Statistics

Percentile Calculator

Find percentile values, quartiles, and IQR from a data set

Last reviewed: How we build & verify
%
?th Percentile
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Q1 (25th Percentile)
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Q2 / Median (50th)
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Q3 (75th Percentile)
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IQR (Q3 - Q1)
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How it works

Locates a value within a distribution, either finding the value below which a given share of the data falls, or finding the rank of a value you already have. Percentiles need no distributional assumption, which makes them safe for skewed data.

Formula
Value at percentile P: index = (P / 100) × (N − 1), interpolating between neighbours
Percentile rank of x = (count below x + 0.5 × count equal to x) / N × 100
Variables
  • Pthe target percentile, 0 to 100
  • Nnumber of values in the sorted dataset
  • indexzero-based position in the sorted list
Worked example
Inputs: Sorted scores 55, 61, 64, 68, 70, 72, 75, 79, 84, 91
  1. N = 10, so for the 90th percentile: index = 0.90 × 9 = 8.1
  2. Value at index 8 is 84, at index 9 is 91
  3. Interpolate: 84 + 0.1 × (91 − 84) = 84.7
  4. Rank of 75: 6 values below, 1 equal → (6 + 0.5) / 10 × 100
Result: 90th percentile ≈ 84.7; the score 75 sits at the 65th percentile
Notes
  • At least nine different percentile definitions are in use. Linear interpolation (the default here, and in NumPy and Excel PERCENTILE.INC) can differ noticeably from the nearest-rank method on small datasets.
  • The median is the 50th percentile, and quartiles are the 25th, 50th, and 75th. Interquartile range is Q3 less Q1.
  • Latency work quotes p95 and p99 because averages hide tail behaviour. A service with a 40 ms mean can still have a 2-second p99 that most users notice.
  • You cannot average percentiles across groups. Combining a p95 from two servers requires the raw data or a mergeable sketch, not the mean of the two figures.

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Frequently Asked Questions

Percentile Calculator runs right in the browser tab you already have open. No install, no account, no cost.

Percentile Calculator follows the standard method used in textbooks and technical references for this calculation, and we show the formula or approach on the page itself so you can check the working rather than trust a black box. Found an edge case that breaks it? Use the feedback button in the bottom-right corner.

Percentile Calculator | ExaCalc