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IQ Percentile Calculator

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Convert 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.

Reviewed by the thecalcu.com team ยท Last updated July 20, 2026

40160

Percentile Rank

50
Standard Deviations from Mean (z-score)
0
Rarity (1 in N People)
2

This calculator computes your Percentile Rank, Standard Deviations from Mean (z-score), Rarity (1 in N People) from the values you enter.

Inputs
IQ Score
Outputs
Percentile RankStandard Deviations from Mean (z-score)Rarity (1 in N People)

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, 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.

Why Use an IQ Percentile Calculator?

A raw IQ number on its own doesn't tell you much without context, a score of 120 sounds high, but knowing it places someone in roughly the top 9% of the population is far more meaningful. This calculator removes the guesswork of manually applying the normal distribution formula, giving an instant, statistically grounded percentile from any IQ score.

It's also useful for understanding score reports from cognitive assessments, school gifted-program eligibility criteria, or general curiosity about how common or rare a particular score actually is.

Who Should Use This Calculator?

  • Students and parents reviewing a cognitive assessment score report and wanting to understand it in percentile terms.
  • Psychology and statistics students learning how standardized scores map onto the normal distribution.
  • Anyone curious about how their test result compares to the general population.
  • Writers and researchers who need a quick, accurate score-to-percentile conversion for reference.

What Insights Does the IQ Percentile Calculator Give You?

The calculator returns three figures. The Percentile Rank is the headline result, the percentage of the population scoring at or below the entered IQ. The z-score shows how many standard deviations the score sits from the mean of 100, which is the raw statistical building block behind the percentile. The Rarity (1 in N) figure translates the percentile into an easier-to-grasp statement of how many people, on average, would need to be sampled to find one score this far from average (in either direction).

How to use this IQ Percentile calculator

  1. Enter your IQ score in the IQ Score field, or drag the slider to the value from your test report.
  2. The calculator instantly computes your Percentile Rank, z-score, and Rarity.
  3. Use the swap or copy button on the result card to save or share your result.
  4. Compare different scores by changing the input value to see how percentile changes across the range.
  5. Read the z-score if you want to understand exactly how many standard deviations your score is from the population mean of 100.
Show formula & methodology โ†“Show less โ†‘

Formula & Methodology

The calculator uses the standard IQ distribution, where scores are normed to a mean (ฮผ) of 100 and a standard deviation (ฯƒ) of 15:

z = (IQ โˆ’ 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, an IQ score of 125:

z = (125 โˆ’ 100) รท 15 = 1.67

Percentile โ‰ˆ 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

What is an IQ percentile?
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.
What is the formula for converting IQ to percentile?
First calculate the z-score as (IQ score โˆ’ 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.
What is the difference between IQ score and IQ percentile?
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.
How do I convert my IQ score to a percentile?
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.
Is an IQ of 115 above average?
Yes, 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.
What does a z-score of 0 mean for IQ?
A z-score of 0 means the IQ score is exactly at the population mean of 100, which corresponds to the 50th percentile, right in the middle of the distribution.
How rare is a very high or very low IQ score?
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.
Are IQ tests standardized the same way worldwide?
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.
Can my IQ percentile change over time?
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.
Does a higher IQ percentile mean guaranteed success?
No, 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.
Also known as
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