IQ Rarity Chart: How Rare Is Your Score?

How to read the chart

Each row answers one question: how many people score at this level or higher? The figures use the modern deviation scale of the WAIS-IV, the WAIS-5 and the Stanford-Binet 5, with a mean of 100 and a standard deviation of 15. Percentile is the share of people scoring lower. Rarity states the same fact the other way round: 1 in N people score this high or higher.

These are theoretical values from the normal curve. The curve fits real test data well in the middle and less well at the edges, so treat the upper rows as projections, not head counts.

IQ rarity chart: 100 to 141

The first table covers the range where most people land, from the average to just past the top 1 percent. Each score links to its own page.

The Mensa line sits at 130, the top 1 percent at 135, and the classic 140 line at 1 in 261.

IQ rarity chart: 145 to 200

The second table covers the far tail, where percentiles need many decimal places and rarity runs into the millions and billions.

The final rows describe rarer events than the human population can supply. At about 8 billion people alive, a 1-in-76-billion score is a figure on paper, not a person you could find.

Why rarity explodes at the top

Near the middle, five points barely move the odds: going from 100 to 105 changes rarity from 1 in 2 to 1 in 2.7. At the top, the same five points multiply them. From 145 to 150, rarity triples, from 1 in 741 to 1 in 2,331. From 155 to 160 it nearly quadruples, to 1 in 31,574.

The 15-point jumps tell the story. A score of 115 is 1 in 6; 130 is 1 in 44; 145 is 1 in 741; 160 is 1 in 31,574; 175 is about 1 in 3.5 million. Each step is rarer than the last by a larger factor, because the tails of the bell curve fall away faster than any exponential.

Concrete numbers help. A stadium of 50,000 people holds about 1,100 at 130 or above and about 67 at 145 or above. A city of 1 million holds about 32 at 160 or above. The whole planet would hold roughly 250,000.

Where the chart stops being a measurement

The math runs forever; the tests do not. The WAIS-IV full-scale IQ runs from 40 to 160, and its norms came from 2,200 US adults. In a sample that size, the normal curve predicts about 3 people above 145 and fewer than one above 160. Scores at the extremes rest on extrapolation, and high scores are measurably less reliable than scores near the median.

That is why reports of IQs far above 160 are widely treated as dubious. The rarer a claimed score, the more likely it came from a childhood ratio formula, an informal norm or an unsupervised test. Scores such as 187 and 228 sit in that territory. At 800, the arithmetic itself gives out: 46.7 standard deviations above the mean, a probability below 1 in 10 to the 100th power.

Norms also age. Raw scores on IQ tests rose through much of the 20th century, about 3 points per decade in the United States on Wechsler tests, so publishers re-norm every generation. An outdated test can flatter a modern test-taker.

The same rarity on other scales

Rarity is the constant; the number depends on the scale. A 1-in-50 result, Mensa's top 2 percent, is 130.8 on the SD 15 scale, 132.9 on SD 16 and 149.3 on the Cattell SD 24 scale. Mensa rounds these to 130, 132 and 148.

The trap runs both ways. A Cattell-scaled 160 is about 1 in 161, the same rarity as roughly 137.5 on the Wechsler scale, between IQ 137 and IQ 138. It is nowhere near a Wechsler 160, which is about 200 times rarer. Ask which scale produced a score before looking it up.

Below 100: the other half of the curve

Half of all people score below 100 by definition. A score of 99 sits at the 47th percentile, 98 at the 45th and 95 at the 37th. All three fall inside the Average band of 90 to 109, which holds about half the population. The curve is symmetrical: about 1 in 44 people score below 70, the mirror image of the share above 130.

Placing your own score

Read any score as a range. A single result carries a confidence interval of roughly five points either way, so a measured 135 spans rarity from about 1 in 44 at 130 to about 1 in 261 at 140. A professional report states that interval; an online result rarely does.

For a quick starting point, our free practice IQ test gives an estimate in minutes; treat it as a screener. Are online IQ tests accurate sets out the limits, and the IQ percentile calculator converts any score. For the headline thresholds, see the top 1 percent IQ, what counts as a high IQ and the IQ classification chart.

Editorial standard: IQ figures for historical figures are retrospective estimates and are labeled as such; scores for living people appear only when the person disclosed them or a reputable outlet reported them. Corrections: contact the editors.