How this calculator works
A percentile maps a cumulative proportion to a data value. Linear interpolation uses one-based position 1 + (n - 1)p and blends adjacent observations. Nearest rank uses ceil(np), with the minimum at p = 0. The exclusive position method uses (n + 1)p and clamps to the minimum or maximum outside interior positions. Both endpoints are allowed, and all methods return the sole value for a singleton.
Formula
Linear position h = 1 + (n - 1)p. If h = j + f, Q(p) = (1 - f)x(j) + f x(j + 1). Nearest-rank position = max(1, ceil(np)).
Worked example
For 10, 20, 30, 40, the 25th percentile has linear position 1.75, giving 17.5. Nearest rank instead selects the first observation, 10.
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Frequently asked questions
Is percentile the same as percentile rank?
No. This tool takes a percentage and returns a value. Percentile rank takes a value and returns a percentage.
Why can software answers differ?
Finite-sample quantile algorithms use different positions and interpolation rules. Match the convention used in your report or course.
Can I enter 0.25 for the 25th percentile?
Choose ratio units for 0.25, or use 25 with the default percent unit. The units selector makes the distinction explicit.