StatReason

Percentile Calculator

Find the value below which a given percentage of your data falls.

What this answers

A percentile answers "what value falls at this position in the sorted data?" The 50th percentile is the median; the 90th percentile is the value below which 90% of your data falls. Percentiles are used everywhere from test score reporting to growth charts to performance benchmarking.

How it is calculated

This calculator uses the Hyndman-Fan Type 7 interpolation method, the same convention R and most spreadsheet software use by default. Values are sorted, and the requested percentile is located by linear interpolation between the two nearest ranked values when it does not land exactly on an existing data point. Different software packages sometimes use a different interpolation rule, which is why percentile results can vary slightly between tools; this site names its exact convention rather than leaving it ambiguous.

Worked example

For the values 1 through 5, the 50th percentile is 3, exactly the median. Try the 0th and 100th percentiles on the same data to confirm they return the minimum and maximum values respectively, the natural boundary cases for any percentile calculation.

Assumption audit

Calculated from your data: the sorted order of your values and the exact interpolated value at your requested percentile.
Evidence to review: with a small sample, a single requested percentile can be sensitive to exactly which values you have; check the full Five-Number Summary for more context.
You must verify: that percentile is the appropriate framing for your question. Do not equate an individual's percentile rank with a fixed probability for that specific person, since percentiles describe a static dataset, not a probability model.

Common mistakes

Confusing a percentile with a percentage score is a frequent mix-up: scoring in the 90th percentile on a test does not mean answering 90% of questions correctly, it means scoring higher than 90% of the people in the comparison group. The two numbers can differ by a wide margin depending on how difficult the test was and how the comparison group performed overall, so always be explicit about which one you actually mean.

Limitations

Percentiles near the extremes (very low or very high) are less stable with a small sample, since they depend on interpolating near the edges of your data where there is the least information to interpolate from.