IQ Percentile: How to Convert an IQ Score

An IQ score and a percentile are two ways of saying the same thing. The score tells you where you sit on the IQ scale; the percentile tells you what share of people you scored higher than. Many people find the percentile easier to understand, because "higher than 91% of people" is more concrete than "120". This guide explains what percentiles are, gives a conversion table for common scores, and shows why every result should come with a range.

What a percentile is

A percentile is the percentage of people in a comparison group who scored below a given result. If you are at the 75th percentile, you scored higher than 75% of the group and lower than 25%.

Two common mix-ups are worth clearing up:

• A percentile is not a percentage of correct answers. Being at the 80th percentile does not mean you answered 80% of the questions correctly. You might have answered half of them correctly on a hard test and still be at the 80th percentile.
• Percentiles are not evenly spaced. Near the middle of the scale, a few IQ points move you many percentiles. At the extremes, a few points move you only a fraction of a percentile. Going from 100 to 110 takes you from the 50th to the 75th percentile, while going from 130 to 140 only takes you from about the 98th to the 99.6th.

IQ to percentile conversion table

IQ scores are scaled with an average of 100 and a standard deviation of 15, and they follow a bell-shaped (normal) distribution. That makes the conversion exact: each score corresponds to one percentile.

| IQ score | Percentile | Higher than about | Rarity | |---|---|---|---| | 85 | 15.9th | 16% of people | 84% score higher | | 90 | 25.2nd | 25% of people | 75% score higher | | 100 | 50th | 50% of people | Exactly average | | 110 | 74.8th | 75% of people | Top 25% | | 115 | 84.1st | 84% of people | Top 16% | | 120 | 90.9th | 91% of people | Top 9% | | 125 | 95.2nd | 95% of people | Top 5% | | 130 | 97.7th | 98% of people | Top 2.3% | | 135 | 99.0th | 99% of people | Top 1% | | 140 | 99.6th | 99.6% of people | Top 0.4% | | 145 | 99.87th | 99.87% of people | Top 0.13% |

Notice the symmetry around 100. A score of 85 is as far below average as 115 is above it, so the 15.9th and 84.1st percentiles mirror each other.

How the conversion works

To convert a score yourself, first turn it into a z-score: how many standard deviations it is from the average.

z = (IQ − 100) ÷ 15

A score of 130 gives z = 2. A score of 85 gives z = −1. You then look up the z-score in a standard normal table, or use a spreadsheet function such as NORM.S.DIST(z, TRUE), which returns the share of the population below that point. For z = 2 the answer is 0.977, which is the 97.7th percentile.

Some useful anchors to remember:

• z = 0 (IQ 100) is the 50th percentile.
• z = 1 (IQ 115) is the 84th percentile.
• z = 2 (IQ 130) is the 97.7th percentile.
• z = 3 (IQ 145) is the 99.87th percentile.

Confidence ranges and the standard error

No test result is perfectly precise. If you took a comparable test on a different day, your score would likely shift a few points because of fatigue, focus, which questions you got, and simple chance. Psychometricians describe this uncertainty with the standard error of measurement (SEM).

The SEM depends on how reliable the test is. A common formula is:

SEM = 15 × √(1 − reliability)

A test with a reliability of 0.90, which is considered good, has an SEM of about 4.7 points. A very reliable test with a reliability of 0.95 has an SEM of about 3.4 points.

From the SEM you can build a confidence range around a score. A 90% range is roughly the score plus or minus 1.645 SEM; a 95% range is the score plus or minus 1.96 SEM. For a test with a reliability of 0.90:

| Observed score | 90% confidence range | Percentile range | |---|---|---| | 100 | about 92 to 108 | about 30th to 70th | | 120 | about 112 to 128 | about 79th to 97th |

That second row is the key insight. A score of 120 sounds precise, but the honest statement is "most likely somewhere between the 79th and 97th percentile". This is why professionally administered tests report ranges, and why you should be cautious about comparing two scores that are only a few points apart.

Why your percentile depends on the comparison group

A percentile only has meaning relative to a specific group. The same performance can produce different percentiles depending on whether you are compared with people your age, with adults in general, or with other people who took the same online test. Online test takers tend to score higher than the general population, so a test that compares you only with them, without adjustment, will place you lower than you would rank in the population as a whole.

Good tests state who the comparison group is and adjust for skews in it. For more on how norm groups are built, read our guide to average IQ. To see how percentiles map onto labels such as "high average" or "very high", see the IQ score chart.

Find your own percentile

The IQTestScale test takes about 20 minutes and covers fluid reasoning, spatial thinking, working memory and quantitative reasoning. Your result shows your score, a likely range around it and your percentile, so you get the honest version of your number rather than a single point. It is a self-assessment for personal insight, not a clinical evaluation.

Take the IQ test