Step 1: the raw score
Every IQ test starts with a raw score: the number of items you answered correctly, sometimes with bonus points for speed. A raw score means nothing on its own. Eighteen correct out of twenty-five could be excellent on a hard test and ordinary on an easy one.
Rules for the raw score matter too. On timed tests an item left unanswered when the clock runs out counts as wrong. Some modern tests go further and weight items by difficulty using item response theory, so solving a hard item counts for more than solving an easy one, and two people with the same number correct can end up with slightly different scores. Either way, the raw score is only the input; the IQ comes from the next step.
Step 2: the deviation IQ formula
To make a raw score meaningful, it is compared with the raw scores of a norm sample of people your age. Two numbers describe that group: its mean and its standard deviation (SD). Your position is expressed as a z-score:
z = (your raw score − mean of your age group) ÷ SD of your age group
The z-score is then placed on the IQ scale:
IQ = 100 + 15 × z
A worked example: suppose adults aged 35 to 44 average 14 correct out of 25, with an SD of 4. If you score 18, your z is (18 − 14) ÷ 4 = 1.0, and your IQ is 100 + 15 × 1.0 = 115. Score 10 and z is −1.0, an IQ of 85. In practice publishers use lookup tables rather than the formula directly, because real score distributions are not perfectly normal, but the logic is the same. This method, introduced by David Wechsler in 1939, is called the deviation IQ.
Step 3: norms and age groups
A score is only as good as its norm sample. Clinical tests such as the WAIS-5 and Stanford-Binet 5 are normed on roughly 2,000 or more people chosen to match the census by age, sex, ethnicity, region and education. Adults are split into age bands of a few years each, so you are compared with your own generation.
Norms also age. Raw scores across many countries rose by about 3 IQ points per decade during the 20th century (the Flynn effect), so a test normed 20 years ago gives scores that are several points too high. Publishers re-norm their tests every 10 to 20 years for that reason.
The old formula: mental age ÷ age × 100
Early tests used the ratio IQ: mental age divided by chronological age, times 100. A 10-year-old who performed like an average 12-year-old scored 120. The formula worked poorly for adults, whose mental age stops rising in the late teens, and it gave different spreads of scores at different ages. It survives only in the name "quotient" and in old reports of very high childhood scores.
Measurement error: SEM and confidence intervals
No test measures perfectly. The standard error of measurement (SEM) estimates how far a measured score is likely to sit from your true score. It depends on the test's reliability (r):
SEM = 15 × √(1 − r)
- A full clinical battery, with full-scale reliability of about 0.96 to 0.98, has an SEM of about 2 to 3 points.
- A short test with r = 0.90 has an SEM of about 4.7 points.
A 95% confidence interval is roughly the score ± 1.96 SEM: about ±4 to ±6 points for a clinical test and about ±9 for a short one. A measured 113 on a short test therefore means "probably between 104 and 122". Serious reports state this interval. If a test gives you a single number with no range, it is hiding the uncertainty, not removing it.
How a full-scale IQ combines subtests
Clinical batteries run 10 or more subtests. Each raw subtest score is converted to a scaled score with a mean of 10 and an SD of 3, the scaled scores are added up within each area, and the sums are converted to index scores and a full-scale IQ, each on the 100 and 15 scale. Our tests follow the same deviation logic, with provisional norms that are refitted as data comes in; the full detail is on our methodology page.
Sources
Wechsler, D. The Measurement of Adult Intelligence. Williams and Wilkins, 1939.
Wechsler, D. WAIS-IV Technical and Interpretive Manual. Pearson, 2008.
Flynn, J. R. "Massive IQ gains in 14 nations: what IQ tests really measure". Psychological Bulletin, 1987.
American Educational Research Association et al. Standards for Educational and Psychological Testing. AERA, 2014.
Frequently asked questions
How is IQ calculated?
Your raw score is compared with a norm sample of people your age. The difference from their average, in standard deviations (z), is converted with IQ = 100 + 15 × z.
How is IQ measured?
With a standardised test of reasoning, verbal ability, working memory and processing speed, given under fixed conditions and scored against age norms. Clinical tests take roughly 45 to 90 minutes with a psychologist.
How is IQ scored?
Correct answers give a raw score, which is converted to a scaled score using norm tables for your age. Full batteries combine subtest scaled scores into index scores and a full-scale IQ.
How is IQ determined for adults?
The same way as for children, but against adult norms split into age bands, so a 60-year-old is compared with other people around 60. Tests such as the WAIS-5 cover ages 16 to 90.
How do IQ tests work?
They present items of increasing difficulty in several areas, count how many you solve, and rank that performance against a representative sample of your age group. The rank is expressed on a scale with mean 100 and SD 15.
What does IQ actually measure?
Mainly general reasoning ability: the common factor behind performance on very different mental tasks. It does not measure knowledge in a particular field, creativity or personality.
Does IQ measure intelligence?
It measures an important part of it, the general reasoning and learning ability psychologists call g. Many abilities people associate with intelligence, such as wisdom or social insight, are outside its scope.