A number on its own tells you very little. An IQ of 118 means nothing until you know what proportion of people score below it, and that is what a percentile is for. It converts a score into a position.
The conversion is not a matter of opinion or of which test you took. It falls out of arithmetic, and once you can do it in your head you will read any score, from any test, far more sensibly.
The two numbers the whole scale rests on
Modern IQ scores are built so that the average is exactly 100 and the standard deviation is 15. Those two numbers define everything else.
The standard deviation is the useful one. It is a measure of spread, and it means roughly 68 of every 100 people score between 85 and 115, which is one standard deviation either side of the middle. About 95 in 100 fall between 70 and 130, which is two. Scores further out than that get rare quickly.
Notice that the scale was designed this way rather than discovered. A raw score of 24 correct answers has no natural meaning. It becomes an IQ of 112 only after being compared against how everyone else of the same age performed, which is a process called norming, and it is worth understanding how raw answers turn into a score before putting much weight on one.
The full table
| IQ score | Percentile | Roughly how rare | In plain words |
|---|---|---|---|
| 145 | 99.9th | 1 in 741 | Higher than 100 of every 100 people |
| 140 | 99.6th | 1 in 261 | Higher than 100 of every 100 people |
| 135 | 99.0th | 1 in 102 | Higher than 99 of every 100 people |
| 130 | 97.7th | 1 in 44 | Higher than 98 of every 100 people |
| 125 | 95.2th | 1 in 21 | Higher than 95 of every 100 people |
| 120 | 90.9th | 1 in 11 | Higher than 91 of every 100 people |
| 115 | 84.1th | 1 in 6 | Higher than 84 of every 100 people |
| 110 | 74.8th | 1 in 4 | Higher than 75 of every 100 people |
| 105 | 63.1th | 1 in 3 | Higher than 63 of every 100 people |
| 100 | 50.0th | 1 in 2 | Higher than 50 of every 100 people |
| 95 | 36.9th | 1 in 3 | Lower than 63 of every 100 people |
| 90 | 25.2th | 1 in 4 | Lower than 75 of every 100 people |
| 85 | 15.9th | 1 in 6 | Lower than 84 of every 100 people |
| 80 | 9.1th | 1 in 11 | Lower than 91 of every 100 people |
| 75 | 4.8th | 1 in 21 | Lower than 95 of every 100 people |
| 70 | 2.3th | 1 in 44 | Lower than 98 of every 100 people |
Calculated from a normal distribution with mean 100 and standard deviation 15. Rarity is how many people you would need to meet, on average, to find one scoring at least this far from the middle.
Two things in that table surprise most people.
The first is how much of the population sits in the middle. A score of 110 sounds comfortably above average, and it is, but one person in four scores at least that high. Half the population falls between 90 and 110. The middle is extremely crowded.
The second is how fast the edges thin out. Going from 100 to 115 moves you past a third of the population. Going from 115 to 130 moves you past another 14 in 100. Going from 130 to 145 moves you past barely two more. The same fifteen points buys you dramatically less ground each time.
This is why small differences at the top of the scale matter more than small differences in the middle, and why the 130 threshold used for giftedness sits where it does. It is also why Mensa’s entry requirement is stated as a percentile rather than a score: the 98th percentile is a fixed slice of the population, while the number that reaches it varies by test.
Why a percentile is still not a precise thing
Every test carries measurement error. A short online test carries more of it than a two hour clinical assessment, but neither is exact. The practical consequence is that a score should be read as a band rather than a point.
If a test reports 118, the honest reading is something like somewhere in the low-to-mid 110s to low 120s, which in percentile terms is roughly the 80th to the 92nd. That is still useful. It is a meaningfully different statement from the 50th percentile or the 99th. It just is not the single pinpoint that the number implies.
This matters most when people compare two scores a few points apart and treat the difference as real. A child who scores 112 and a child who scores 117 have not been meaningfully separated by that test.
In my experience
The single most useful thing I ever did with a score was stop saying the number out loud and start saying the sentence instead.
When my daughter’s result came back I caught myself repeating the figure to my husband, twice, as though saying it again would sharpen it. It did not mean anything to either of us. What changed the conversation was translating it: she is somewhere around the point where roughly one child in six scores higher. That sentence we could actually think about. It put her in a classroom of thirty with four or five children likely to be quicker on this particular kind of puzzle, which is a real and quite ordinary picture.
Numbers invite you to compare and rank. Sentences invite you to picture. I would translate every score into a sentence before letting anyone in the family hear it.
Reading your own result
Find your score in the table, read across to the percentile, and then say the plain words version aloud. That is the whole technique.
If the number came out lower than you hoped, go and look at what a low score does not mean before drawing any conclusion, because the list of ordinary explanations is long and ability is near the bottom of it.
If you have not taken a test yet and want a number to place, the free IQ test for kids reports an age-adjusted score, and the free IQ test for adults does the same for anyone over sixteen. Both give a range rather than a bare figure, for the reason set out above.
And if you took a test as a child and are wondering whether that figure still applies, scores move more in childhood than most people expect.