Percentile Calculator

Percentile calculator at a glance#

What is a percentile?#

A percentile is the value below which a given percent of the data falls. The 90th percentile of a set of test scores is the score that about 90% of the scores are at or below. The 50th percentile is the median, and the 25th and 75th percentiles sit near the first and third quartiles.

How do I use the percentile calculator?#

Enter your data set, separated by commas or spaces, and the percentile you want, any number above 0 up to 100. The calculator shows the value at that percentile, plus a table of every 5th percentile from the 0th to the 100th.

What is the 90th percentile of 48, 55, 61, 66, 70, 72, 75, 78, 84, 89 and 95?#

It's 89. With 11 sorted values, the 90th percentile lands exactly on the 10th value, so no interpolation is needed. The 25th percentile of the same scores is 63.5 and the 75th is 81.

Percentile vs percentage#

A percentage is a share of a total. A percentile is a position in a group. If a test has 960 marks, 30% of 960 is 288 marks. The 30th percentile of the test is a different thing: the score that 30% of the people who took it scored at or below. You can't work it out from the 960 alone, because it depends on everyone's scores.

OpenStax Introductory Statistics makes the same point: scoring in the 90th percentile of an exam doesn't necessarily mean you got 90% on the test. It means 90% of the test scores are the same as or less than yours. A score of 72% could be in the 95th percentile on a hard test and in the 40th on an easy one.

How the calculator finds a percentile#

Imagine you have a list of 11 test scores sorted in ascending order. The calculator applies linear interpolation to find percentiles.

1. Sort the data and count the total number of values. In this case, n equals 11.
2. Determine the position of the desired percentile using the formula: position = 1 + (P ÷ 100) × (n − 1). For the 25th percentile, this becomes 1 + 0.25 × 10, which is 3.5.
3. If the calculated position is an integer, the value at that position is the percentile.
4. If not, interpolate between the values on either side.

Position 3.5 lands midway between the 3rd value, 61, and the 4th value, 66. Here, the 25th percentile is determined by 61 + 0.5 × (66 − 61), giving us 63.5.

The same process applies to the 90th percentile. It gives 1 + 0.9 × 10, which equals 10, which points to the 10th value, 89. For the 33rd percentile, position 4.3 gives 66 + 0.3 × (70 − 66), which is 67.2.

This approach aligns with the type 7 method used in R by default, as per R's documentation. With this method, the 0th percentile always corresponds to the smallest value, and the 100th is always the largest.

How to find a percentile rank#

The calculator works from a percentile to a specific value, but you might need to find the reverse: the percentile rank of a score you already have. OpenStax provides a formula for this calculation. Count the values below your score, labeled as x, and the values equal to it, labeled as y. Then apply the formula: (x + 0.5y) ÷ n × 100 and round the result to a whole number.

Say your score is 78 within a dataset of 11 test scores. Here, 7 scores are below your score and 1 is equal to it. Using the formula, the percentile rank is (7 + 0.5 × 1) ÷ 11 × 100 = 68.18, placing it about the 68th percentile.

It's common for some teachers and textbooks to only consider the scores below. A common homework question: in a class of 30, Maria scored 84 and 22 scored lower. If only the scores below are counted, her percentile rank would be 22 ÷ 30 × 100 = 73.3, around the 73rd percentile. However, applying the OpenStax method, which includes half of her own score, the calculation becomes (22 + 0.5) ÷ 30 × 100 = 75. Always follow the method your class or test requires and clearly state which one you used.

Common percentiles and quartiles#

The 25th, 50th, and 75th percentiles divide data into quarters, which makes them similar to quartiles. However, they're not always identical. The quartile calculator identifies Q1 and Q3 as the medians of each half of the dataset, whereas this calculator uses interpolation. For the 11 test scores, the quartile method gives 61 and 84, while this calculator outputs 63.5 and 81 for the 25th and 75th percentiles. The 50th percentile and the median are always in agreement.

The 90th and 95th percentiles indicate the upper end of the dataset. In the table below, the 90th percentile is 89, the second-highest score, and the 95th is 92, between the top two scores.

Percentiles from a mean and standard deviation#

Some questions about percentiles might give you a mean and a standard deviation instead of an entire list of values. For instance, say the average score on an exam was 132 with a standard deviation of 15.7, and your score was 108. If the scores are normally distributed, the first step is finding the z-score: (108 − 132) ÷ 15.7 = −1.53. Next, you would look up the proportion of a normal distribution below that z-score, which is approximately 0.063, indicating that a score of 108 lies near the 6th percentile.

This calculator operates from a list of values, so it doesn't handle this scenario. The z-score calculator is designed to determine the z-score and the proportion of values below a given score for normally distributed data.

Percentiles of the example test scores#

These are the values the calculator returns for the 11 test scores 48, 55, 61, 66, 70, 72, 75, 78, 84, 89, and 95.

Sources#

• OpenStax, Introductory Statistics 2e, section 2.3: Measures of the Location of the Data
• R documentation, Sample Quantiles (quantile), type 7
• OpenStax, Introductory Statistics 2e, section 6.1: The Standard Normal Distribution

Frequently asked questions#

Is the 50th percentile the same as the median?#

Yes. With this calculator's method, the 50th percentile is always the median. For the 11 test scores, both are 72, the 6th value.

What does it mean to be in the 90th percentile?#

It means about 90% of the scores are at or below yours. On a test taken by 1,000 people, a score in the 90th percentile is at least as high as roughly 900 of the scores. This doesn't say anything about how many questions you answered correctly.

Why does my textbook give a different percentile?#

There are several formulas. OpenStax finds the position as (P ÷ 100) × (n + 1) and averages the two neighboring values when the position isn't a whole number. For the 25th percentile of the 11 test scores, that position is 0.25 × 12 = 3, the 3rd value, 61. This calculator's rule gives 63.5. Both are valid, so check which method your course uses.

What is the nearest rank method?#

The nearest rank method always picks an actual value from the data. To find it, you multiply P divided by 100 by n, then round up to the next whole number, and take the value at that position. For example, if you're looking for the 25th percentile of the 11 test scores, you calculate 0.25 times 11, which equals 2.75. This rounds up to 3, so you pick the 3rd value, which is 61. For the 90th percentile, you do 0.9 times 11, which comes to 9.9. Rounding that up gives you 10, and the value is 89, matching what this calculator shows.

Can I use this calculator for a baby's growth percentile?#

No. A growth percentile compares a child's height or weight against reference charts for children of the same age and sex. It doesn't compare against a list of values you enter. Your child's doctor can provide the growth chart information.

Can I enter a percentile of 0?#

The percentile box accepts any number above 0 up to 100. Even so, the table under the result will still show the 0th percentile, representing the smallest value within your data.