IQ Percentile Calculator
HealthConvert an IQ score into a percentile rank instantly. See how a score compares to the general population using the standard mean-100, SD-15 IQ distribution.
Percentile Rank
50
Standard Deviations from Mean (z-score)
0
Rarity (1 in N People)
2
What is a IQ Percentile?
The IQ Percentile Calculator converts a raw IQ score into a percentile rank, showing exactly where that score falls relative to the general population. IQ scores are standardized so the population mean is 100 and the standard deviation is 15 โ this calculator uses that standard normal distribution to work out what percentage of people would be expected to score at or below any given value.
This is a companion tool to this site's other self-assessment calculators, such as the Happiness Calculator, for anyone curious about how a specific score compares statistically rather than just what the raw number means on its own.
How to use this IQ Percentile calculator
- Enter your IQ score in the IQ Score field, or drag the slider to the value from your test report.
- The calculator instantly computes your Percentile Rank, z-score, and Rarity.
- Use the swap or copy button on the result card to save or share your result.
- Compare different scores by changing the input value to see how percentile changes across the range.
- Read the z-score if you want to understand exactly how many standard deviations your score is from the population mean of 100.
Formula & Methodology
The calculator uses the standard IQ distribution, where scores are normed to a mean (ฮผ) of 100 and a standard deviation (ฯ) of 15: z = (IQ โ 100) รท 15 The z-score is then converted to a percentile using the cumulative distribution function (CDF) of the standard normal distribution, approximated numerically for speed and accuracy. Worked example โ an IQ score of 125: z = (125 โ 100) รท 15 = 1.67 Percentile โ ฮฆ(1.67) ร 100 = 95.2% This means a score of 125 is higher than approximately 95% of the population, or roughly 1 in 21 people.
Frequently Asked Questions
An IQ percentile tells you what share of the population scores at or below a given IQ score. A percentile of 84 means the score is higher than 84% of people tested, based on the standard IQ distribution with a mean of 100 and a standard deviation of 15.
First calculate the z-score as (IQ score โ 100) รท 15, then convert that z-score into a percentile using the cumulative standard normal distribution. This calculator applies both steps automatically using a numerical approximation of the normal distribution function.
The IQ score is a standardized number centered on 100, while the percentile expresses the same result as a ranking against the population. Two people can have IQ scores 15 points apart yet very different percentile gaps, because the normal distribution is denser near the middle than at the extremes.
Enter your IQ score into the input field and the calculator instantly returns your percentile rank, z-score, and an estimate of how rare that score is in the general population.
Yes โ an IQ of 115 corresponds to roughly the 84th percentile, meaning it's higher than about 84% of the population, since it sits exactly one standard deviation (15 points) above the mean of 100.
A z-score of 0 means the IQ score is exactly at the population mean of 100, which corresponds to the 50th percentile โ right in the middle of the distribution.
Scores more than two standard deviations from the mean (below 70 or above 130) are relatively rare, generally affecting only about 2-3% of the population combined at each extreme, because the normal distribution's tails thin out quickly.
Most modern IQ tests (Wechsler, Stanford-Binet, and similar) are normed to a mean of 100 and a standard deviation of 15, which is the standard this calculator uses, though the underlying test questions and administration vary by publisher and country.
An individual's raw cognitive test score can shift somewhat with retesting, practice effects, age, and the specific test used, so IQ percentile is best treated as a snapshot from a particular test rather than a fixed lifetime number.
No โ IQ percentile reflects performance on a specific type of standardized cognitive test and is only one factor among many (including effort, opportunity, and emotional intelligence) that influence real-world outcomes.
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