IQ percentiles explained
A percentile is the share of people you scored above. It is more useful than the IQ number itself, because it tells you where you sit rather than handing you an abstraction.
The IQ number is an abstraction. The percentile is the part that tells you something you can actually picture.
What a percentile is
Your percentile is the share of the population that scored below you. At the 75th percentile, roughly 75 people in every 100 scored lower.
That is it. No further interpretation is built in, which is why it travels better than the score itself.
How it is derived
IQ scores are laid out on a normal distribution with a mean of 100 and a standard deviation of 15. Your score is first converted into a distance from the mean, measured in standard deviations. The percentile is then the proportion of the curve sitting below that point.
| IQ | Standard deviations | Percentile |
|---|---|---|
| 145 | +3 | 99th |
| 130 | +2 | 98th |
| 115 | +1 | 84th |
| 100 | 0 | 50th |
| 85 | -1 | 16th |
| 70 | -2 | 2nd |
Two things stand out immediately.
The middle is crowded. Between 85 and 115 you move through 68 percentile points across just 30 IQ points. Small score differences near the mean move your ranking a lot and mean very little, which is why the average band covers such a wide spread of numbers.
The top is empty. Between 130 and 145, another 15 IQ points, you move only from the 98th to the 99th percentile. The percentile scale simply runs out of room.
Rarity is the more useful number up top
Once you are past about 130, percentiles stop discriminating. Rarity takes over.
Rarity is the reciprocal of the tail above your score. If 2 percent of people score 130 or higher, that is one person in 50, or more precisely about 1 in 44.
| IQ | Percentile | Rarity |
|---|---|---|
| 160 | 99th | about 1 in 31,500 |
| 145 | 99th | about 1 in 741 |
| 130 | 98th | about 1 in 44 |
| 120 | 91st | about 1 in 11 |
| 110 | 75th | about 1 in 4 |
Both 145 and 160 are the 99th percentile. One is forty times rarer than the other. That is why our score range pages publish rarity alongside percentile for every score rather than percentile alone.
It is also why claims about extremely high IQs deserve scrutiny. A number that sounds merely impressive can describe a frequency exceeding the population of the planet, which we get into in the highest IQ ever recorded.
Why you cannot be in the 100th percentile
You cannot score higher than 100 percent of people, because you are one of them. Percentiles are conventionally capped at 99 for this reason, and any site reporting a 100th percentile result is not doing the arithmetic.
A caution on comparing across tests
The percentile a score maps to depends on the standard deviation the test uses. On an SD 15 scale, 132 is roughly the 98th percentile. On an SD 24 scale, the same percentile sits at about 148.
Both describe the same rarity. The numbers look nothing alike. This is the single most common source of confusion in Mensa qualifying scores, where people compare figures from scales that were never comparable.
If you want your own percentile and rarity worked out, our free IQ test reports both alongside the score. The arithmetic is the same normal-distribution maths described here, documented on our methodology page.
Key takeaways
- A percentile is the share of people who scored below you.
- Percentiles are derived from the normal distribution using your distance from the mean in standard deviations.
- Scores cluster densely near 100, so small differences there move percentile a lot and mean little.
- Above roughly 130 the percentile scale runs out of room, and rarity becomes the informative figure.
- 145 and 160 are both the 99th percentile, but 160 is around forty times rarer.
- Percentiles only compare across tests if the tests share a standard deviation.