Percentile Calculator
The value at any percentile of a data set, by nearest rank or linear interpolation, or the percentile rank of a value.
Result
Result: 5.5
Exact arithmetic on the values entered. Nothing is estimated.
- What this is
- Linear interpolation between the neighbouring values, the spreadsheet PERCENTILE.INC method
- First quartile, Q1
- 4
- Median
- 4.5
- Third quartile, Q3
- 5.5
- Count
- 8
https://calcgallery.com/statistics/percentile-calculator/
Results follow the mathematical operation and values shown. Check that you selected the intended operation, convention and dataset type before relying on the result. Read the full disclaimer
How to use the Percentile Calculator
- Choose whether you want the value at a percentile, or the percentile of a value.
- For a value at a percentile, choose the method and enter the percentile.
- Enter the data, one number per row, and read the result with the method it used.
Two ways to find a percentile
Nearest rank. Sort the data and take the value at position ⌈p × n⌉, rounding the position up. It always returns one of your own values, which suits data where a value in between would be meaningless, such as shoe sizes.
Linear interpolation. Sort the data and go p × (n − 1) of the way from the first value to the last, interpolating between the two neighbouring values when that position falls between them. This is the spreadsheet method, and it is what the quartiles on the mean, median and mode page use.
On large data sets the two methods come close together. On small ones they can differ noticeably, which is why the method is named alongside every result.
The percentile of a value
The other direction asks what share of the data lies below a given value. Values below it count in full, values equal to it count half, and the total is divided by the number of values.
Quartiles
The 25th, 50th and 75th percentiles are the quartiles Q1, the median and Q3. They are always given by linear interpolation, whichever method you choose for the main result, so that they match the other pages on the site.
With your numbers
- Position = 0.75 × (8 − 1) = 5.25 from the start; value = 5.5
Quick reference
Exact arithmetic on the values entered. Nothing is estimated.
| Example | Result |
|---|---|
| 75th, linear, 2 to 9 | 5.5 |
| 75th, nearest rank, 2 to 9 | 5 |
| 50th, linear, 2 to 9 | 4.5 |
| Rank of 5 in 2 to 9 | 62.5 |
| 90th, linear, 1 to 10 | 9.1 |
| Rank of 85 in five scores | 60 |
Common questions about the Percentile Calculator
- Why do different calculators give different percentiles?
- Because there is no single definition. Hyndman and Fan listed nine in use in statistical software in 1996, and they give different answers on small data sets. On 2, 4, 4, 4, 5, 5, 7, 9 the 75th percentile is 5 by nearest rank and 5.5 by linear interpolation. Neither is a mistake. This page offers the two most common and always says which it used.
- Which method matches Excel or Google Sheets?
- Linear interpolation. It is what PERCENTILE, PERCENTILE.INC and QUARTILE.INC use. PERCENTILE.EXC uses a different rule again, which this page does not offer.
- What does "at the 90th percentile" mean?
- That 90% of the data lies below that point. A child’s height at the 90th percentile is taller than 90 out of 100 children of the same age. It is a position within a group, not a score out of 100: being at the 90th percentile on a test says nothing about how many questions were answered correctly.
- How are ties handled for a percentile rank?
- A value equal to the one you entered counts as half below it. So the rank of 5 in 2, 4, 4, 4, 5, 5, 7, 9 is (4 + ½ × 2) ÷ 8 = 62.5%. Counting ties fully below or fully above gives 75% or 50%, which is why the half-count is the usual convention.