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Use this IQ Percentile Calculator to convert an IQ score into percentile rank, percent above, and percent below. It is useful when you already have a standardized IQ score and want to understand how that score compares with the broader norm group on the matching test scale.

Reviewed by: AjaxCalculators Editorial Team
Last updated: April 22, 2026
Method source: Normal-distribution percentile conversion using a fixed mean of 100 and the selected standard deviation (typically 15 or 16)
Editorial standards: AjaxCalculators Editorial Policy

What This IQ Percentile Calculator Calculates

This calculator converts an existing IQ-style standardized score into:

• Percentile rank
• % below your score
• % above your score

It supports two common score scales:

• SD = 15 — used by most modern IQ-style scales such as Wechsler and SB5
• SD = 16 — used by some older Stanford-Binet scales such as SB-IV

How the IQ Percentile Calculator Works

This page assumes the IQ score follows a normal distribution with:

Mean = 100

It then standardizes the score with the chosen standard deviation:

z = (IQ − 100) / SD

After that, it converts the z-score into a percentile using the cumulative distribution function of the standard normal distribution:

Percentile = Φ(z) × 100%

It also reports:

• % below = percentile
• % above = 100% − percentile

This means the page is not “testing” intelligence. It is converting a score that already came from a standardized test into a rank-style interpretation.

Assumptions and Important Notes

• This calculator is a score-to-percentile converter, not an IQ test.
• It assumes the score comes from a properly normed test centered at 100.
• The correct percentile depends on choosing the same SD scale used by the actual test.
• Most modern IQ tests use SD = 15.
• Some older Stanford-Binet scales used SD = 16, which can produce slightly different percentile ranks for the same raw IQ number.
• Percentile rank is only meaningful if the original score itself is valid and correctly normed.

Worked Example

Example A: IQ 115 on SD = 15

Step 1: Compute the z-score
z = (115 − 100) / 15 = 1.00

Step 2: Convert z to percentile
A z-score of about 1.00 corresponds to about the 84th percentile.

Step 3: Interpret the result
That means about 84% of the norm group scores at or below 115, and about 16% score above it.

Example B: IQ 115 on SD = 16

Step 1: Compute the z-score
z = (115 − 100) / 16 = 0.9375

Step 2: Convert z to percentile
That gives a percentile slightly lower than the SD = 15 result.

This example shows why the selected SD matters. The same IQ number can map to different percentile ranks on different norm scales.

How to Use This IQ Percentile Calculator

1. Enter the IQ score you already have.
2. Select the correct standard deviation used by that test.
3. Review the percentile rank, percent below, and percent above.
4. Use the result only as a norm-based comparison, not as a diagnosis or as proof of ability in all settings.

How to Interpret the Result

Percentile rank tells you what percentage of the comparison group scored at or below that IQ value.

% below your IQ tells you the same thing in plain-language form.

% above your IQ tells you what percentage of the norm group scored higher.

For example, being at the 95th percentile does not mean “95% correct.” It means the score is higher than about 95% of the people in the relevant norm group.

Practical Uses of an IQ Percentile Calculator

• convert a standardized IQ score into a percentile rank
• compare how the same IQ score looks on SD 15 versus SD 16 scales
• understand “top x%” or “bottom x%” from a normed score
• check percentile interpretation for school, psychology, or giftedness discussions
• review how normal-distribution scoring works in a simple way

References

1. Penn State STAT 200: IQ scores commonly modeled as normal with mean 100 and SD 15
2. NIST: cumulative distribution function of the standard normal distribution
3. SB5 publisher page
4. SB5 review noting mean 100 and SD 15
5. SB-IV review noting mean 100 and SD 16

Related Calculators

• Percentile Calculator
• Z Score Calculator
• Standard Deviation Calculator
• Variance Calculator
• Mean Median Mode Calculator

Disclaimer: This calculator is for educational and norm-interpretation use only. It does not measure IQ, diagnose any condition, or replace a professionally administered and interpreted cognitive assessment.