OneTaskBy Tim King · Updated
Percentile Calculator
Find the 90th Percentile From a List of Numbers, Interpolated or Nearest-Rank
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How the Percentile Calculator works
This percentile calculator works either way round. Paste a list of numbers and find the value at any percentile, such as the 90th, or enter a value and find its percentile rank, the share of the data that falls below it. Both common methods are shown with the working.
The pth percentile is the value below which p percent of the data falls. The median is the 50th percentile, the quartiles are the 25th and 75th, and growth charts, test scores and response times are all routinely described this way because a percentile says where a value stands.
How the percentile calculator works
The main formula sorts the data and finds the position (n − 1) × p ÷ 100, counting from zero, then interpolates between the two values either side. This is the method used by Excel's PERCENTILE.INC and most software. The nearest-rank method, rounding up n × p ÷ 100, is shown alongside.
First example. For the default 20 test scores the 90th percentile is about 91.8, so only two students scored higher.
Second example. In 10, 20, 30, 40, 50 the value 40 has a percentile rank of 75%, since it sits three-quarters of the way up the sorted list.
How many values sit below the 25th percentile? About a quarter of them, five of the 20 here.
Every common percentile of your data, interpolated
| Percentile | Value | Nearest rank |
|---|---|---|
| 1st | 55.57 | 55 |
| 5th | 57.85 | 55 |
| 10th | 61.6 | 58 |
| 15th | 63.7 | 62 |
| 20th | 66.4 | 64 |
| 25th | 68.5 | 67 |
| 30th | 69.7 | 69 |
| 33rd | 70.27 | 70 |
| 40th | 72.2 | 71 |
| 45th | 73.55 | 73 |
| 50th | 74.5 | 74 |
| 55th | 75.9 | 75 |
| 60th | 77.8 | 77 |
| 66th | 80.08 | 81 |
| 70th | 81.9 | 81 |
| 75th | 84.5 | 84 |
| 80th | 86.4 | 86 |
| 85th | 88.3 | 88 |
| 90th | 90.2 | 90 |
| 95th | 92.15 | 92 |
| 97.5th | 93.575 | 95 |
| 99th | 94.43 | 95 |
| 99.5th | 94.715 | 95 |
| 100th | 95 | 95 |
Tips
- Methods differ on small data. With few values, interpolation and nearest-rank can disagree; say which you used.
- Percentile is not percentage. Scoring 70% on a test might put you at the 90th percentile.
- Paste straight from a spreadsheet. Commas, spaces, tabs and new lines all work as separators.
FAQ
What is the difference between a percentile and a percentile rank?
A percentile is a value: the 90th percentile of these scores is about 91.8. A percentile rank is a position: a score of 80 has a percentile rank of about 60, meaning roughly 60% of scores are lower. This calculator switches between the two with the Find menu at the top.
Why does Excel give a different percentile?
Excel has two functions. PERCENTILE.INC matches the interpolation result here. PERCENTILE.EXC uses (n + 1) × p and excludes the end points, so it gives slightly different answers, especially for small data sets and extreme percentiles. Neither is wrong; they are different conventions.
Is the 50th percentile the same as the median?
Yes. With interpolation the 50th percentile always equals the median: the middle value for an odd count, or the average of the two middle values for an even count. The 25th and 75th percentiles are close to the quartiles, though textbook quartile methods can differ slightly.
See also: all Statistics tools, Arithmetic, Number Theory, Algebra and Geometry, Trigonometry and Calculus.
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