IQ percentile calculator

How the calculator works

IQ scores are designed to follow a normal distribution (the bell curve) with an average of 100 and a standard deviation of 15. That makes it simple to turn a score into a percentile:

1. Work out how far the score is from the average in standard deviations: z = (IQ − 100) ÷ 15.
2. Look up the share of a normal distribution that falls below z. That share is the percentile.

For example, an IQ of 120 gives z = 1.33. About 91% of a normal distribution lies below 1.33, so 120 sits at roughly the 91st percentile.

The reverse direction works the same way: pick a percentile, find the z that has that share below it, and convert back with IQ = 100 + 15 × z.

Reading the result

• The percentile is the share of the reference group that scores lower. The 75th percentile means you scored higher than about three quarters of that group.
• “Top x%” is the same idea from the other side. The 98th percentile is the top 2%.
• Percentiles squeeze together near the middle and stretch out at the ends. Going from 100 to 110 moves you 25 percentile points; going from 130 to 140 moves you less than 2.

A few common conversions

When percentiles mislead

A percentile is only as good as the score behind it. Two things matter:

• Measurement error. A score from a short test can easily be ten points too high or too low. That is why this site reports a range and shows the percentile band of the whole range, not of one number.
• The comparison group. Online tests compare you with the people who took that test, not with a representative sample of the population. See are online IQ tests accurate? for what that means in practice.

If you want a score to put into the calculator, take the free quick test. It takes about 12 minutes, needs no email and shows your result immediately.