Percentile Calculator
Find the value at any percentile of your data, or work backwards to the percentile rank of a score. Three standard methods, clearly labelled.
Percentiles in practice
Percentiles describe position without assuming any particular shape. Growth charts use them (a child at the 75th percentile for height is taller than three in four children of the same age), as do standardised tests, website response times (“p95 latency”) and salary surveys.
The 25th, 50th and 75th percentiles are the quartiles, and the 50th is the median. If you know the mean and standard deviation of normally distributed data, a z-score plus the z-table gives the percentile without the raw data.
Frequently asked questions
What does the 90th percentile mean?
It is the value below which about 90% of the data fall. If your test score is at the 90th percentile, you scored higher than roughly 90% of test-takers. It is not the same as scoring 90%.
Why do different calculators give different percentiles?
There are several accepted definitions (Hyndman and Fan catalogued nine). The inclusive method matches Excel PERCENTILE.INC, Google Sheets PERCENTILE and R’s default. The exclusive method matches PERCENTILE.EXC and Minitab. Nearest rank never interpolates and is common in textbooks. The differences shrink as the data set grows.
How do I calculate a percentile by hand?
Sort the data. For the inclusive method, compute the position h = (n − 1) × p/100 + 1. If h is a whole number, the percentile is that value; otherwise interpolate between the values on either side. For p = 90 and n = 25, h = 22.6, so take the 22nd value plus 0.6 of the gap to the 23rd.
What is a percentile rank?
The reverse question: given a value, what percentage of the data is below it? This page uses the mid-rank formula (count below + half the count equal) ÷ n × 100, which is standard for test scores.
Can I find a percentile from a mean and standard deviation?
Yes, if the data are approximately normal. Convert the value to a z-score and look up its cumulative area. The z-score calculator does this directly.