Percentile Rank Calculator

What the percentile rank calculator does

The percentile rank of a value is the percentage of the data that falls at or below it. If your test score has a percentile rank of 80, you did as well as or better than 80 percent of the group. This calculator takes a score and a data set and works that rank out.

It is the number behind phrases like "top 10 percent" and "above the 90th percentile", and it is how a single result is placed against everyone else's. Below is how it works and exactly what it counts.

How to use it

1. Enter the score whose rank you want, in the first field.
2. Enter your data values, one per box, starting with the first five and adding more with the buttons, up to thirty.
3. Press Calculate for the percentile rank, or Reset to clear it.

How percentile rank is worked out

It is a straight proportion. Count how many of your values are at or below the score, divide by the total number of values, and turn it into a percentage:

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

So a score that sits above most of the data lands at a high rank, and one near the bottom lands low. The score you are ranking does not have to be one of the data values, which lets you ask where a new or hypothetical result would fall among the rest.

The "at or below" definition

There is a small choice buried in that formula, and it is worth being open about. This calculator counts values at or below the score, using the "or equal to" part. Some textbooks instead count only the values strictly below, and others split the difference by counting half of any values equal to the score. Each rule shifts the rank a little when there are ties.

None of these is the single correct one, they are just different conventions, so a percentile rank from another source may not match to the decimal. As long as you know this tool uses at or below, the number it gives is consistent and easy to reason about.

A worked example

Take the nine values 3, 5, 7, 8, 12, 13, 14, 18, 21, and suppose you want the percentile rank of the score 12.

Five of the nine values, 3, 5, 7, 8, and 12 itself, are at or below 12. So the percentile rank is 5 ÷ 9 × 100 = about 55.6. In plain terms, a score of 12 sits as high as or higher than roughly 56 percent of this data.

Percentile rank versus percentile

These two terms are easy to mix up, and they run in opposite directions. A percentile rank starts with a score and gives you a percentage: the score 12 is at the 56th percentile. A percentile starts with a percentage and gives you a score: the 56th percentile is around the value 12.

So if you have a value and want to know its standing, you want the percentile rank, which is this tool. If you have a percentage and want the value at that position, our percentile calculator runs it the other way.

Entering your data, and the rounding

Fill in a box for each value, adding boxes as you need them, up to thirty. Every box must hold a number for the calculator to run, and so must the score field. The order of the values does not matter, since the calculation only counts how many sit at or below the score. The result is shown to one decimal place.

Questions people ask

What is a percentile rank?

The percentage of a data set that falls at or below a given score. A rank of 80 means the score is as high as or higher than 80 percent of the values.

Is percentile rank the same as percentile?

They are two sides of the same coin. A percentile rank turns a score into a percentage, while a percentile turns a percentage into a score.

What happens when values equal the score?

This calculator counts them as at or below, since it uses the "or equal to" rule. Other conventions handle ties differently, which can shift the rank slightly.

Does the score have to be in the data?

No. You can rank any score, including one not in your data, to see where it would fall among the existing values.

References

A quick note on where the methods here come from. Percentile rank and the different conventions for handling ties are set out in the NIST/SEMATECH e-Handbook of Statistical Methods, the US government's public statistics reference. OpenStax Introductory Statistics is a free, widely used textbook that covers percentiles and ranks.

1. NIST/SEMATECH e-Handbook of Statistical Methods (percentiles and ranks). https://www.itl.nist.gov/div898/handbook/
2. OpenStax, Introductory Statistics (percentiles). https://openstax.org/details/books/introductory-statistics-2e