Percentile Calculator

How to Use the Percentile Calculator

1. 1. Paste your data. Numbers separated by commas, spaces or new lines, in any order — at least two of them.
2. 2. Choose what to find. Pick the value at a percentile to answer "what score marks the 90th percentile?", or the percentile rank of a value to answer "what percentile is a score of 80?".
3. 3. Enter P or x. For a percentile value, also choose the method: nearest rank, or interpolation matching Excel's PERCENTILE.INC or PERCENTILE.EXC.
4. 4. Read the result and the working. The sorted data, the rank or position, and the interpolation are shown, with a table comparing all three methods.

Three Ways to Find the Value at a Percentile

The Pth percentile is a value with about P% of the data at or below it. With a finite list that point usually falls between two data values, and the conventions differ in where they look and whether they interpolate:

For the example data — 20 exam scores from 55 to 98 — the 90th percentile comes out three ways. The sorted scores end 88, 90, 92, 95, 98, so the 18th value is 92 and the 19th is 95. Nearest rank takes rank ⌈0.9 × 20⌉ = 18 and returns 92. The inclusive method lands at position 1 + 19 × 0.9 = 18.1, a tenth of the way from 92 to 95: 92 + 0.1 × 3 = 92.3. The exclusive method lands at position 21 × 0.9 = 18.9: 92 + 0.9 × 3 = 94.7.

The exclusive method can't reach the extremes. Its position (n + 1) × P ÷ 100 must lie between 1 and n, so with 20 values it only covers P from 100 ÷ 21 ≈ 4.76 to 2000 ÷ 21 ≈ 95.24 — outside that range Excel returns #NUM!, and so does this calculator. Whichever method you use, quote it alongside the result; with small samples the choice moves the answer.

Percentile Rank: Below, At or Below, or Mid-Rank

The reverse question — what percentile is this score? — has its own three definitions. Count B, the values strictly below x, and E, the values equal to x, out of n:

• Percent below: B ÷ n × 100. A score that beats everyone else in a class of 20 gets 95, never 100.
• Percent at or below: (B + E) ÷ n × 100 — the empirical cumulative distribution. The top score gets 100.
• Mid-rank: (B + 0.5 × E) ÷ n × 100 — tied scores split the difference. This is the usual formula for test-score percentile ranks.

In the example data, a score of 80 has 10 scores below it and appears once, giving 50%, 55% and 52.5%. A score of 72 appears twice with 5 below it, giving 25%, 35% and 30% — the gap between definitions widens with ties. If x is not in the data at all, E = 0 and all three agree.

Converting a class rank ("12th of 340") to a percentile is a related but different calculation — the Class Rank Calculator does that directly.

Frequently Asked Questions

How do you calculate a percentile?

Sort the data, then find the position that corresponds to P. By nearest rank, take the value at rank ⌈P ÷ 100 × n⌉. By the inclusive method Excel uses, go to position 1 + (n − 1) × P ÷ 100 and interpolate between the two values either side. The calculator shows both steps with your numbers.

What is the difference between a percentile and a percentage?

A percentage is a score out of 100 — 80% means 80 of 100 marks. A percentile is a position in a group — the 80th percentile means about 80% of the group scored at or below you. You can score 60% on a hard test and still be at the 90th percentile.

What does the 90th percentile mean?

It is the value with about 90% of the data at or below it and about 10% above. Being at the 90th percentile means you did better than roughly 90% of the comparison group — it puts you in the top 10%, not the top 90%.

Why does Excel give a different percentile from my textbook?

Excel's PERCENTILE.INC interpolates at position 1 + (n − 1) × P ÷ 100, while many textbooks use nearest rank or the (n + 1) position that PERCENTILE.EXC uses. All are legitimate definitions. Pick the matching method above, or look at the comparison table, which shows all three at once.

Can a percentile rank be 0 or 100?

With the at-or-below definition, the highest value always has a percentile rank of 100. With percent below, the lowest value always gets 0. The mid-rank definition never reaches either end for a value in the data, which is one reason test publishers prefer it.

What is the 50th percentile?

It is the median. The inclusive and exclusive methods both give the ordinary median — the middle value, or the average of the two middle values. Nearest rank gives the lower of the two middle values when n is even.