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Percentile Calculator

Find any percentile and quartile of a data set by the OpenStax or Excel methods, and a value’s percentile rank.

By Nitin Raturi · Last reviewed

Your data

How to use the Percentile Calculator

Find any percentile of a data set, and where a value ranks.

  1. Paste or type the data.
  2. Enter the percentile you want.
  3. Choose the method your course or software uses.
  4. Enter a value to see its percentile rank.

Good to know

  • The 50th percentile is the median; the 25th and 75th are the quartiles.

Data

The numbers, in any order, separated by commas, spaces or new lines.

How to fill it in

  • Enter 2 to 10,000 numbers.

Numbers separated by commas, spaces or new lines.

Percentile (k)

The percentile to find: 25 for the first quartile, 50 for the median, 90 for the 90th.

How to fill it in

  • Enter 0 to 100.

Example

For OpenStax’s 29 ages, the 83rd percentile is 71.5.

Method

How to find a percentile that falls between two data values.

How to fill it in

  • OpenStax: average the two neighbouring values.
  • Exclusive: interpolate at k(n + 1)/100, as Excel’s PERCENTILE.EXC.
  • Inclusive: interpolate at (n − 1)k/100 + 1, as PERCENTILE.INC.

Example

The same 83rd percentile is 71.9 exclusive and 71.24 inclusive.

Keep in mind: Different methods give different answers for small data sets; say which you used.

Value to rank

A value whose percentile rank you want.

How to fill it in

  • Enter any number.

Example

In the ages, 58 is the 64th percentile and 25 the 12th.

83rd percentile

71.5

Of 29 values, the 83rd percentile is 71.5 (position 24.9). 58 is at the 64th percentile.

Q1, median, Q3
29.5, 47, 68
Interquartile range
38.5
Percentile rank of 58
63.793103

Method: OpenStax (average neighbours). Percentile rank = (values below + half the values equal) ÷ n × 100, rounded to a whole number.

ChangelogHow we test this calculatorEmbed this calculator

How this calculator works

  1. Step 1Sortsmallest to largestOrder the data.
  2. Step 2Locatei = k(n + 1) ÷ 100Position of the kth percentile.
  3. Step 3Between valuesaverage or interpolateDepends on the method.

The kth percentile is the value with about k percent of the data below it. The calculator sorts the data and finds the position of that percentile.

When the position falls between two data values, textbooks and spreadsheets differ. The calculator offers the OpenStax method and the two Excel methods, and names which one it used.

Worked example: OpenStax’s 29 ages

83rd percentile of 29 ages
i
83 × (29 + 1) ÷ 100
  1. Position24.9
  2. 24th and 25th values71 and 72
  3. OpenStax: average71.5
  4. Exclusive: interpolate71.9
  5. Inclusive (Excel PERCENTILE.INC)71.24

Read the result

  • 5864th percentile18 below, 1 equal, of 29: (18 + 0.5) ÷ 29.
  • 2512th percentile3 below, 1 equal, of 29.

Quartiles of the ages: 29.5, 47, 68. The middle half of the data lies between the first and the last.

Assumptions and limits

  • Named methodState which method you used.
  • Small samplesMethods disagree most when n is small.
  • EndsPercentiles near 0 or 100 may clamp to the ends.
  • Rank roundingRanks are rounded to whole numbers, as OpenStax does.

A percentile places a value within its data set. The centre and spread describe the whole set.

For the mean, median and mode, use the average calculator, and for spread, the standard deviation calculator. If the data follow a normal curve, the z-score calculator gives a similar answer from the mean.

Common mistakes

  • Mistake: Forgetting to sort the data.

    Instead: The calculator sorts it for you.

  • Mistake: Comparing answers from different methods.

    Instead: Use the same method throughout.

Checking the method

A separate script checks the linear methods with Python’s statistics.quantiles and reproduces OpenStax’s 71.5, 64th and 12th percentile examples.

Read how we test our calculators, or browse more maths calculators.

Frequently asked questions

What is the 83rd percentile of OpenStax’s 29 ages?

71.5, averaging the 24th and 25th values (71 and 72).

Why do calculators give different percentiles?

They use different methods. The same 83rd percentile is 71.9 by PERCENTILE.EXC and 71.24 by PERCENTILE.INC.

How do I find the percentile rank of a value?

(values below + half the values equal) ÷ n × 100. In the ages, 58 is the 64th percentile.

What percentile is 25 in the same data?

The 12th percentile: 3 values below it and 1 equal, out of 29.

What are the quartiles?

The 25th, 50th and 75th percentiles. For the ages: 29.5, 47, 68.

Sources and methodology

The formulas are standard time-value-of-money results. We check every figure against golden values worked out independently, by closed form and by month-by-month simulation; see the methodology.

Written and maintained by Nitin Raturi, a software engineer (about the author). Last reviewed 4 Nov 2026; next review due by . Found an error? Tell us.

Changelog

  • : Initial release.

  • Average Calculator

    Compare mean, median, repeated modes and an optional weighted average from your list.

  • Standard Deviation Calculator

    Find the sample or population standard deviation of a list, with variance, mean and standard error.

  • Normal Distribution Calculator

    Find the probability between two values of a normal distribution, and the value at any percentile.

  • Z-Score Calculator

    Find how many standard deviations a value is from the mean, with the normal probabilities below and above it.