Percentile Calculator

What the percentile calculator does

A percentile tells you where a value sits within a set of numbers: the 90th percentile is the point that 90 percent of the data falls at or below. This calculator works in both directions. Give it a score and it finds the percentile that score sits at, or give it a percentile and it finds the score at that position.

Percentiles are how test results, growth charts, and rankings are read, since they turn a raw number into a place in the pack. Below is how it gets there, and one thing worth knowing about why two percentile tools can give slightly different answers.

How to use it

1. Choose a direction. Pick Find Percentile to turn a score into a percentile, or Find Score to turn a percentile into a score.
2. Enter your data in the box, separated by commas, spaces, or new lines.
3. Enter the score or the percentile in the field below, then press Calculate, or Reset to clear it.

How a percentile is worked out

The two directions work differently. To turn a score into a percentile, the calculator counts how many of your values fall at or below that score, and divides by how many values there are:

Percentile = (count of values at or below the score ÷ total count) × 100

To turn a percentile into a score, it sorts your data and finds the position that the percentile points to. That position usually lands between two values rather than exactly on one, so it takes the two neighbours and slides between them in proportion, a step called linear interpolation. That is why the score at a percentile is often not one of your original numbers.

The method it uses, and why tools disagree

There is no single agreed way to place a percentile, and different software makes different choices. This calculator uses linear interpolation with the position set at p over 100 times one less than the count, then one added. That is the same method as Excel's PERCENTILE.INC function and the default in R and many statistics packages, so its answers will line up with those.

It is worth knowing this because another tool, or a quartile calculator using a different rule, can report a slightly different score for the same percentile and the same data. Neither is wrong. They are just built on different conventions, and the gaps are usually small. When you compare a percentile across two tools, check that both use the same method before worrying about a mismatch.

A worked example, both directions

Take the nine numbers 3, 5, 7, 8, 12, 13, 14, 18, 21, already sorted.

Going from a score to a percentile: for the score 12, five of the nine values sit at or below it, so its percentile is 5 ÷ 9 × 100 = about the 56th percentile. Going from a percentile to a score: the 25th percentile lands at the third value, giving 7, and the 75th lands at the seventh, giving 14. A quartile calculator using the exclusive method would instead report 6 and 16 for those same quarter points, which is the method difference from the section above in plain view.

Percentiles and quartiles

Quartiles are just three particular percentiles. The first quartile is the 25th percentile, the second quartile is the 50th, which is the median, and the third quartile is the 75th. So a percentile calculator can find your quartiles by asking for those three positions.

The catch is the one already noted: quartile calculators often use a half-based method rather than interpolation, so the numbers can differ a little. If you need quartiles specifically for a box plot, our quartile calculator uses the method those are usually built with.

Entering your data, and the rounding

You can separate your numbers with commas, spaces, or new lines, in any mix, and the calculator sorts them for you, so the order you type them in does not matter. In Find Score mode it also shows a table of the score at every fifth percentile, from the 0th to the 100th, for a quick overview. Results are shown to two decimal places with trailing zeros trimmed.

Questions people ask

What is a percentile?

The point below which a given percentage of the data falls. The 90th percentile is the value that 90 percent of the numbers sit at or below.

What is the difference between the two modes?

Find Percentile takes a score and tells you its percentile. Find Score takes a percentile and tells you the value at that position. They are the same idea run in opposite directions.

Why is the score at a percentile not one of my numbers?

Because the position usually falls between two values, and the calculator slides between them in proportion. That interpolation gives a result that is often not an original data point.

Why does another calculator give a different percentile?

Because there are several accepted methods for placing percentiles. This tool uses linear interpolation, matching Excel's PERCENTILE.INC. A tool using a different rule can differ slightly, and neither is wrong.

References

A quick note on where the methods here come from. The definition of percentiles and the way they are computed are set out in the NIST/SEMATECH e-Handbook of Statistical Methods, the US government's public statistics reference. The reason different software reports different percentiles is laid out in Hyndman and Fan's survey of quantile methods, the standard reference on the subject.

1. NIST/SEMATECH e-Handbook of Statistical Methods (percentiles and percentile computation). https://www.itl.nist.gov/div898/handbook/
2. Hyndman, R. J. and Fan, Y. (1996), Sample Quantiles in Statistical Packages, The American Statistician. https://www.tandfonline.com/doi/abs/10.1080/00031305.1996.10473566