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The first IQ scores came from dividing mental age by chronological age. The formula worked reasonably well for children and produced nonsense for adults — which is exactly why every major test replaced it.
Two different formulas have both been called "IQ," more than a century apart, and most people who quote a number have never seen either one written down. The first is retired everywhere except history books. Knowing why explains what the score on a modern test report is actually doing.
The idea builds on an even older scale. Alfred Binet and Théodore Simon developed the first practical, age-graded intelligence scale in 1905, for identifying children in Paris who needed additional educational support — an item structure sorted by the age at which a typical child could pass each one, but with no single summary ratio attached. The German psychologist William Stern added that part in 1912, proposing what he called the mental quotient: divide a child's "mental age" — the age level of items they could successfully answer on a graded test — by their actual chronological age. Lewis Terman adapted the idea for the 1916 Stanford-Binet scale, published by Houghton Mifflin, multiplying Stern's quotient by 100 to clear the decimal: IQ equals mental age divided by chronological age, times 100. An eight-year-old who passed items typical of a ten-year-old scored a ratio IQ of 125 — ten divided by eight, times 100. A same-age child who could only pass items typical of a six-year-old scored 75.
For children within a limited age range, the formula produces sensible, intuitive numbers, and it is easy to see why it caught on: it turns a raw test performance directly into a single figure that reads as "ahead of" or "behind" same-age peers, without requiring a norm table to interpret.
Mental age, as the concept was originally built, tracks the age level of items a person can pass — and that only works as a measure while raw ability is still climbing steeply with age, which is true through most of childhood and adolescence. Cognitive performance on the kind of item-graded scale mental age relies on flattens out by the late teens; adults do not keep passing items pitched at ever-higher "mental ages" at anything like a child's rate. Push the ratio formula past that point and it stops producing sensible numbers: a person whose measured ability has not changed at all would show a mechanically falling ratio IQ as their chronological age climbed in the denominator while their mental age stayed roughly flat. The formula was never built for the part of life where it would get used most.
A formula that produces a falling score for an adult whose ability has not changed was never a scoring system for adults.
David Wechsler discarded the ratio entirely for the Wechsler-Bellevue Intelligence Scale, published by The Psychological Corporation in 1939. His method, deviation IQ, compares a person's raw score only against the scores of other people in their own narrow age band, converts that comparison into a standard score, and fixes the mean at 100 and the spread at a chosen standard deviation — 15, on the scale Wechsler chose and every major modern test besides the older Stanford-Binet forms has followed since. Our note on why some scales use 15 and others use 16 covers how that specific choice was made and what it does to a printed number.
The improvement is structural, not cosmetic. Because every age band is scored against its own norm group and converted to the same fixed mean and spread, one standard deviation above average means the same percentile rank — the same rarity — whether the person being scored is 10 or 40. Ratio IQ never had that property, because its effective spread shifted with age in ways that were never fully constant or predictable. A deviation score of 115 means the same thing, in population-rarity terms, at every age it is reported for. A ratio score of 115 did not.
Put a number on the difference. Take two children both described, in an old-style write-up, as having "an IQ of 140." If both scores are ratio IQs, a 140 at age 6 and a 140 at age 12 do not represent the same rarity within their respective age groups, because the ratio formula's effective spread is not constant across ages — the two children are not equally exceptional relative to their peers even though the printed number is identical. If both scores are deviation IQs on the same SD-15 scale, a 140 at age 6 and a 140 at age 12 represent the same rarity, roughly one in 260 people, because deviation scoring builds that consistency in by construction rather than leaving it to chance.
The formula is retired from every current test, but ratio-style reasoning survives in a specific, checkable place: retrospective estimates of historical figures' intelligence. Catharine Cox's 1926 study Early Mental Traits of Three Hundred Geniuses, published under Terman's Stanford Genetic Studies of Genius series, estimated childhood IQ scores for long-dead historical figures by scoring biographical accounts of their early achievements against age norms — a ratio-style method applied after the fact, to people who never sat a standardized test. Cox and her collaborators were explicit that these were estimates built from incomplete biographical records rather than test results, subject to the same childhood-only ceiling described above and to the added uncertainty of scoring a life story rather than a live test session — caveats that mostly evaporated by the time the resulting numbers reached popular retelling. Our note on where celebrity IQ figures actually come from traces how numbers built this way, or built on even less than this, keep circulating as if they were test results.
If a number is described only as "IQ" with no scale attached — no standard deviation, no publisher, no test name — there is no way to know whether it came from a modern deviation-scored test, an old ratio-based estimate, or an internet quiz with no scoring key at all. A properly reported score always states the test and the scale it was measured on, which is what lets it be converted, compared or checked against a real distribution rather than taken on faith.
Convert a score between scales the way a psychometrician would — the tool handles the SD-15, SD-16 and older-scale conversions directly, on real deviation-scored figures.
Find your IQ score now! →The retired formula is worth knowing about for exactly one reason: it explains why "IQ" was never one fixed thing, even before online tests and social media multiplied the confusion. A properly reported modern score — the kind a supervised, deviation-scored test produces — carries its scale with it. A number with no scale attached, ratio-era or not, carries nothing at all.
Ratio IQ divides a person's "mental age" — the age level of test items they can pass — by their actual chronological age, then multiplies by 100. Deviation IQ compares a person's raw score only against others of the same age and converts that comparison into a standard score with a fixed mean of 100 and a fixed standard deviation, usually 15. Every major modern test uses deviation scoring; ratio IQ was retired by the mid-twentieth century.
Ratio IQ depends on mental age climbing steadily with chronological age, which is roughly true through childhood but stops being true once cognitive performance on age-graded items levels off in the late teens. Applied past that point, the formula produces a falling score for an adult whose actual ability has not changed, because chronological age keeps climbing in the denominator while mental age does not keep pace.
David Wechsler introduced deviation scoring for the Wechsler-Bellevue Intelligence Scale in 1939, comparing each person's score only to others their own age and converting it to a standard score with a fixed mean and standard deviation. Stanford-Binet adopted the same approach in its 1960 Form L-M revision, and it has been the universal standard since.
No. Estimates like Catharine Cox's 1926 study of historical figures' childhood IQ were built retrospectively from biographical accounts, scored against age norms in a ratio-style method, applied to people who never sat a standardized test. They are estimates built from incomplete records, not test results, and that caveat is usually lost by the time the numbers circulate.
Corrections: spotted an error? Email corrections@iqmetrics.org and we will update this story and note the change here.
Wechsler scales use a standard deviation of 15, older Stanford-Binet forms used 16, and the Cattell scales use 24. One standing prints as three different numbers — and one printed 140 is a one-in-260 result on one of those scales and a one-in-21 result on another.
Mensa admits at the 98th percentile of a supervised, properly normed test. That single rule produces a different qualifying figure on every scale — and none of them is the 130 the internet keeps repeating.
A score of 160 is four standard deviations above average — about one person in 31,560. The sample the score is measured against holds roughly 2,200 people, which is why the top of the table is calculated rather than observed.
Our IIF-certified assessment reports your score with its scale, percentile and confidence range — and a breakdown of the cognitive domains behind it.
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