The IQ scale and its ranges, explained

The scale is a bell curve with fixed landmarks

Every standardized IQ score is a position on a normal curve. Once the mean is set to 100 and the standard deviation to 15, the landmarks are arithmetic: one standard deviation above the mean is 115, two is 130, three is 145. The same distances below the mean give 85, 70 and 55. Because the curve is symmetric, the share of people above 115 equals the share below 85, about 16% each.

• 70: about the 2nd percentile; two standard deviations below the mean.
• 85: about the 16th percentile; one standard deviation below.
• 100: the 50th percentile; the middle of the norm sample.
• 115: about the 84th percentile; one standard deviation above.
• 130: about the 98th percentile; the region most high-IQ societies use as an entry line.
• 145: about the 99.9th percentile; roughly one person in a thousand.

Why range labels differ between tests

Test manuals divide the curve into bands and name them. One publisher calls 90–109 "average" and 110–119 "high average"; another uses "superior" where a third says "well above average"; older manuals used labels that are no longer considered acceptable. The bands are conventions for reporting, not categories of person, and the same score can carry a different word depending on the manual. When you compare two reports, compare percentiles, not labels.

Every score has an error band

Test manuals publish a standard error of measurement, commonly around three to five points for a full-scale score. A report therefore states a confidence interval, for example "108, 95% confidence interval 103–113". A score is a range with a most likely value, not a point. Two scores that differ by less than the interval width are not distinguishable, and a score from a single sitting can move by a few points on another day.

Standard deviation 15 or 16

Most current tests use a standard deviation of 15. Some editions of the Stanford-Binet used 16, which stretches the scale slightly: a score of 132 on an SD-16 test sits at the same percentile as 130 on an SD-15 test. The converter below lets you choose either, because the right value is the one printed in the report you are reading.

Convert a standardized score to a percentile

Enter a score from a real, professionally administered test report to see the percentile and the approximate "one in N" rank it implies. The converter does not estimate your IQ and does not remember what you type; it applies the normal distribution to a number you already have.