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.
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.
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