% of people score within one standard deviation of the mean: 85 to 115.
• 95.4% score within two standard deviations: 70 to 130.
• 99.7% score within three standard deviations: 55 to 145.

Split into bands, 34.1% of people score between 100 and 115, 13.6% between 115 and 130, 2.1% between 130 and 145, and only about 0.13% above 145. The same shares mirror below 100.

To make that concrete, picture a town of 100,000 people that matches the curve exactly. About 15,900 of them would score 115 or higher, about 2,275 would score 130 or higher, about 135 would reach 145, and roughly 3 would reach 160. Going from 130 to 145 shrinks the group about 17-fold; going from 145 to 160 shrinks it about 43-fold. That acceleration is the single most important thing to understand about the tails.

Z-scores: finding any IQ on the curve

A z-score tells you how many standard deviations a score sits from the mean. For IQ, the formula is short:

z = (IQ − 100) ÷ 15

Take an IQ of 127. Subtract 100 to get 27, divide by 15, and you get z = 1.8. The area under the normal curve to the left of 1.8 is 0.964, so a 127 is higher than about 96.4% of the norm group. There is no simple closed formula for that area, so it is computed numerically, as the NIST handbook notes; any statistics package or spreadsheet does it in one step.

It also works in reverse: what score do you need to reach a given position on the IQ bell curve? (For any individual score, the calculator on our IQ scale page does the conversion for you.)

• 75th percentile: about 110
• 90th percentile: about 119
• 95th percentile: about 125
• 98th percentile: about 131
• 99th percentile: about 135
• 99.9th percentile: about 146

How rarity grows with each standard deviation

Because each standard deviation is a fixed 15 points, the cleanest way to see the shape of the IQ distribution is to step along the curve one standard deviation at a time. We computed every value from the cumulative normal distribution with a mean of 100 and a standard deviation of 15, the scale used by the Wechsler tests and the Stanford-Binet 5. The rarity column shows how many people you would need, on average, to find one who scores at least that far from 100 in the same direction.

This table shows the curve’s structure rather than every score. The full IQ chart in 5-point steps, with classifications and a percentile calculator, is on our IQ scale and percentile page, and each score has its own page, for example what an IQ of 130 means or what an IQ of 145 means.

Two patterns jump out. First, the distribution is symmetric: 85 is exactly as common as 115, and 70 is as rare as 130. Second, rarity explodes at the edges. Each step of one standard deviation multiplies rarity by about 7 between +1 and +2, about 17 between +2 and +3 and about 43 between +3 and +4. In 5-point terms, ten points separate an IQ of 120 (1 in 11) from 130 (1 in 44), but the same ten points separate 150 (1 in 2,331) from 160 (1 in 31,574).

These numbers are about position, not labels. Pearson’s WISC-V reports describe 110 to 119 as High Average, 120 to 129 as Very High and 130 and above as Extremely High; older charts call 120 to 129 “superior” and 130+ “very superior.” For what most people would call a strong result, see our guide to what a good IQ score is. Where “genius” begins is a separate debate, covered in what IQ is considered genius.

Same percentile, different number: SD 15, 16 and 24

Not every IQ scale uses a standard deviation of 15. The Wechsler tests do, and so does the fifth edition of the Stanford-Binet, which reports composite scores “with a mean of 100 and standard deviation of 15,” according to Wiley’s Essentials of Stanford-Binet (SB5) Assessment. The 1960 Stanford-Binet Form L-M set one standard deviation at 16 points, as a 1966 North Texas State University thesis comparing Form L-M with the WISC describes. Mensa International’s explainer on IQ notes that tests can put one standard deviation at 16 or 24 points instead of 15, and an article by American Mensa’s supervisory psychologist Abbie Salny, reprinted by a Mensa local group, gives the Cattell IIIB a standard deviation of 24. Same person, same performance, different number:

You can see this in the wild. American Mensa’s list of qualifying test scores asks for 130 on the Wechsler scales and the Stanford-Binet 5, 132 on the older Stanford-Binet and 148 on the Cattell. Those are the same bar, about two standard deviations above the mean, measured with three different rulers. The same page states that American Mensa does not accept unsupervised testing, including internet-based tests, as proof of eligibility.

Why the tails of the IQ distribution are less reliable

The bell curve is a model, and it fits best in the middle. Out in the tails, three problems pile up.

1. Norm samples run out of people. With 2,020 adults in the WAIS-5 norm sample, a perfect bell curve predicts about 46 people at 130 or above, about 3 at 145 or above and fewer than one at 150. Percentiles that far out can’t be read off real people in the sample; they lean on the mathematical curve. Pearson’s report is candid about this for children: among the 2,200 children in the WISC-V norm sample, “only 16 children obtained any composite score of 150 or higher.”

2. Tests hit a ceiling. Each WISC-V subtest tops out at a scaled score of 19, so a child who answers nearly everything correctly can’t show how much further they could go. At the request of the National Association for Gifted Children, Pearson built extended norms that raise the subtest maximum to 28 and composite scores to 210, using the regular norm sample plus 108 highly gifted children. In the report’s case study, a 9-year-old’s Verbal Comprehension score moved from 155 on the regular norms to 180 on the extended ones, and about 43% of the gifted sample received a higher Full Scale IQ.

3. Measurement error never goes away. Every score comes with a confidence interval. In the WISC-V extended tables, a Full Scale IQ of 160 carries a 95% confidence interval of 152 to 163, so a few points of difference at the top of the scale is often noise.

The lower tail has its own wrinkle. A study in PNAS of about 3 million Swedish and more than 2 million Israeli military conscripts found that mild intellectual disability (roughly the lowest 3% of scores) behaves like the low end of the normal distribution, while severe intellectual disability (the lowest 0.5%) is “a distinct disorder,” likely driven by different factors such as new genetic mutations (Reichenberg et al., 2016). The very bottom of the curve is not simply more of the same.

All of this is why extreme claims deserve skepticism. On the 100-and-15 scale, an IQ of 180 would be about 1 in 20 million, which matches Pearson’s own estimate of one child in 20,000,000 same-age peers. An IQ of 200 would be about 1 in 76 billion, far more people than live on Earth.

The Flynn effect: why the IQ bell curve keeps being re-normed

The bell curve stays centered on 100 only because test makers keep moving it. Through much of the 20th century, raw performance on IQ tests rose decade after decade, a pattern known as the Flynn effect. A 2014 meta-analysis in Psychological Bulletin (Trahan et al.) pooled 285 studies with 14,031 people tested since 1951 and found an average gain of 2.31 points per decade; for modern Stanford-Binet and Wechsler tests (since 1972), the estimate was 2.93 points per decade.

Why does that matter for the curve? If a test’s norms are 20 years old, today’s test taker is being compared with a weaker reference group, so the score comes out too high. The same paper gives an example: a WISC-R score of 73 earned 20 years after the test was normed corresponds to about 67 on current norms, which falls below the cut-off of 70 used in intellectual disability decisions. That is why publishers periodically re-norm their tests, a process OpenStax calls recalibration.

The trend is not one-way. In Norway, where almost every young man took a military ability test, average scores rose from 99.5 for men born in 1962 to 102.3 for those born in 1975, then fell back to 99.4 by the 1989 birth cohort. Because the rise and the decline showed up even between brothers in the same family, the authors concluded that both were driven by environment rather than genes (Bratsberg and Rogeberg, 2018).

In the United States, a Northwestern-led analysis of 394,378 online test takers from 2006 to 2018 found lower scores in verbal reasoning, matrix reasoning and letter-and-number series, but higher scores in 3D rotation (Northwestern University). The lead author, Elizabeth Dworak, cautioned that the shift may reflect test taking rather than ability: “It doesn’t mean their mental ability is lower or higher.”

The practical takeaway: an IQ is a position on a specific curve, built from a specific norm sample at a specific time. A score from the 1990s and a score from 2026 were measured with two slightly different rulers.

Where do you sit on the bell curve?

Reading the curve is one thing; knowing your own spot on it is another. Take the IQtonics IQ test to find out: 40 questions with a 20-minute time limit, covering five areas (patterns, spatial reasoning, numbers, logic and memory). The questions get progressively harder, and harder questions carry more points.

Your result is reported on the same scale used throughout this article, mean 100 and standard deviation 15 (our methodology page explains how the test is built and scored), with your percentile and a cognitive profile that shows your strengths, your best area and the areas to improve. Starting the test is free; your full results unlock with a trial membership, which renews automatically unless you cancel. It is an online test, not a clinical assessment, so read your score as a range rather than a single point, and see how accurate online IQ tests are for the honest fine print.