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Converts a standard IQ score into a percentile rank using the normal distribution, per the standard test-standardization convention used by modern IQ tests: scores are scaled to a mean of 100 and a standard deviation of 15, and are approximately normally distributed across the population. This is a well-defined statistical calculation. For general reference and educational purposes only — not a diagnostic or clinical psychological assessment. Consult a qualified psychologist for actual IQ testing and interpretation.
How it works
Enter an IQ score. The tool converts it to a z-score using the mean-100/SD-15 convention, then applies the standard normal cumulative distribution function to compute a percentile rank.
- Enter iQ score.
- Click Calculate to see your results.
Examples
IQ 100
z = 0, percentile = 50th (exactly average).
IQ 115
z = 1 (one standard deviation above the mean), percentile ≈ 84th.
Who should use it
- Understanding what an IQ score means relative to the population.
- Statistics and psychometrics education.
Industry applications
- Psychometrics and statistics education
- General reference
Advantages
- Statistically well-defined, exact calculation (no reference-data table needed).
- Transparent step-by-step z-score and CDF calculation.
Limitations
- Assumes a perfectly normal population distribution, which is an idealization.
Common mistakes to avoid
- Assuming all IQ tests use exactly mean 100/SD 15 — most modern tests do, but always check the specific test's scaling convention.
Best practices
- Use an IQ score from a properly administered, standardized test for a meaningful percentile conversion.
Tips
- A percentile of 84 means the score is higher than about 84% of the population — it does not mean the person answered 84% of questions correctly.