Reference

IQ percentile chart

A percentile tells you the share of people who score at or below a given point. It is the only IQ number that means the same thing on every test using the same scale.

Convert a score

Enter any score between 40 and 200. The conversion assumes the standard scale — a mean of 100 and a standard deviation of 15 — which is what the Wechsler tests and most modern instruments use.

If your score came from a test using the Cattell scale, with a standard deviation of 24, this calculator will overstate your percentile substantially. Check which scale your result is on before using any conversion table, including this one.

The full chart

Every value is computed from the normal distribution rather than copied from another site, which is why the rarity column is exact rather than rounded to a memorable figure.

How to read a percentile

A percentile of 84 means you scored at or above 84 percent of the comparison group. It does not mean you answered 84 percent of the items correctly, and it does not mean you are 84 percent as intelligent as anyone.

The distinction matters because percentiles compress at the middle and stretch at the ends, which is the opposite of how the score scale behaves. Between 95 and 105 — ten points — sit about 26 percent of all people. Between 145 and 155, the same ten points, sit about one person in two thousand.

That is why a five-point difference near the middle of the scale is genuinely unimportant, while the same five points at 145 represents a large change in rarity. Neither difference is measurable reliably on a single test, which is a separate problem.

Rarity, and why it is more useful than percentile at the top

Above the 95th percentile, percentiles stop being informative because they all round to numbers that look similar. Rarity fixes that.

This table is also the clearest argument against taking very high reported scores at face value. To measure someone at 160 you would need a norm sample containing enough people at that level to calibrate against — roughly one in thirty thousand. Most standardisation samples run to a couple of thousand people. Scores at that end are extrapolations from the curve, not measurements against real people.

The thresholds people actually ask about

Five numbers come up repeatedly, and it is worth knowing what each one is and where it comes from.

Every one of these is a region rather than a line once measurement error is taken into account. A confidence interval of plus or minus five points means a person whose true score sits near a threshold will land on either side of it depending on the day, which is why good practice never decides a placement on a single number.

The arithmetic, if you want it

The conversion is the cumulative distribution function of the normal distribution. Convert the score to a z-score by subtracting the mean and dividing by the standard deviation, then look up the cumulative probability.

For a score of 120: z = (120 − 100) / 15 = 1.333. The cumulative probability at z = 1.333 is about 0.909, so the percentile is 90.9 and the rarity is about one in eleven.

Everything in the tables above is generated that way. No rounding to friendly numbers, which is why some of the figures look less tidy than the ones you will see elsewhere.