How is a percentile calculated?

To find the p-th percentile, sort the data, then compute the rank position as L = (p / 100) times (n + 1) where n is the number of values. If L is a whole number, the percentile is the value at that position. If not, linear interpolation blends the two neighbouring values in proportion to the fractional part of L.

What is the difference between a percentile and a quartile?

Quartiles are just specific percentiles: Q1 is the 25th percentile, Q2 (the median) is the 50th, and Q3 is the 75th. Any percentile from 1 to 99 can be calculated; quartiles are the three that divide the sorted data into four equal groups.

Why does the 90th percentile sometimes fall between two values?

When the rank position L falls between two data points, linear interpolation blends them. For a 10-value data set, P90 has position 0.90 times 11 = 9.9, so the result is the 9th value plus 0.9 times the difference between the 9th and 10th values.

Percentile Calculator

A percentile tells you the value below which a given percentage of the data falls. The 25th percentile (P25) is the value below which 25% of observations sit; the 90th percentile (P90) is below 90% of the data. Percentiles are widely used in education to rank test scores, in health to plot growth charts, in salary surveys to show pay distributions, and in quality control to identify thresholds. The 25th, 50th, and 75th percentiles are also known as the first, second, and third quartiles. This calculator uses the linear interpolation method, which is the approach recommended by most statistics textbooks and used by common software packages. The rank position for the p-th percentile is calculated as (p/100) times (n+1), where n is the count of values. If that position is a whole number, the result is the value at that position in the sorted list. If it falls between two positions, the result is interpolated between the two neighbouring values. You enter your data as a comma-separated list and specify an optional custom percentile. The calculator returns P25, P50, P75, P90, and your custom percentile all at once. The minimum of two data values is required. Results suit students working through statistics problems, researchers summarising distributions, and professionals comparing a specific value against a reference data set. Values are sorted automatically regardless of the order you enter them.

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Data values (comma-separated)

Custom percentile

12.00

P50 (median)

P256.50

P7517.50

P9020.80

P90 (custom)20.80

How it works

The calculator sorts the values in ascending order. For a given percentile p, the rank position L is (p/100) times (n+1). The integer part of L identifies the lower neighbouring value and the fractional part f determines how far to interpolate toward the next value. If f is zero the result is exactly the value at position L; otherwise the result is value[floor(L)] plus f times (value[ceil(L)] minus value[floor(L)]). This produces a smooth, continuous function over any percentile between 0 and 100.

Worked example

With data 3, 5, 7, 9, 11, 13, 15, 17, 19, 21 (n = 10, already sorted): P25 rank = 0.25 x 11 = 2.75, so P25 = 5 + 0.75 x (7-5) = 6.50. P50 rank = 5.5, so P50 = 11 + 0.5 x (13-11) = 12.00. P75 rank = 8.25, so P75 = 17 + 0.25 x (19-17) = 17.50. P90 rank = 9.9, so P90 = 19 + 0.9 x (21-19) = 20.80. These match the default values pre-filled above.

Related calculators

Quartile and IQR Calculator: find Q1, Q2, Q3, and the interquartile range for a data set.
Five Number Summary Calculator: get min, Q1, median, Q3, and max in one step.
Outlier Calculator: identify outliers using the IQR fences method.
Frequency Distribution Calculator: build a frequency table from raw data values.

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