What Is Intelligence Quotient (IQ)? Definition, Formula and What It Measures

Intelligence quotient (IQ) is a standardised score that compares a person’s performance on reasoning tasks with that of other people of the same age, scaled so that the average is 100 and about two thirds of people score between 85 and 115. The word “quotient” comes from the first IQ formula, mental age divided by chronological age; modern tests use the deviation IQ instead, which places a person on the bell curve of their own age group. IQ is a relative position, not a fixed quantity of intelligence, and a good individual test reports it within about 5 points. This guide explains what IQ stands for, the formulas with worked examples, how IQ is measured and what a score does and does not tell you.

• Full form: intelligence quotient. A quotient is the result of a division, from the original formula.
• Ratio IQ (1912 to 1916): mental age divided by chronological age, times 100. A child of 10 performing like the average 12-year-old scores 120.
• Deviation IQ (1939 on): 100 plus 15 times the number of standard deviations above or below the average of the same age group.
• Scale: mean 100; about 68% of people score between 85 and 115 and about 95% between 70 and 130.
• Limits: it measures reasoning and related skills, not creativity, character or worth, and a score is a range of about 5 points either side.

What does IQ stand for?

IQ stands for intelligence quotient. A quotient is what you get from a division, and the name comes from the first IQ formula, which divided the age a child’s test performance reflected by the child’s real age. The idea took four steps, and the table shows who took each.

Our news piece on deviation IQ versus ratio IQ tells the story in full, and IQ and mental age explains the older idea. The history of testing itself is in the history of intelligence testing.

What is the IQ formula?

There have been two. The ratio formula is IQ = (mental age / chronological age) x 100. A 10-year-old who performs like the average 12-year-old has a mental age of 12, so 12 divided by 10, times 100, is 120. The formula breaks down for adults, because mental age stops rising while chronological age keeps going, and it can produce large numbers for young children: a 7-year-old with a mental age of 12 scores about 171 (12 divided by 7, times 100) without being as rare as that suggests. For that reason no current test uses it.

The deviation formula is IQ = 100 + 15 x z, where z is the person’s raw score minus the average raw score of their age group, divided by the standard deviation of that group. A person one standard deviation above the average of their age group has a z of +1 and an IQ of 115. The table shows the standard points on the scale.

Some older scales use a standard deviation of 16 (early Stanford-Binet editions) or 24 (Cattell), and the same performance prints as a different number on each. Our explainer on standard deviation 15 versus 16 walks through the arithmetic, the IQ score converter moves a score between scales, and the IQ percentile calculator gives the percentile for any score. The curve itself is in the IQ bell curve.

What does an IQ test measure?

General reasoning ability and the skills that go with it. Scores on different mental tasks tend to correlate positively, which Charles Spearman described in 1904 as a general factor, g, and modern batteries combine several tasks into one composite for that reason. The Wechsler adult scale reports four index scores alongside the total, and the table shows what each checks.

Each index has its own guide: see which part of the brain IQ tests measure, verbal IQ, spatial IQ, the digit span test and processing speed and IQ. For the split between knowledge and reasoning see fluid versus crystallised intelligence.

How is IQ measured?

By a standardised test given under fixed conditions. A trained examiner gives an individual test, scores each answer by the manual’s rules, turns raw scores into scaled scores using the norms for the person’s age band, and combines them into a composite on the 100-and-15 scale. The norms come from a sample of thousands of people. Group tests exist, but the figures cited in clinical and research work come mostly from individual batteries. The table lists the main ones.

A full individual test takes about an hour or more, depending on the battery and the person (see how long an IQ test takes). Our guides to how IQ tests work, how to read an IQ test report and the official IQ test show how a real result is produced and reported, and IQ score margin of error explains why a score is a range.

What is a good, average or high IQ?

On the standard scale 100 is the average, 90 to 109 is the Average band on the main tests and holds about half of all people, and about 130 and above is the top 2%, the usual gifted cut-off. Labels differ slightly by test; our guides to IQ ranges and IQ classifications list them, what the average IQ test score is covers the middle, and the IQ level chart gives every score from 40 to 160. For single scores see an IQ of 100 and is 120 IQ high.

Is IQ fixed?

Neither fixed nor random. Rank order is fairly stable: a meta-analysis of 205 longitudinal studies found a stability of about .76 for adults at age 20 across a five-year gap, with lower stability in childhood (Breit and colleagues, 2024). Scores also move for known reasons. Retaking a cognitive test raises scores by about .26 standard deviations, roughly 4 points (Hausknecht and colleagues, 2007), each extra year of schooling is linked to a gain of about 1 to 5 IQ points (Ritchie and Tucker-Drob, 2018), and raw performance rose about 0.28 points a year over the twentieth century (Pietschnig and Voracek, 2015). See can you improve your IQ and does school raise IQ.

What does IQ predict?

In groups, school and work outcomes, but loosely. In more than 70,000 English children, intelligence at age 11 correlated 0.81 with a general achievement factor built from national exam results at 16 (Deary and colleagues, 2007), and a meta-analysis of longitudinal studies found correlations of .56 with educational attainment, .43 with occupational level and .20 with income (Strenze, 2007). Squared, those say how much of the spread in an outcome goes with the score: about 31%, 18% and 4%. The rest depends on motivation, health, opportunity and luck, so IQ shifts the odds without setting a ceiling. See does IQ predict school success and does IQ predict income.

Is every "quotient" an IQ?

No. Emotional intelligence is sometimes called EQ, but it is a different idea from IQ (see IQ versus EQ). Some school tests also print an IQ-style number under another name: the HSPT high-school entrance exam reports a Cognitive Skills Quotient on a mean-100, standard-deviation-15 scale, built from its verbal and quantitative subtests and the student’s age, but its publisher describes it as a school score meant to predict academic performance, resting on group-test items rather than an individual IQ battery. Our piece on HSPT scores explains the difference.

Quick answers about intelligence quotient

• What is intelligence quotient? A score that compares reasoning with others of the same age, with 100 as the average.
• What is the full form of IQ? Intelligence quotient.
• What is the IQ formula? Ratio: mental age divided by chronological age, times 100. Deviation: 100 plus 15 times the standard-deviation distance from the age-group average.
• Who invented IQ? Binet and Simon built the first scale in 1905, Stern proposed the quotient in 1912, Terman scaled it to 100 in 1916 and Wechsler introduced the deviation IQ in 1939.
• How is IQ measured? With a standardised test given by a trained examiner and scored against age-band norms.
• What is a normal IQ? 90 to 109 on the main tests; 100 is the average.
• Does IQ measure intelligence? It measures general reasoning ability, which is part of intelligence; see the pros and cons of IQ testing.

Sources

• Breit, M., Scherrer, V., Tucker-Drob, E.M. and Preckel, F. (2024): The stability of cognitive abilities: a meta-analytic review of longitudinal studies, Psychological Bulletin, 150(4), 399-439.
• Strenze, T. (2007): Intelligence and socioeconomic success: a meta-analytic review of longitudinal research, Intelligence, 35(5), 401-426.
• Deary, I.J., Strand, S., Smith, P. and Fernandes, C. (2007): Intelligence and educational achievement, Intelligence, 35(1), 13-21.
• Hausknecht, J.P., Halpert, J.A., Di Paolo, N.T. and Moriarty Gerrard, M.O. (2007): Retesting in selection: a meta-analysis of coaching and practice effects for tests of cognitive ability, Journal of Applied Psychology, 92(2), 373-385.
• Pietschnig, J. and Voracek, M. (2015): One century of global IQ gains: a formal meta-analysis of the Flynn effect (1909-2013), Perspectives on Psychological Science, 10(3), 282-306.
• Ritchie, S.J. and Tucker-Drob, E.M. (2018): How much does education improve intelligence? A meta-analysis, Psychological Science, 29(8), 1358-1369.
• Binet, A. and Simon, T. (1905), Methodes nouvelles pour le diagnostic du niveau intellectuel des anormaux, L’Annee psychologique, 11, 191-244.
• Stern, W. (1912), Die psychologischen Methoden der Intelligenzpruefung und deren Anwendung an Schulkindern, Barth, Leipzig.
• Terman, L.M. (1916), The Measurement of Intelligence, Houghton Mifflin.
• Wechsler, D. (1939), The Measurement of Adult Intelligence, Williams and Wilkins.
• Spearman, C. (1904), General intelligence, objectively determined and measured, American Journal of Psychology, 15(2), 201-293.
• Percentile figures are computed from the normal distribution. The test ages and labels are those in our own guides to the WPPSI-IV, the Stanford-Binet and WISC-V scores.