How this calculation works
The IQ Percentile Calculator converts raw intelligence quotient (IQ) scores into statistical population percentile ranks and rarity frequencies based on the standard normal Gaussian distribution curve.
Mathematical formula and logic
Z-score = (IQ - 100) / Standard Deviation. Percentile = Φ(Z) × 100, where Φ is the cumulative standard normal distribution function.
Worked example
An IQ score of 130 on the Wechsler scale (SD 15) corresponds to a Z-score of +2.00, placing the individual in the 97.72nd percentile (1 in 44 people). An IQ of 145 represents the 99.87th percentile (1 in 741 people).
Calculation assumptions
- Population mean IQ is normalized to 100.
- Scores follow a standard normal Gaussian bell curve distribution.
Frequently asked questions
What IQ score is required to join Mensa?
Mensa requires a score at or above the 98th percentile on an approved intelligence test, which corresponds to an IQ of 130 or higher on the Wechsler scale (SD 15) or 132 on Stanford-Binet (SD 16).
What is an average IQ score?
By definition, an IQ score of 100 is the exact median population average. Scores between 90 and 109 fall within the Normal / Average range (representing approx 50% of the population).
What percentage of the population has an IQ above 140?
On a standard SD 15 test, an IQ of 140 corresponds to the 99.62nd percentile, representing approximately 1 in 261 people (less than 0.4% of the population).
What is the Flynn Effect in IQ testing?
The Flynn effect refers to the observed rise in average IQ scores over generations, requiring test publishers to periodically re-standardize test norms to keep the average at 100.
What is the difference between SD 15 and SD 16 tests?
Wechsler scales use a standard deviation of 15, while Stanford-Binet historically used 16. A score of 130 on SD 15 equals a score of 132 on SD 16 (both representing +2.0 standard deviations).