Modern IQ scores are calculated by comparing your raw score (the points you earned on the test) with the scores of a large, representative norming sample of people your age. Your position in that group is converted to a scale with an average of 100 and a standard deviation of 15, so an IQ of 115 means you scored one standard deviation above your age group's average. The older "ratio IQ" formula, mental age divided by chronological age times 100, is no longer used.
From raw score to IQ, step by step
Individually administered tests such as the WAIS-5 for adults or the WISC-V for children follow the same basic pipeline:
- Raw score. Each subtest produces a count of correct answers or points. Some subtests award extra points for speed.
- Age-based comparison. The raw score is looked up in a table built from the norming sample for your age band. A raw score that is excellent for a 75-year-old may be ordinary for a 25-year-old.
- Scaled score. Each subtest result becomes a scaled score with a mean of 10 and a standard deviation of 3.
- Composite. Scaled scores are summed and converted, through another table, into index scores and a full-scale IQ, each with a mean of 100 and a standard deviation of 15.
- Confidence interval. The examiner reports a range, typically at 90% or 95% confidence, because no test measures without error.
The rest of this article explains why the pipeline looks like that, starting with the formula it replaced.
The original formula: ratio IQ
Alfred Binet and Théodore Simon's tests in early-1900s France ranked children by mental age: the age at which an average child passes the same set of tasks. In 1912 the German psychologist William Stern proposed dividing mental age by chronological age, and Lewis Terman's 1916 Stanford–Binet multiplied the result by 100 to drop the decimal. That is the ratio IQ:
IQ = (mental age ÷ chronological age) × 100
A 10-year-old who performs like a typical 12-year-old gets (12 ÷ 10) × 100 = 120. A 10-year-old who performs like a typical 8-year-old gets 80.
The formula is intuitive for children but breaks down in two ways. First, performance on most reasoning tasks stops rising steeply in the late teens, so mental age levels off while chronological age keeps climbing: an ordinary 40-year-old would appear to decline every year. Second, the spread of ratio IQs was not the same at every age, so a score of 130 could be rarer at one age than at another. Both problems made ratio IQ unsuitable for adults and awkward for comparing children of different ages.
Deviation IQ: how scores are calculated today
David Wechsler's 1939 adult scale, the Wechsler–Bellevue, replaced the ratio with a deviation score: how far you sit from the average of your own age group, measured in standard deviations. The Stanford–Binet adopted deviation IQs in its 1960 revision, and every major modern test uses them.
The core arithmetic is a z-score rescaled to familiar numbers:
z = (your score − age-group mean) ÷ age-group standard deviation
IQ = 100 + 15 × z
Suppose adults aged 30 to 34 in the norming sample average 40 raw points on a test, with a standard deviation of 8. If you score 52, you are 12 points, or 1.5 standard deviations, above the mean. So z = 1.5 and IQ = 100 + 15 × 1.5 = 122.5. In a normal distribution, that is higher than about 93% of your age group.
Publishers do not apply this formula to raw scores literally. Raw scores are rarely perfectly bell-shaped, so the norming data are smoothed across age groups and normalized: each raw score is assigned the IQ that matches its percentile rank. The result behaves like the formula above but stays accurate when raw scores are skewed.
| IQ | Standard deviations from mean (z) | Share of age group scoring lower |
|---|---|---|
| 55 | −3 | 0.1% |
| 70 | −2 | 2.3% |
| 85 | −1 | 15.9% |
| 100 | 0 | 50% |
| 115 | +1 | 84.1% |
| 130 | +2 | 97.7% |
| 145 | +3 | 99.9% |
For every point from 55 to 145, see the IQ scale table. For why the bell shape appears at all, see the bell curve explained.
Why the composite can be more extreme than its parts
A full-scale IQ is not the simple average of the index scores. Because the subtests are correlated but not perfectly, scoring well above average on every one of them is rarer than scoring well above average on any single one. The composite table reflects that rarity, so a person whose index scores all sit around 120 will usually receive a full-scale IQ somewhat above 120. The same logic pulls consistently low profiles further below 100.
Not every test uses a standard deviation of 15
Most current tests use 15, but not all scales do. The Stanford–Binet used 16 through its fourth edition before moving to 15 in the SB5, and scores reported on the Cattell scale use 24. A 148 on a scale with a standard deviation of 24 represents the same rarity, about the 98th percentile, as a 130 on the standard scale. When you compare scores from different tests, compare percentiles, not the raw IQ numbers.
What a norming sample is, and why it decides everything
The conversion tables are only as good as the people behind them. A norming (or standardization) sample is a group tested under controlled conditions to define what "average" means. For the WAIS-IV, published in 2008, the publisher tested 2,200 adults aged 16 to 90, divided into age bands and stratified to match US census proportions for sex, race and ethnicity, education level and geographic region. The WISC-V used a similar design with 2,200 children.
Representativeness matters more than size. Fifty thousand self-selected volunteers who chose to take an online test are unlikely to mirror the population on age, education or interest in puzzles, and nobody can say in which direction or by how much without testing a representative group. Compare everyone against that crowd and you are using an unknown yardstick.
Norms are also tied to testing conditions. Clinical norms assume a trained examiner, standard instructions, a quiet room and fixed time limits. Change the conditions, for instance by removing time limits or letting people test at home, and the published norms no longer strictly apply.
Why tests are re-normed: the Flynn effect
Through much of the 20th century, average raw performance on IQ tests rose in many countries, by roughly 3 IQ points per decade in James Flynn's widely cited estimates. A 2015 meta-analysis by Pietschnig and Voracek, covering data from 1909 to 2013, confirmed large gains worldwide but found them slowing in recent decades. Some countries, including Norway, have since recorded declines among more recent birth cohorts.
The practical consequence is norm drift. If a test's norms were collected 20 years ago and scores had been rising about 3 points per decade, today's test-takers would be compared with a weaker reference group and score roughly 6 points too high. That is why publishers periodically re-norm their tests (the WAIS-5, published in 2024, replaced the WAIS-IV from 2008) and why clinicians in high-stakes settings, such as intellectual disability evaluations, pay attention to the age of the norms. The causes are covered in our article on the Flynn effect.
Percentiles and IQ scores are two views of the same result
On a properly normed test, an IQ score and a percentile carry identical information. IQ 115 and "84th percentile" both say you outscored about 84% of your age group. The IQ number is convenient for statistics, because equal steps are equal distances along the bell curve. The percentile is easier to read, because it says directly how many people you outscored.
The two differ in one useful way: percentiles bunch up at the extremes. Going from IQ 100 to 115 moves you 34 percentile points; going from 130 to 145 moves you just over 2. Our guide to interpreting your IQ results has a conversion table in both directions.
Why our test reports a percentile, not an IQ
Turning a raw score into a genuine IQ requires the representative norming study described above. We have not run one, so we do not claim to give you a clinical IQ. Our test works out where your result falls among the people who have taken the same form, here or on My Path, where the same test runs — a percentile against our own respondents — and its result page converts that position to the mean-100 scale as an estimated IQ, labelled as an estimate and shown with a range.
- Your overall result is a weighted composite of six domains modeled on the Cattell–Horn–Carroll framework. Each domain is weighted by its typical loading on general ability, so fluid reasoning counts most and processing speed least.
- The comparison group is still small, dozens of sittings per form, so percentiles will shift as more people take the test.
- The result is shown as a range: ±12 percentile points on the 12-question short form and ±7 on the 60-question full form. These are deliberately conservative fixed widths, not a measured standard error.
- The test is untimed, which is one more reason clinical IQ norms could not be applied to it.
That makes the result an honest, rough comparison rather than a clinical score. It is not a diagnosis and is not suitable for hiring or admissions. Our methodology page covers the details.
What the calculation cannot tell you
A deviation IQ is exact arithmetic applied to an inexact measurement. Even the best clinical tests report scores with a confidence interval several points wide, and the descriptive labels attached to score ranges ("Average," "Superior," "Extremely High") differ between tests and between editions of the same test. The number summarizes performance on a particular set of tasks, on a particular day, compared with a particular group of people. Read it with all three in mind.