Question
How is IQ calculated?
Short answer
IQ is calculated by comparing your test performance with a large sample of people your own age, then placing the result on a scale where that age group averages 100 with a standard deviation of 15. This is called a deviation IQ. A score of 115 means one standard deviation above your age group.
Want your own number? The test is 25 visual puzzles, about 12 minutes, no sign-up.
Step 1: a raw score
You answer the items. Each test turns your answers into a raw score, often the number correct, sometimes adjusted for time. On its own, a raw score means little: 30 out of 40 could be excellent on a hard test and ordinary on an easy one.
Step 2: compare with your age group
Test publishers give the test to a large standardization sample at each age. Your raw score is compared with the results of people your own age in that sample (Wikipedia: Intelligence quotient). This is why a 25-year-old and a 70-year-old with different raw scores can both score 100.
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 outlined triangle pointing up on its own (option 2).
How to solve it
- Compare the first two panels and name exactly what changed.
- The whole figure turns a quarter turn counterclockwise.
- The large shape becomes outlined.
- Nothing else changes.
- Apply the same changes to the third panel: a large hatched triangle pointing right on its own.
- So the missing panel shows a large outlined triangle pointing up on its own.
That was 1 puzzle. The full test has 25.
Step 3: put it on the scale
The comparison is expressed in standard deviations from the age-group mean, a number called a z-score. The IQ is then 100 plus 15 times that z-score. A z-score of +1 gives 115, which is higher than about 84.1% of people. A z-score of -1 gives 85. David Wechsler introduced this deviation IQ with the Wechsler-Bellevue scale in 1939 (Wikipedia: WAIS), and modern tests such as the Wechsler scales and the Stanford-Binet all report it.
Step 4: add a range
No test is perfectly precise, so clinical manuals report a confidence interval, often around plus or minus 5 points at 95% (Wechsler, 2008). A careful report gives you the range along with the number.
Why it works this way
Scaling to the age group makes scores comparable across ages and across tests that share the same scale. It also means an IQ is always relative: it describes where you stand, not how much you know. Read why the average IQ is 100 and whether an IQ score is a percentage for the common follow-ups, or the bell curve guide for the math.
Sources
- Intelligence quotient. Wikipedia. en.wikipedia.org/wiki/Intelligence_quotient
- Wechsler Adult Intelligence Scale. Wikipedia. en.wikipedia.org/wiki/Wechsler_Adult_Intelligence_Scale
- Wechsler, D. (2008). WAIS-IV Technical and Interpretive Manual. Pearson.