Percentile Calculator
This percentile calculator finds the value below which about p percent of the data falls, or the percentile rank of a value you choose. In ten test scores from 55 to 100, the 90th percentile is 95.5.
Sources: NIST e-Handbook, OpenStax Introductory Statistics 2e Updated
40th percentile
29
- Count (n)
- 5
- Minimum
- 15
- Median
- 35
- Maximum
- 50
Show steps Here’s how we got it
Put the values in order, smallest first
15, 20, 35, 40, 50
n = 5
Find the rank
rank = 40/100 × (5 − 1) + 1 = 2.6
Find the two values the rank sits between
Rank 2.6 is between the 2nd value (20) and the 3rd value (35)
Interpolate
20 + 0.6 × (35 − 20) = 29
Move 0.6 of the way from the lower value to the upper value.
The percentile formulas
Sort the n values from smallest to largest and number them 1 to n. For the pth percentile, find the rank with one of these methods, which follow the NIST/SEMATECH e-Handbook:
| Method | Rank | Then |
|---|---|---|
| Linear interpolation, inclusive | Interpolate between the two nearest values | |
| Linear interpolation, exclusive | Interpolate; ranks below 1 or above n give the smallest or largest value | |
| Nearest rank | Take the value at that position |
To interpolate at a rank of k plus a fraction f, start at the kth value and move f of the way to the next one:
For the percentile rank of a value, with B values below it and E values equal to it:
How to find a percentile: the 90th percentile of ten scores
Ten test scores: 55, 60, 70, 70, 75, 80, 85, 90, 95 and 100. What score is at the 90th percentile?
Put the values in order, smallest first
55, 60, 70, 70, 75, 80, 85, 90, 95, 100
n = 10
Find the rank
rank = 90/100 × (10 − 1) + 1 = 9.1
Find the two values the rank sits between
Rank 9.1 is between the 9th value (95) and the 10th value (100)
Interpolate
95 + 0.1 × (100 − 95) = 95.5
Move 0.1 of the way from the lower value to the upper value.
Answer: 95.5
Why percentile methods give different answers
A small data set has wide gaps between its values, and each method fills them a little differently. Take the 40th percentile of 15, 20, 35, 40 and 50: the rank is 2.6, 2.4 or 2 depending on the formula.
Use the method your course or software asks for. Spreadsheet PERCENTILE.INC matches the default here, and the NIST handbook describes the p(n + 1) version.
Percentiles, quartiles and the median
The 25th, 50th and 75th percentiles are the quartiles, and the 50th is the median. The quartile calculator finds all three at once, with the interquartile range and the outlier fences.
A percentile is a position in the group, not a score out of 100. If you want the score as a share of the marks, that is a job for the percentage calculator. To describe how spread out the scores are, use the standard deviation.
Percentile practice question
In the same ten scores (55, 60, 70, 70, 75, 80, 85, 90, 95, 100), what is the percentile rank of a score of 85?
Check your answer
Answer: 65th percentile 65% of the data is below 85 (counting ties as half).
Put the values in order, smallest first
55, 60, 70, 70, 75, 80, 85, 90, 95, 100
n = 10
Count the values below 85
6 values are below 85
Count the values equal to 85
1 value equals 85
Values tied with yours count as half below and half above.
Divide by n and multiply by 100
6 + 0.5 × 1/10 × 100 = 6.5/10 × 100 = 65
Questions about percentiles
How do you calculate a percentile?
Sort the data. Work out a rank from the percentile and the number of values, then read off the value at that rank. If the rank falls between two positions, interpolate between the two values. With the default method here, the rank is p ÷ 100 × (n − 1) + 1.
Why are there different percentile methods?
A data set has gaps between its values, and statisticians have not settled on one way to fill them. The methods agree closely for large data sets and can differ noticeably for small ones. For 15, 20, 35, 40, 50, the 40th percentile is 29, 26 or 20 depending on the method.
Which method should I use?
The one your course, exam board or software uses. Rank = p(n − 1) + 1 is the method behind the spreadsheet function PERCENTILE.INC. Rank = p(n + 1) is the method described in the NIST handbook. Nearest rank always returns a value that is actually in the data.
How do you find the percentile rank of a value?
Count the values below it, add half of the values equal to it, divide by the total number of values and multiply by 100. In a list of 10 scores with 5 below 80 and one equal to 80, the rank of 80 is (5 + 0.5) ÷ 10 × 100 = 55.
Is the 50th percentile the same as the median?
Yes with the two interpolation methods on this page: both give the median at p = 50. Nearest rank gives the same result for an odd number of values. For an even number it returns the lower of the two middle values instead of their average.
What is the difference between percent and percentile?
A percent is a score out of 100. A percentile is a position in a group. Scoring 80% means you got 80 out of every 100 marks. Being at the 80th percentile means you scored higher than about 80% of the group.
Sources
- NIST/SEMATECH e-Handbook of Statistical Methods, 7.2.6.2 Percentiles — rank p(N + 1) with interpolation, clamped to the smallest and largest values; and the alternative 1 + p(N − 1) used by Excel (checked October 12, 2026)
- OpenStax Introductory Statistics 2e, 2.3 Measures of the Location of the Data — the percentile of a value: (values below + 0.5 × values equal) ÷ n × 100 (checked October 12, 2026)