How IQ Is Calculated – From Raw Score to IQ Number

The Original Ratio IQ Method

The very first approach to calculating IQ was the ratio method, introduced by German psychologist William Stern in 1912 and popularized by Lewis Terman's Stanford-Binet test. The formula was straightforward:

IQ = (Mental Age / Chronological Age) × 100

A child's "mental age" was determined by the level of test items they could successfully complete. If an 8-year-old child performed at the level typical of a 10-year-old, their mental age was 10, and their IQ would be calculated as (10 / 8) × 100 = 125. If they performed at their own age level, their IQ was exactly 100.

The ratio method worked reasonably well for children, but it had a critical flaw: it became meaningless for adults. Cognitive development does not continue to accelerate linearly throughout life, so the concept of "mental age" breaks down past adolescence. A 40-year-old who performs like a 50-year-old is not proportionally smarter in the same way a child who is two years ahead might be. This limitation led psychologists to develop a better approach.

The Modern Deviation IQ Method

David Wechsler, the creator of the widely used Wechsler intelligence scales, introduced the deviation IQ system in 1939. Instead of comparing mental age to chronological age, this method compares your performance to a same-age reference group using statistical standard scores.

Here is how it works in principle:

1. Collect raw scores from a norming sample. The test publisher administers the test to thousands of people who are carefully selected to represent the general population. Each person's raw score (total correct answers) is recorded.
2. Calculate the mean and standard deviation. For each age group in the norming sample, the average raw score and the spread of scores (standard deviation) are calculated.
3. Convert your raw score into a z-score. A z-score tells you how many standard deviations above or below the mean your performance falls. The formula is: z = (your raw score − mean raw score) / standard deviation of raw scores.
4. Transform the z-score into an IQ score. The z-score is rescaled to a distribution with a mean of 100 and a standard deviation of 15: IQ = 100 + (z × 15).

For example, if the norming group's average raw score is 50 with a standard deviation of 10, and you scored 60, your z-score would be (60 − 50) / 10 = 1.0. Your IQ would be 100 + (1.0 × 15) = 115. You performed one standard deviation above the mean, placing you at approximately the 84th percentile.

Standard Scores and Standard Deviation

The concept of standard deviation is central to IQ calculation. Standard deviation measures how spread out scores are from the average. A small standard deviation means most scores are clustered close to the mean; a large one means scores are more widely scattered.

Most major IQ tests (WAIS, WISC, and Stanford-Binet 5) use a standard deviation of 15 points. This means:

• An IQ of 115 is one standard deviation above the mean (84th percentile).
• An IQ of 130 is two standard deviations above the mean (98th percentile).
• An IQ of 85 is one standard deviation below the mean (16th percentile).
• An IQ of 70 is two standard deviations below the mean (2nd percentile).

However, not all tests use the same standard deviation. The original Cattell Culture Fair Intelligence Test used a standard deviation of 24 points, meaning a Cattell IQ of 132 is roughly equivalent to a Wechsler IQ of 120. When comparing scores from different tests, you must account for the scale being used. Our guide on types of IQ tests explains the major test families and their scoring conventions.

How Norming Groups Work

The accuracy and fairness of an IQ score depend entirely on the quality of the norming group. A norming group (also called a standardization sample) is the population of people whose test results are used to establish the scoring tables. If the norming group is not representative, the resulting scores will be biased.

Major test publishers invest heavily in norming. For example, when Pearson developed the WAIS-IV, the norming sample included 2,200 adults stratified by age, sex, education level, race/ethnicity, and geographic region to match U.S. Census data. Separate norms were computed for 13 different age bands, ensuring that a 25-year-old is compared to other adults in their twenties, and a 70-year-old is compared to their own age peers.

This age-banding is important because cognitive abilities naturally shift across the lifespan. Processing speed tends to peak in early adulthood and decline gradually, while vocabulary knowledge continues to grow well into middle age. Without age-specific norms, older adults would appear to have lower IQs simply because they are being compared to younger, faster test-takers – even though their overall cognitive ability may be perfectly healthy for their age.

Subtest Scores and Index Scores

On comprehensive IQ tests like the WAIS, the calculation is more complex than a single raw-to-IQ conversion. The test is divided into multiple subtests, each producing its own raw score. These raw scores are first converted to scaled scores with a mean of 10 and a standard deviation of 3.

Related subtests are then grouped into composite index scores. For instance, the WAIS-IV combines Similarities, Vocabulary, and Information into the Verbal Comprehension Index (VCI). Each index score uses the same mean-100, SD-15 scale as the Full-Scale IQ.

Finally, the index scores (or a weighted combination of subtest scaled scores) are summed and converted into the Full-Scale IQ (FSIQ) using a separate norming table. The FSIQ represents overall cognitive ability, but the individual index scores can be equally informative – they reveal whether a person has a relatively even cognitive profile or significant strengths and weaknesses across domains.

Why Different Tests Give Different Scores

It is common for someone to receive slightly different IQ scores on different tests, and this does not necessarily mean one test is wrong. Several factors explain these discrepancies:

• Different content. A test heavy on verbal reasoning may produce a different score than one focused on non-verbal patterns, especially if you have uneven cognitive strengths. Learn more in our comparison of IQ test types.
• Different norming samples. If one test was normed in the U.S. and another in the U.K., the reference groups differ, and so will the scores.
• Different standard deviations. As noted above, a Cattell SD-24 score is not directly comparable to a Wechsler SD-15 score without conversion.
• Flynn effect and norming date. Tests normed with older data tend to produce higher scores because the average population performance has risen over time. A score of 110 on a test normed in 2000 might be equivalent to 107 on the same test re-normed in 2020.
• Measurement error. Every test has a standard error of measurement. Small score differences (5 points or less) are usually within the normal range of measurement imprecision and should not be over-interpreted.

For this reason, psychologists always consider IQ scores as estimates, not precise measurements. Our article on IQ test accuracy and limitations explores this topic in greater depth.