IQ 150: how rare is it?

On a scale with a mean of 100 and SD 15, IQ 150 is about percentile 99.96. The normal-curve estimate is about 1 in 2,300 at or above this score.

IQ 150 in numbers

Percentileof people score at or below	99.96
Rarityat or above	1 in 2,300
Commonly used band130 and above	Extremely High

Band labels are the commonly used WISC-V ones, as listed by Smart Kids with Learning Disabilities: Understanding IQ Test Scores. Labels are conventions in common use; each test publisher words its own.

Where it sits on the curve

Shaded: the people who score above it (0.04%).

The same position on other scales

Same percentile on every row; the number changes because the scales use different standard deviations.

Scale	Score	Percentile
SD 15	150	99.96
SD 16	153	99.96
SD 24	180	99.96

How rare is an IQ of 150?

An IQ of 150 is about percentile 99.96, or about 1 in 2,300 at or above it. On a scale with a mean of 100 and SD 15, it is 3.3 standard deviations above the mean.

The nonprofit Smart Kids with Learning Disabilities lists “Extremely High” for the band from 130 and above in commonly used WISC-V labels. This label describes a score range, not how many people have a score in it.

Why is rarity at this height modeled?

Rarity at this height is estimated from the normal curve rather than counted among people who took a test. The figure comes from extending the curve into its upper tail.

That makes the estimate a mathematical model, not a headcount for a particular population. It depends on the assumed score distribution and scale. Use the percentile calculator to compare percentile and rarity at different scores.

How does IQ 150 compare across other scales?

The same position on another scale can have a different score number. On older Stanford-Binet editions with SD 16, the equivalent position is 153; on the Cattell scale with SD 24, it is 180.

Mensa's own page gives 148 as its Cattell-scale qualifying score and says standard deviations of “16 or 24” points are used. Read a score with its test and scale in mind. The IQ scale explains how different scales relate.

Questions

Is IQ 150 the same as percentile 99.96?

On the mean-100, SD-15 scale, IQ 150 corresponds to about percentile 99.96. A percentile describes a score's position relative to the reference group used for that scale; it is not the score number itself.

Does 1 in 2,300 mean exactly that many people have IQ 150?

No. The figure refers to people at or above the score and is modeled from the normal curve. It does not count everyone tested or predict a headcount in a particular group.

Why can IQ 150 appear as 153 or 180?

The numbers use other scales with different standard deviations. An equivalent position is 153 on older Stanford-Binet editions with SD 16 and 180 on the Cattell scale with SD 24. The scale changes the score number.