Percentile Calculator
Find any percentile of a list of numbers by the NIST and spreadsheet methods side by side, and see where a value ranks within the list.
A percentile is the value below which a given percent of a sorted list falls. For the twelve scores 55, 62, 68, 70, 71, 75, 78, 80, 84, 88, 90 and 95, the 90th percentile is 93.5 by the NIST rule, which places it at 0.9 times 13 = 11.7 positions in, and 89.8 by the spreadsheet PERCENTILE.INC rule. A score of 80 has 7 of 12 (58.3333%) of the scores below it.
Results are computed from the numbers you enter and shown to four decimal places. The calculator treats every value as one observation: it treats repeats as separate entries, does not work from grouped or binned data, or compare you with a published reference population such as growth or test-score charts. Different software uses different percentile definitions, so another tool may report a slightly different value for the same list; the method is labelled with each result.
12 values read, up to 10,000.
90th percentile (NIST method)
93.5
- Spreadsheet PERCENTILE.INC method
- 89.8
- Smallest / largest
- 55 / 95
- Values below 80
- 7 of 12 (58.3333%)
- Values at or below 80
- 8 of 12 (66.6667%)
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About the Percentile Calculator
There is more than one correct way to compute a percentile, and the calculator shows the two you are most likely to meet. Both sort the list and find a position, then interpolate between the two values on either side. The NIST e-Handbook rule, definition 6 in Hyndman and Fan's 1996 survey of statistics packages, uses p times (N + 1), so the 90th percentile of twelve values sits at position 11.7 in the sorted list. Spreadsheet PERCENTILE.INC is definition 7 and uses p times (N - 1) on a zero-based count, which puts the same percentile at position 9.9 and gives 89.8 instead of 93.5. The median agrees, 76.5 both ways, but the 25th percentile comes out 68.5 by NIST and 69.5 in a spreadsheet. Short lists show the biggest gaps. Percentile rank works the other way: it counts how many values sit below yours. For 80 that is 7 of 12 (58.3333%), or 8 of 12 (66.6667%) counting 80 itself.
Frequently asked questions
How do I find a percentile by hand?+
Sort the numbers. For the NIST method multiply the percent, as a decimal, by the count plus one; for 0.9 and 12 values that is 11.7. Take the 11th value and add 0.7 of the gap to the 12th: 90 plus 0.7 times 5 is 93.5.
Why does Excel give a different answer?+
PERCENTILE.INC uses the count minus one instead of the count plus one, so it places the percentile slightly closer to the middle of the list. Both are standard definitions; say which one you used when you report a result.
What is the difference between a percentile and a percentile rank?+
A percentile turns a percent into a value: the 90th percentile of these scores is 93.5. A percentile rank turns a value into a percent: a score of 80 is above 7 of 12 (58.3333%) of them.
What happens at 0 and 100?+
Both methods return the smallest value at 0 and the largest at 100. The NIST method also stops at the first or last value when the position falls outside the list, which happens for extreme percentiles of short lists.
Methods: Hyndman RJ, Fan Y, "Sample quantiles in statistical packages," The American Statistician 1996;50(4):361-365; NIST/SEMATECH e-Handbook of Statistical Methods, 7.2.6.2 Percentiles.
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