How Is IQ Calculated? The Formula Most Sites Get Wrong

How is IQ calculated? On every major modern test, your raw score — the number of questions you got right — is compared with the scores of a large sample of people who took the same test. Your position in that group is then converted to a scale where the average is 100 and the standard deviation, the yardstick for how spread out scores are, is 15.

The formula most websites give instead — mental age ÷ chronological age × 100 — has not been used by a major test since 1960. Nothing in a modern score involves division. The "quotient" in intelligence quotient is a fossil.

The formula at the top of Google was retired in 1960

Search for how IQ is calculated and the old ratio formula still dominates the results. Britannica's entry on IQ leads with it and works an example: a ten-year-old who performs like a twelve-year-old scores 12 ÷ 10 × 100 = 120. Only the final line concedes that "few tests continue to involve the computation of mental ages."

Few is generous. The Wechsler adult scales have compared people with their own age group since the first WAIS appeared in 1955. In 1960 the Stanford-Binet — the test that made the ratio formula famous — dropped it too. The formula has been obsolete for over sixty years.

The two methods also answer different questions. The ratio asked: how far ahead of your age are you? The modern method asks: where do you rank among people your age? Those sound similar. They are not, and the difference is the whole story.

Where mental age ÷ chronological age × 100 came from

The story starts in Paris. In 1905, Alfred Binet and Théodore Simon published the first practical intelligence scale: thirty tasks in rising order of difficulty, built to spot schoolchildren who needed a different kind of teaching. The idea everyone remembers arrived with their 1908 revision. Test items were grouped by age, so a six-year-old who passed the items a typical eight-year-old passed was said to have a mental level of eight.

Binet said level. "Mental age" was the American translation, and it smuggled in a claim Binet never made — that intelligence climbs a fixed ladder, one rung per year.

In 1912 the German psychologist William Stern turned the level into a ratio. Divide mental age by chronological age, he proposed, and you get one number for a child's relative standing. He called it the Intelligenzquotient. His version had no 100 in it: a child exactly at the expected level scored 1.

The 100 came from Stanford. Lewis Terman's 1916 revision of the Binet-Simon scale — the original Stanford-Binet — multiplied Stern's quotient by 100, turning an awkward 1.33 into a quotable 133. That version swept America, and it is the formula still circulating online more than a century later.

Why psychologists abandoned the ratio formula

The ratio breaks the moment you apply it to adults. It only makes sense if every extra year of life brings a matching step up in mental ability, forever. It doesn't. Run the arithmetic on a 40-year-old who reasons like a capable 20-year-old: 20 ÷ 40 × 100 gives an IQ of 50, a number the scale reserved for severe disability. The formula wasn't measuring adults. It was punishing them for having birthdays.

The problems were spotted early. In 1926 the psychologist L. L. Thurstone called the mental-age concept "a failure," full of ambiguities and inconsistencies. When David Wechsler built the first adult Wechsler scale, the WAIS of 1955, he dropped mental age entirely and compared each person with others the same age. By 1960 the Stanford-Binet had followed, and the ratio IQ was dead in mainstream testing.

How is IQ calculated today? By ranking, not dividing

Every major modern test uses what's called a deviation IQ. It takes three steps.

First, the publisher gives the test to a norm sample — a large group recruited to mirror the whole population. The newest Wechsler adult scale, the WAIS-5, was normed in 2023 and 2024 on 2,020 people aged 16 to 90. The sample was matched to the US census on five demographic variables. Its predecessor, the WAIS-IV, used 2,200 people.

Second, statisticians map how scores are distributed in that sample, age band by age band. A 17-year-old and a 75-year-old face different comparison groups.

Third, your raw score is placed within your age band and re-expressed on a fixed scale: mean 100, standard deviation 15. Score exactly at your age group's average and you get 100. Score one standard deviation above it and you get 115.

Notice what's missing: a quotient. Nothing gets divided by anything. "IQ" survives as a name the way "dialing" a phone does — the mechanism it once described is gone.

A worked example, from raw score to percentile

Numbers make this concrete. Imagine a 36-question test, and you answer 27 correctly. That 27 means nothing on its own. Raw scores have no scale: 27 could be brilliant on a hard test or middling on an easy one.

Now bring in the norm sample. Suppose adults your age averaged 21 correct answers, with a standard deviation of 4. You beat the average by 6 points. Divide your lead by the spread: 6 ÷ 4 = 1.5. That figure, called a z-score, says you sit one and a half standard deviations above your peers.

Convert it to the IQ scale: 100 + (1.5 × 15) = 122.5, reported as about 122. On a normal curve, a z-score of 1.5 lands near the 93rd percentile. Start to finish, 27 raw points became "higher than about 93 percent of your age group," dressed up as a familiar number.

Professional tests add layers, not new logic. On a Wechsler scale, each subtest's raw score is first converted to a scaled score with a mean of 10 and a standard deviation of 3, always within your own age band. The scaled scores are summed, and the total is looked up in a norm table that yields the Full Scale IQ. Those tables are built from the sample's real results, so they can stray a hair from the perfect bell curve.

What each IQ score means as a percentile

Because the scale is fixed, every score translates straight into a rank:

• 85 — about the 16th percentile
• 100 — the 50th percentile, dead average
• 115 — about the 84th percentile
• 130 — about the 98th percentile
• 145 — about the 99.9th percentile

About 68 percent of people score between 85 and 115, and about 95 percent between 70 and 130.

The percentile is the honest version of the number. "An IQ of 130" sounds like a quantity of something in your head. "Higher than 98 percent of your age group" is what the calculation actually established.

Why a score of 100 has an expiry date

A deviation IQ means something only relative to its norm sample — and norm samples go stale. In 1984 the researcher James Flynn showed that American performance on IQ tests rose steadily from 1932 to 1978, at about three IQ points per decade. In 1987 he reported gains of 5 to 25 points in a single generation across 14 countries. The rise is now called the Flynn effect.

Publishers respond by re-norming. A fresh sample takes the test, the average is reset to 100, and everyone afterward is compared with the new group. That is one reason the WAIS-IV of 2008 gave way to the WAIS-5 in 2024. The psychologist Ulric Neisser estimated in 1997 that if the average American child of 1932 were scored on 1997 norms, they would land near 80. Same children, same answers — different comparison group.

So a score of 100 is not a fixed amount of intelligence. It marks the average of one sample of people, tested in particular years.

The calculation ends with a range, not a point

One thing the old formula never had: an error bar. Every serious test reports a standard error of measurement — how much a score would wobble if you took the same test again without learning anything in between. Multiply that error by about two and you get the 95 percent confidence interval. With a measurement error of 3 points, a measured IQ of 122 really means "somewhere between about 116 and 128."

Manuals print these ranges next to every score, and they are sometimes lopsided. On the WAIS-IV, a Full Scale IQ of 130 carries a published interval of 125 to 133, pulled slightly toward the average — because part of any extreme score is luck, and luck doesn't repeat.

That, complete, is the modern answer. Historically: mental age over chronological age, times 100 — Binet's levels, Stern's ratio, Terman's polish, retired in 1960. Today: a raw score, ranked within a census-matched sample of your age group and mapped onto a curve where 100 is average — with a margin of error attached. An IQ score is not a quantity extracted from your head. It's a percentile wearing a number that made sense a century ago, and read that way, it tells you exactly as much as it should.