Percentile Calculator — Step-by-Step Solutions

The Percentile Calculator analyses where values fall within a dataset. Find the percentile rank of a specific value, determine the value at any given percentile, compute quartiles (Q1, Q2, Q3) with IQR and outlier detection, or calculate all nine deciles with a visual box plot.

Enter your data as comma-separated values and choose your analysis mode. The calculator sorts data, applies linear interpolation, and displays results with step-by-step workings and an SVG box plot.

Enter data (comma-separated)

Value to find percentile rank for

Your calculations will appear here

How to Use the Percentile Calculator

Choose a mode: Percentile Rank (what percent of the data falls below a value), Value at Percentile (the data value sitting at a given percentile), Quartiles (Q1, median, Q3 and the IQR), or Deciles + Box Plot.
Type or paste your data into the box as comma-separated numbers. The order does not matter, the calculator sorts it for you.
For Percentile Rank, enter the value you want to look up. For Value at Percentile, enter a percentile between 0 and 100, such as 90.
Read the result panel, and in the quartile and decile modes check the box plot to see how the data are spread.

Formula and Theory

A percentile tells you the relative standing of a value inside a data set. The 90th percentile is the value below which about 90% of the observations fall. Test scores, growth charts and income statistics are all reported this way because it shows position without needing the scale of the original numbers.

The percentile rank of a value is (L + 0.5 x S) / N x 100, where L is the count of values below it, S is the count equal to it and N is the total count. Counting half of the ties means a value equal to others sits in the middle of its tied block.

To go the other way, from a percentile to a value, the calculator ranks the sorted data and interpolates linearly: position = (P / 100) x (N - 1), counting from 0. If the position falls between two data points, the result is a weighted blend of them. This is the same method as Excel PERCENTILE.INC and NumPy default.

Different software uses different percentile definitions, so small differences between tools on small data sets are normal. The quartiles here use the same interpolation, so Q2 is the median.

Worked Examples

Example 1: Percentile rank of a value

Problem: For the data 12, 15, 18, 22, 25, 30, 35, 40, 45, 50, find the percentile rank of 25.

Solution: Values below 25: 12, 15, 18, 22, so L = 4. Values equal to 25: S = 1. N = 10. Rank = (4 + 0.5 x 1) / 10 x 100 = 45.

Answer: 45th percentile

Example 2: Value at the 75th percentile

Problem: Using the same ten values, find the 75th percentile.

Solution: Position = 0.75 x (10 - 1) = 6.75, counting from 0. The sorted values at positions 6 and 7 are 35 and 40. Interpolate: 35 + 0.75 x (40 - 35) = 35 + 3.75 = 38.75.

Answer: 38.75

Example 3: Quartiles and IQR

Problem: Find Q1, Q2, Q3 and the IQR for the same data.

Solution: Q1: position 0.25 x 9 = 2.25, so 18 + 0.25 x (22 - 18) = 19. Q2: position 4.5, so (25 + 30) / 2 = 27.5. Q3: 38.75 as above. IQR = 38.75 - 19 = 19.75.

Answer: Q1 = 19, Q2 = 27.5, Q3 = 38.75, IQR = 19.75

Example 4: Percentile rank with ties

Problem: Scores are 70, 75, 75, 80, 85, 90. What is the percentile rank of 75?

Solution: One score is below 75 (the 70), so L = 1. Two scores equal 75, so S = 2. N = 6. Rank = (1 + 0.5 x 2) / 6 x 100 = 2 / 6 x 100 = 33.33.

Answer: 33.3rd percentile

Frequently Asked Questions

What does the 90th percentile mean?

It is the value that about 90% of the observations fall below. If your exam score is at the 90th percentile, you scored higher than roughly 90% of the group.

Is a percentile the same as a percentage?

No. A percentage is a share of a total, such as 72 out of 100 marks. A percentile describes rank within a group, so a score of 72% could be at the 40th or the 95th percentile depending on how others did.

How do I find a percentile by hand?

Sort the data, compute the position (P / 100) x (N - 1), and read the value at that position, interpolating between neighbours if the position is not a whole number.

Why does another tool give a slightly different answer?

There are several accepted percentile definitions. This calculator uses linear interpolation between ranks (the inclusive method). Others use (N + 1) positions or round to the nearest rank, which can shift small data sets by a little.

How is the percentile related to the median and quartiles?

The median is the 50th percentile, Q1 is the 25th and Q3 is the 75th. The interquartile range is Q3 minus Q1 and covers the middle half of the data.

How many data points do I need?

Any amount works for rank and value lookups, but percentiles are more meaningful with a decent sample. The quartile mode needs at least 4 values.