Percentile Calculator

About the Percentile Calculator

Percentiles describe position within a group. Scoring at the 90th percentile means doing as well as or better than about 90 percent of the group, whatever the actual score. Percentiles are how standardised test results, children's growth, website response times and salaries are often reported, because they show where a value stands relative to others rather than in absolute terms.

This percentile calculator works both ways. It finds the value at any percentile of a data set — for example, the 90th percentile of a list of scores — showing the position in the sorted list and the interpolation between neighbouring values. Or it finds the percentile rank of a particular value, with the counts of values below and equal to it and the results under other common definitions.

How to Use the Percentile Calculator

Enter your numbers, separated by commas, spaces or new lines.

Choose Value at a percentile and enter the percentile, from 0 to 100; or choose Percentile rank of a value and enter the value to rank.

The result appears with the working.

The Formulas

  Value at percentile p (inclusive method, as Excel PERCENTILE.INC):
    position = (n − 1) × p ÷ 100      (first sorted value = position 0)
    interpolate between the values either side of that position

  Percentile rank of value x:
    rank = (number below x + ½ × number equal to x) ÷ n × 100

Step-by-Step Example: Value at a Percentile

The 90th percentile of 55, 62, 68, 70, 74, 78, 81, 85, 90, 96.

  Position:  (10 − 1) × 0.90 = 8.1
  Values at positions 8 and 9:  90 and 96
  Value:     90 + 0.1 × (96 − 90) = 90.6

The 90th percentile is 90.6. The 50th percentile, the median, is 76, halfway between 74 and 78.

Step-by-Step Example: Percentile Rank

What percentile is a score of 81 in the same list?

  Below 81:  55, 62, 68, 70, 74, 78  → 6 values
  Equal:     81                       → 1 value
  Rank:      (6 + ½ × 1) ÷ 10 × 100 = 65

A score of 81 is at the 65th percentile. Under the stricter definitions, 60 percent of scores are below it and 70 percent are at or below it.

Percentile Versus Percentage

A percentage is a proportion of a total — 81 out of 100 marks is 81 percent. A percentile is a position relative to others — the same 81 marks might be at the 40th percentile in a strong class or the 95th in a weak one. The two are often confused, but they answer different questions: how much, versus how you compare.

Why Methods Differ

For large data sets, every reasonable percentile method gives almost the same answer. For small ones, the choice of where to place a percentile between two data points matters, and statistical software uses at least nine variations. This calculator uses the widely used inclusive method, matching Excel's PERCENTILE.INC and the default in many packages. Percentile ranks also have several definitions — counting values strictly below, at or below, or below plus half of those equal — so the calculator shows all three.

Common Percentiles

A few percentiles come up so often that they have names of their own.

Some percentiles have their own names. The median is the 50th percentile. The quartiles are the 25th and 75th. Deciles are the 10th, 20th and so on. In performance monitoring, the p95 and p99 — the 95th and 99th percentiles of response times — show how slow the worst cases are, which an average would hide.

Percentiles in Growth Charts and Tests

Paediatric growth charts plot a child's height and weight against percentiles of a reference population: a child on the 50th percentile for height is of average height for their age, and one on the 10th is shorter than 90 percent of peers. Standardised tests report percentile ranks so that scores from different versions or years can be compared fairly. In both cases the percentile describes position, not quality — the 10th percentile for height is perfectly healthy if the child grows steadily along it.

Finding a Cut-Off

Percentiles are often used to set thresholds. A scholarship for the top 10 percent of applicants needs the 90th percentile of scores as its cut-off; a quality check that rejects the worst 5 percent of parts needs the 5th or 95th percentile of the measured dimension. For the example scores, a top-10-percent cut-off would sit at about 90.6, so only the score of 96 would clear it. With so few values, a single score changes the result noticeably, which is why cut-offs are more stable when based on large data sets.

Understanding Your Result

For a value at a percentile, the headline is the value; the position, interpolation and what it means lines show how it was found and read.

For a percentile rank, the headline is the rank; the counts line shows how many values are below and equal; the other definitions line gives the strictly-below and at-or-below percentages.

When Should You Use This Calculator?

Use it to find cut-off scores such as the top 10 percent.

Use it to see where a score or measurement stands in a group.

Use it for response times, incomes, prices and other skewed data.

Use it for statistics homework on percentiles and ranks.

Common Mistakes

Confusing percentiles with percentages. One is position, the other proportion.

Forgetting to sort the data. Positions refer to the sorted list.

Counting positions from 1 in the inclusive formula. It counts from 0.

Expecting every tool to agree on small data sets. Methods differ.

Treating a low percentile as a bad result. It only describes position.

Using too little data for extreme percentiles. The 99th percentile of 20 values is little more than the maximum; extreme percentiles need large samples.