IQ Percentile Calculator

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Use this IQ Percentile Calculator to convert an existing standardized IQ-style score into an estimated percentile rank. The calculator uses a mean of 100 and a selected standard deviation of 15 or 16.

Calculation Method

First calculate the z-score:

z = (IQ score − 100) ÷ standard deviation

Then convert the z-score into a percentile:

Percentile = Φ(z) × 100

The percentage above the score is:

% above = 100 − percentile

Example

For an IQ score of 115 on a scale with standard deviation 15:

z = (115 − 100) ÷ 15 = 1.00

A z-score of 1 corresponds to approximately the 84.13th percentile.

Approximately 15.87% of the reference distribution is above that score.

Important Note

This calculator does not administer an IQ test or measure intelligence. It only converts an existing standardized score using a normal-distribution model.

Official test reports may use test-specific norms, age groups, confidence intervals, and scoring rules that differ from this estimate. Do not use this calculator alone for diagnosis, educational placement, disability, employment, or legal decisions.

Sources

• Penn State STAT 200 — Standard Normal Distribution and IQ Score Example
• NCBI Bookshelf — Overview of Psychological Testing