Question
What was the original IQ formula?
Short answer
The original IQ formula was mental age divided by chronological age, times 100. A 10-year-old who performed like an average 12-year-old scored 12 / 10 x 100 = 120. William Stern suggested the quotient and Lewis Terman adopted it for the Stanford-Binet. Modern tests no longer use it; they use the deviation IQ instead.
Want your own number? The test is 25 visual puzzles, about 12 minutes, no sign-up.
The ratio IQ, step by step
Early intelligence tests estimated a child's mental age: the age at which an average child performs at the same level. The intelligence quotient turned that into one number: mental age divided by chronological age, times 100 (Britannica, IQ).
| Child | Mental age | Age | Ratio IQ |
|---|---|---|---|
| Performs like an average 12-year-old | 12 | 10 | 120 |
| Performs at their own age | 10 | 10 | 100 |
| Performs like an average 8-year-old | 8 | 10 | 80 |
Under this formula 100 was average by definition (Britannica, IQ). The idea came from the German psychologist William Stern and was adopted by Lewis Terman for the Stanford-Binet (Britannica, intelligence test).
Try one · Logical Reasoning
Which tile completes the second pair?
Tap the option you think is right, or show the answer.
Show the answer
The missing panel shows a large hatched circle, with small solid shapes: a triangle at the bottom-right corner and a triangle at the left side (option 4).
How to solve it
- Compare the first two panels and name exactly what changed.
- The main shape and the small shapes swap forms: the main shape takes the form of the small ones, and the small ones take the form of the main shape.
- Nothing else changes.
- Apply the same change to the third panel: a large hatched triangle pointing up, with small solid shapes: a circle at the bottom-right corner and a circle at the left side.
- So the missing panel shows a large hatched circle, with small solid shapes: a triangle at the bottom-right corner and a triangle at the left side.
That was 1 puzzle. The full test has 25.
Why it was replaced
The ratio was built around children, whose abilities grow year by year, and it has no natural meaning for adults: a 40-year-old is not expected to perform twice as well as a 20-year-old. David Wechsler's answer, introduced with the Wechsler-Bellevue scale in 1939, was the deviation IQ: compare each person with people of the same age and express the result on a scale with mean 100 (Wikipedia: WAIS). The APA task force noted in 1996 that IQ originally meant the mental-age ratio but that the procedure is no longer used (Neisser et al., 1996), and Britannica notes that few tests still compute mental ages (Britannica, IQ).
The modern formula
Today's IQ is a standard score with mean 100 and standard deviation 15 within each age group (Wikipedia: Intelligence quotient). If z is how many standard deviations your performance sits above or below your age group's average, then IQ = 100 + 15 x z. One standard deviation above average is 115; two below is 70. You can turn any score into a percentile with the IQ percentile calculator.
Where to read more
See how IQ is calculated, deviation IQ, who invented the IQ test and a short history of IQ tests.
Sources
- Encyclopaedia Britannica. IQ, revised by Jeannette L. Nolen (read via Wayback Machine, December 2024) www.britannica.com/science/IQ
- Encyclopaedia Britannica. intelligence test (read via Wayback Machine, January 2025) www.britannica.com/science/intelligence-test
- Neisser, U., Boodoo, G., Bouchard, T. J., Jr., Boykin, A. W., Brody, N., Ceci, S. J., Halpern, D. F., Loehlin, J. C., Perloff, R., Sternberg, R. J., & Urbina, S. (1996). Intelligence: Knowns and unknowns. American Psychologist, 51(2), 77-101. doi.org/10.1037/0003-066X.51.2.77
- Wechsler Adult Intelligence Scale. Wikipedia. en.wikipedia.org/wiki/Wechsler_Adult_Intelligence_Scale
- Intelligence quotient. Wikipedia. en.wikipedia.org/wiki/Intelligence_quotient