Percentile Calculator

How it works

A percentile describes a position in a set of data. The value at the 75th percentile is the point below which about three quarters of the values fall; the percentile rank of a value is the percentage of the data that lies below it. Both questions start by sorting the values you enter from smallest to largest.

There is no single agreed way to find the value at a percentile when it falls between two data points. The linear interpolation method (Excel's PERCENTILE.INC, Google Sheets, R's default) treats the sorted values as rank 0 to n − 1, finds the rank p ÷ 100 × (n − 1), and interpolates between the two values it lies between. The nearest-rank method instead rounds up to a whole rank and returns an actual data value, which is what some textbooks and exam boards use.

The percentile rank of a value counts how many data values are below it, plus half of any that equal it, as a percentage of the whole list. Counting ties as half keeps the rank symmetric: a value sitting exactly in the middle of a list gets the 50th percentile whether or not it appears in the data.

Formula

sorted list s[0] … s[n−1]
linear:   rank = p ÷ 100 × (n − 1);  value = s[⌊rank⌋] + (rank − ⌊rank⌋) × (s[⌊rank⌋+1] − s[⌊rank⌋])
nearest:  ordinal rank = ⌈p ÷ 100 × n⌉;  value = s[ordinal rank − 1]   (p = 0 gives s[0])
percentile rank of x = (count below x + ½ × count equal to x) ÷ n × 100

Example

Twelve test scores: 55, 62, 68, 71, 74, 77, 80, 83, 86, 90, 94, 98. For the 75th percentile by linear interpolation the rank is 0.75 × 11 = 8.25, which lies a quarter of the way from the ninth value (86) to the tenth (90): 86 + 0.25 × 4 = 87. By the nearest-rank method the ordinal rank is ⌈0.75 × 12⌉ = 9, so the answer is the ninth value, 86.

The percentile rank of a score of 80 in the same list: six scores are below 80 and one equals it, so (6 + 0.5) ÷ 12 × 100 = 54.17. A score of 80 is at about the 54th percentile.

Assumptions and limitations

• At least two values are needed; order does not matter. Numbers can be separated by commas, spaces or new lines.
• Percentiles between two data points depend on the method. Excel's PERCENTILE.EXC, Minitab and some textbooks use rank = p ÷ 100 × (n + 1), which this calculator does not offer; their results can differ from both methods here, especially for small lists.
• The 0th and 100th percentiles are the minimum and maximum under both methods.
• Percentile rank counts a value equal to x as half above and half below, so x need not be one of the data values.
• Results are rounded to four decimal places for display.

Frequently asked questions