How IQ is calculated

Every professional IQ test, from the Wechsler scales to the Stanford-Binet, turns your answers into a score in the same three steps. Only the tables differ.

• Count the raw score. Items right, sometimes with bonus points for speed. On its own this number means nothing: 41 out of 60 could be brilliant or ordinary.
• Compare it with your age group. The publisher has tested a large norm sample, usually around 2,000 people chosen to match the census on age, sex, education and region. Your raw score is placed against the people in that sample who are your age.
• Rescale the position. Your distance from their average, in standard deviations, is your z-score. The IQ is 100 + 15 × z. One standard deviation above average is 115; two is 130.

Say a reasoning test has 60 items. In the norm sample, 30 to 34-year-olds averaged 38 right with a standard deviation of 8. These numbers are invented for the example; real ones are in each publisher's manual.

You score 46. That is 8 points above the average, or exactly one standard deviation. Your z-score is +1.0 and your IQ is 100 + 15 × 1.0 = 115, the 84th percentile.

A 70-year-old also scores 46. The 70 to 74 norm group might average 29 with an SD of 8. Now 46 is 17 points above the average, z = +2.1, and the IQ is about 132. Same raw score, different IQ, because each person is compared with their own age group. This is why the average IQ is 100 at every age.

A full battery such as the WAIS or WISC does the comparison twice. First, each subtest's raw score becomes a scaled score with a mean of 10 and a standard deviation of 3, using that subtest's age table. So a scaled score of 13 is one SD above average, and 7 is one SD below.

Second, the scaled scores for a group of subtests are added up, and the sum is looked up in another table to give an index score or the Full Scale IQ, both on the 100 and 15 scale. On the WAIS-5, seven of the subtests feed the Full Scale IQ. The sum is normed again, rather than averaged, because adding several subtests narrows the spread: being one SD above average on all seven is rarer than being one SD above on one.

That last point surprises people. If someone scores a scaled 13 on every subtest, their Full Scale IQ comes out above 115, not at it, because consistently good performance across seven tasks is less common than one good result. Our guides to WAIS index scores and WISC-V scores show how to read the parts.

The word IQ comes from the first method. In 1912 the German psychologist William Stern proposed dividing a child's mental age (the age whose typical performance they matched) by their real age. Lewis Terman's 1916 Stanford-Binet multiplied the result by 100 to get rid of decimals. A 10-year-old who performed like a typical 12-year-old scored 12 ÷ 10 × 100 = 120.

It worked tolerably for children and failed for adults. Raw reasoning scores rise steeply through childhood and level off in the late teens, so an adult's mental age stops growing while their real age keeps going up. Testers patched this by treating everyone above about 16 as 16, which only hid the problem. Ratio IQs also spread out differently at different ages, so the same number was rarer at one age than another.

David Wechsler's 1939 adult scale replaced the ratio with the deviation method above, and the Stanford-Binet followed in its 1960 revision. The ratio formula survives in the "mental age" idea; our mental age calculator works it backwards from an IQ for children.^[1]

The quality of an IQ score is mostly the quality of its norm sample. Publishers test a stratified sample matched to census figures, then smooth the results into age tables. The WAIS-5 norms were collected in 2023 to 2024 from about 2,000 adults aged 16 to 90; the WISC-V used 2,200 children aged 6 to 16.

Two consequences follow. Norms age: populations scored higher on old norms through the 20th century, which is the Flynn effect, so tests are re-normed every 10 to 20 years. And the far tails are thin: in a sample of 2,000, only about three people would be expected above 145, so scores near 160 rest on extrapolation from the curve, not on many real people. That is why a report gives a confidence interval; our confidence interval calculator shows how wide it is for any score.

An online test has the same three steps but a weaker second one. Most sites never test a census-matched norm sample. Some compare you with everyone who has taken their test, a group that is younger and keener on puzzles than the population, and some simply map percent correct onto a range they choose. Neither is wrong as long as the site says so, but the result is an estimate, not a normed IQ.

Ask any test three questions: who is in the comparison group, how many people, and how reliable is the score. The guide to online IQ test accuracy goes through what good answers look like.