How this calculator works
The score is centred on the entered mean and scaled by the reference standard deviation. A standard normal cumulative distribution converts the result to a lower-tail percentile. This is a mathematical model, not a substitute for the age-specific norms and confidence interval in a psychological report. The result is an estimate for information only and is not medical advice.
Formula
z = (score - mean)/standard deviation; percentile = 100 x Phi(z). The fraction above is 1 - Phi(z).
Worked example
With mean 100 and SD 15, a score of 115 gives z = 1 and percentile 84.1345%. A score of 100 gives z = 0 and percentile 50%.
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Frequently asked questions
Which standard deviation should I choose?
Use the scale stated in the original test report. A different standard deviation changes the percentile associated with the same numerical score.
Does a high percentile diagnose anything?
No. Test validity, administration, age norms and measurement uncertainty require professional interpretation.
Why can a displayed percentile reach 100%?
Rounding and numerical tail limits can display 100% for extreme scores. That does not mean no one could score higher.