Percentile Rank Calculator
Where a value sits in a dataset — the percentage of observations at or below it, by each of the standard conventions.
Percentile rank is the share of the data at or below a value.
How the percentile rank calculator works
Percentile rank is the share of the data at or below a value. Three conventions exist and they disagree: the strict definition counts only values below; the weak definition includes ties; and the mid-rank definition counts half the ties, which is the one most test scores use.
The calculator reports all three, because "the 90th percentile" means a different number depending on which your source used.
Formula: PR = (values below + ½ × ties) / n × 100
Worked examples
| Inputs | Percentile rank (mid-rank) | Note |
|---|---|---|
| 80 in a set of ten scores | 65% | 65th percentile by mid-rank |
| The lowest value | 5% | 5th percentile by mid-rank |
| A value not in the set | 90% | 90th percentile |
FAQFrequently asked questions
What is a percentile rank?
The percentage of the data at or below a value. A score at the 90th percentile beat 90% of the group.
Why do sources disagree about the same value?
Because there are three conventions for handling ties. Standardised tests usually use the mid-rank; some software uses strict.
Is the 50th percentile the median?
Yes, by the mid-rank definition — that is what makes it the natural convention.
Can a value be at the 100th percentile?
Only under the weak definition. Mid-rank caps the highest value below 100 whenever it is unique.
How does this differ from a percentage score?
Completely. 80% correct on a test is a raw score; the 80th percentile means you beat four fifths of the candidates. An easy test makes the first high and the second low.
Where these figures come from
- NIST Digital Library of Mathematical Functions — reference definitions for elementary and special functions
- Wolfram MathWorld — definitions and formulas for every topic on this page
- NIST/SEMATECH e-Handbook of Statistical Methods — the statistical formulas (mean, variance, z, confidence intervals, sample size)
- Australian Curriculum (ACARA) — Mathematics — the terms and methods taught in Australian schools
Last checked: September 2026. Formulas are fixed by mathematics and do not change with tax years or regulations.