What Is IQ? IQ Definition, Formula and How IQ Is Calculated

You hear the term all the time: a friend “must have a high IQ,” a news story quotes a celebrity’s score, a school mentions testing. But the IQ definition most people carry around is fuzzy. This guide explains what IQ means, where the number 100 comes from, both formulas used to calculate it (with worked examples), and what a score can and can’t tell you.

IQ definition: a score, not a thing you have

The simplest accurate IQ definition is this: IQ is a score on a standardized test, expressed relative to people your age. It is not a measure of your worth, your knowledge or your potential, and it is not “intelligence” in the broad, everyday sense.

Intelligence is the big, messy concept: learning, reasoning, planning, understanding complex ideas, adapting to new situations. An IQ test samples a slice of that with standardized tasks, then turns your performance into one number by comparing it with a large reference group. So when someone says “her IQ is 120,” what that really means is: on this test, she outperformed most people her age.

Notice the two built-in limits. The score depends on which test was used, and it only means something relative to the norm group the test was calibrated on. Both points come up again below, because they explain almost every confusing IQ claim you will see online.

What does IQ stand for?

IQ stands for intelligence quotient. A quotient is the answer to a division problem (12 ÷ 10 = 1.2), and the name is a fossil from the original formula, which literally divided one age by another. The term traces back to the German Intelligenzquotient: according to the introduction to Terman’s 1916 book in York University’s Classics in the History of Psychology archive, the numerical index was devised in 1912 by German psychologist William Stern and became the most noteworthy feature of Lewis Terman’s Stanford revision of the Binet scale.

Today’s tests no longer divide anything, but the name stuck. In everyday English “IQ” has also drifted into a looser sense of know-how, as in “hockey IQ” or “emotional IQ.” This article sticks to the psychological meaning.

A short history of IQ testing

IQ testing did not start as a hunt for geniuses. It started as a practical school problem in Paris.

The introduction to Binet and Simon’s 1905 paper explains the goal plainly: the commission needed a way to identify children who required special instruction. In the 1908 revision a task was placed at a given age if 75% of children that age passed it, so a 6-year-old who performed like a typical 8-year-old had a mental level of 8. That idea, mental age, is the seed of the first IQ formula.

The original IQ formula: mental age ÷ age × 100

The classic IQ formula, as summarized in UC Berkeley psychologist John Kihlstrom’s lecture notes on intelligence, is:

IQ = (mental age ÷ chronological age) × 100

This is called a ratio IQ. Stern’s original quotient was just the division; according to Mensa International’s explainer on IQ, Terman added the multiplication by 100 so scores would read 130 rather than 1.3. That step simply removes the decimal, so a child whose mental age matches their real age always scores exactly 100.

A worked example

• A 10-year-old who passes the tasks a typical 12-year-old passes: 12 ÷ 10 × 100 = 120.
• An 8-year-old performing at the level of a typical 6-year-old: 6 ÷ 8 × 100 = 75.
• A 9-year-old performing exactly like other 9-year-olds: 9 ÷ 9 × 100 = 100.

For children this is intuitive, which is why the formula spread so fast.

Why the ratio IQ broke down for adults

The ratio formula assumes that test performance climbs steadily with every birthday. In childhood it roughly does. In adulthood it doesn’t: a typical 40-year-old does not solve twice as many reasoning problems as a typical 20-year-old. Run the formula on a 40-year-old who performs exactly like an average 20-year-old and you get 20 ÷ 40 × 100 = 50, an absurd result for a perfectly ordinary adult.

David Wechsler took the problem head on. According to the Gale Encyclopedia of Psychology, he considered the Binet tests too narrow and inappropriate for adults, built his 1939 scale for adults, and introduced a new calculation that compared people with their peer group instead of computing a mental age. That approach, the deviation IQ, is what every major test uses today.

How is IQ calculated today? The deviation IQ

Modern tests calculate IQ differently. Instead of asking “what age do you perform like?”, the test asks “how far above or below the average of your own age group did you score, measured in standard deviations?”

To answer that, the publisher first gives the test to a large norm sample, divided into age groups, and records each group’s average raw score and standard deviation. Your raw score is then converted in two steps:

1. Find your z-score: z = (your raw score − your age group’s average) ÷ your age group’s standard deviation.
2. Put it on the IQ scale: IQ = 100 + 15 × z.

How to calculate IQ: a step-by-step example

Kihlstrom’s notes use a tidy illustration: imagine a test where your age group averages 40 correct answers with a standard deviation of 12.

Scores between the rows work the same way. With 46 correct, z = (46 − 40) ÷ 12 = 0.5, so IQ = 100 + 15 × 0.5 = 107.5, which a test would report as about 108. Computed from a normal distribution with mean 100 and SD 15, that sits around the 69th percentile.

The beauty of this method is that it works identically at age 8, 38 or 80. A 70-year-old and a 25-year-old who each score 115 are both one standard deviation above their own age group, even if their raw answers differ.

The IQ standard deviation: why 15 points matters

The IQ standard deviation of 15 is the ruler of the whole scale. Because modern tests are built so scores follow a bell-shaped normal distribution, every 15 points marks one standard deviation, and the share of people in each band follows directly (computed from a normal distribution with mean 100 and SD 15):

That is all you need to read most scores: an IQ of 115 beats roughly 84% of people, and an IQ of 130 beats about 98%. For the full IQ scale with every range, classification and percentile, see our IQ chart; for what counts as a strong result, read our guide to what a good IQ score is. If you want the statistics behind the curve, including z-scores, rarity at the extremes and the different scales some tests use, read our explainer on the IQ bell curve and percentiles.

One caution: 15 is the convention on the Wechsler scales and most modern tests, but a few tests have used a different standard deviation, so the same performance can be reported as different numbers. Always check which scale a score is on before comparing it with someone else’s.

How is IQ measured? Inside a modern IQ test

One of the most widely used clinical tests in the US is the Wechsler Adult Intelligence Scale, now in its fifth edition. According to Pearson’s WAIS-5 overview brochure, it covers ages 16 through 90 and takes about 45 minutes for the seven core subtests that make up the Full Scale IQ; the full battery of 10 primary subtests takes around 60 minutes. It reports five primary index scores:

• Verbal Comprehension: similarities and vocabulary.
• Visual Spatial: block design and visual puzzles.
• Fluid Reasoning: matrix reasoning and figure weights.
• Working Memory: holding and manipulating digits in mind.
• Processing Speed: fast, accurate symbol tasks such as coding.

The brochure notes that the WAIS-5 norm samples were collected in 2023 and 2024 and match the most recent US census on five key demographic variables. That norming step is what makes a score meaningful: your answers are compared with a sample built to look like the country.

Norms also go stale. Average performance on IQ tests rose through the 20th century, a pattern called the Flynn effect. A 2015 meta-analysis by Pietschnig and Voracek covering 271 samples and almost 4 million people in 31 countries estimated full-scale gains of about 0.28 IQ points per year between 1909 and 2013. A test scored with old norms will therefore overstate today’s test-takers, which is why publishers re-norm their tests every so often to keep 100 in the middle.

Clinical tests like the WAIS are administered one-to-one by a trained examiner and are used for diagnosis and educational decisions. Online tests are a different tool: quicker and more accessible, but not diagnostic. To see the kinds of items involved, browse our guide to IQ test questions with examples, and for a frank look at which web tests deserve your time, read are online IQ tests accurate?

What IQ predicts, and what it misses

IQ matters to researchers because it lines up with real-life outcomes more consistently than most psychological measures. In a 2015 review in Molecular Psychiatry, Robert Plomin and Ian Deary call intelligence one of the best predictors of education, occupation, health and mortality. The honest part is the size of those links:

Here is how to read those numbers:

• School: The meta-analysis by Roth and colleagues found a strong link, yet a correlation of .54 still leaves about 71% of the differences in grades to effort, teaching, motivation and everything else.
• Work: Older research ranked cognitive ability as the top hiring predictor. A 2022 reanalysis by Paul Sackett and colleagues argued earlier estimates were overcorrected; as the Society for Industrial and Organizational Psychology summarizes, cognitive ability came out at .31 and structured interviews led at .42. Useful, not decisive.
• Health: In the Wraw et al. study, IQ was measured with the military’s AFQT when participants were teenagers or young adults. The Calvin et al. meta-analysis pooled 16 studies and more than 1.1 million people, but in the studies that could adjust for education the link shrank by about half, a reminder that IQ travels with schooling and income.

These are averages across thousands of people. They say something real about groups and very little about what any single person will achieve.

What an IQ test doesn’t measure

The idea that one score can summarize many abilities goes back to Charles Spearman’s 1904 paper “General Intelligence,” Objectively Determined and Measured, which argued for a general factor, now called g, running through different mental tests. Researchers have since found hints of a similar factor in other species, from primates in our ranking of the smartest animals to Border Collies among the smartest dog breeds. IQ tests capture that general factor well. They don’t capture creativity, motivation, persistence, social and emotional skill (see IQ vs EQ), practical wisdom, expertise or character, and each of those shapes a life. For the other ways psychologists carve up the mind, from fluid vs crystallized ability to Gardner’s multiple intelligences, see our guide to types of intelligence.

Is IQ genetic?

Partly, and the details matter. Twin studies compare identical twins, who share all their genes, with fraternal twins, who share about half. Plomin and Deary report that the heritability of intelligence rises from about 20% in infancy to perhaps 80% in later adulthood. A study of about 11,000 twin pairs in four countries found it climbing from 41% at age 9 to 55% at 12 and 66% at 17, likely because children increasingly choose and shape their own experiences as they grow.

Heritability describes differences within a population, not a ceiling for you. “60% heritable” does not mean 60% of your IQ came from your genes. And environment clearly moves scores: Ritchie and Tucker-Drob’s 2018 meta-analysis of more than 600,000 participants found that each additional year of education raises IQ by roughly 1 to 5 points, calling education the most consistent, robust and durable method yet found for raising intelligence. For what else does and doesn’t move scores, see can you increase your IQ?

Find out where you fall on the IQ scale

You now have a working definition of IQ: a deviation score, centered on 100, with 15 points per standard deviation, calculated against people your age. The natural next question is where you land on that curve.

You can take the IQtonics IQ test: 40 questions across five areas (patterns, spatial reasoning, numbers, logic and memory), with a 20-minute time limit. Questions get progressively harder, and harder questions carry more points.

Your result is reported on the same mean-100, SD-15 scale described above (our methodology page explains how the test is built and scored), with your percentile and a cognitive profile showing your strengths, best area and areas to improve. Starting the test is free; your full results unlock with a trial membership, which renews automatically unless you cancel. It is an online test, not a clinical assessment, but you can read your score directly against the tables in this guide.