What this calculator does
This finds the value sitting at a given percentage position in the data. In the set 55, 60, 63, 67, 70, 72, 75, 80, 85, 90, the 90th percentile is 85.5.
That result is not a value in the data, which surprises people. With ten points, the 90th percentile falls at rank 8.1 on a zero-based scale, between the eighth value of 85 and the ninth of 90, so the calculator interpolates a tenth of the way between them. Only when a percentile lands exactly on a data point does it return one.
The formula
The target rank is (n−1) multiplied by the percentile as a decimal, which places the 0th percentile at the first value and the 100th at the last. Where the rank falls between two points, the result is interpolated linearly between them in proportion to the fractional part. This is the method used by most spreadsheet software for its default percentile function.
| Term | Meaning |
|---|---|
| Percentile | The value below which a given percentage of the data falls. |
| Linear interpolation | Estimating between two adjacent data points in proportion to the fractional rank. |
| Quartile | The 25th, 50th and 75th percentiles. |
| Median | The 50th percentile, which for an even count is interpolated between the two middle values. |
The inputs explained
| Field | What to enter |
|---|---|
| Data (comma or space separated) | Your data, comma or space separated. It does not need to be sorted. |
| Percentile (%) | The percentile you want, from 0 to 100. 25, 50 and 75 give the quartiles. |
When to use it
Finding quartiles for a box plot
The 25th, 50th and 75th percentiles are the three values a box plot is built from.
Setting a threshold
Selecting the top 10% of a data set means finding the value at the 90th percentile and using it as the cutoff.
Reporting response times
Service level targets are usually quoted at a high percentile, such as the 95th or 99th, rather than as an average.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
What value sits at each percentile?
Five percentiles from the same ten-point data set.
| Percentile | Value at that percentile | Sample size | Minimum, maximum |
|---|---|---|---|
| 10th | 59.500 | 10 | 55.000, 90.000 |
| 25th | 64.000 | 10 | 55.000, 90.000 |
| 50th | 71.000 | 10 | 55.000, 90.000 |
| 75th | 78.750 | 10 | 55.000, 90.000 |
| 90th | 85.500 | 10 | 55.000, 90.000 |
Questions
Why is the percentile not one of my data values?
Because the target rank usually falls between two points, and the value is interpolated between them. With ten data points the 90th percentile sits at rank 8.1, one tenth of the way from the eighth value to the ninth. Only ranks that land exactly on a point return that point.
Which percentile method does this use?
Linear interpolation on rank (n−1)p, which is the method behind the default percentile function in most spreadsheet software. Several other conventions exist and they disagree on small data sets, so results may differ slightly from a statistics package using a different definition.
What is the difference between percentile and percentile rank?
They are inverses. This calculator takes a percentage and returns a value. Percentile rank takes a value and returns the percentage of data at or below it. One asks what value sits here, the other asks where does this value sit.
Why do service levels use the 95th percentile?
Because averages hide the bad cases. A mean response time looks healthy even when a meaningful minority of requests are very slow, whereas the 95th percentile describes what the worst-served users actually experience, which is usually what a service commitment is about.
For the reverse operation, see the percentile rank calculator. For the interquartile range, see the interquartile range calculator.