Percentile Calculator
Find the value at a chosen percentile of a list of numbers, using inclusive linear interpolation.
Percentile
How we calculated this
Method: inclusive linear interpolation, the same as the PERCENTILE.INC function in Excel and Google Sheets. Sort the values, find the position h = (percentile ÷ 100) × (n − 1) counting the first value as 0, then move that far between the two values either side of it.
Sorted values
Worked example
Inputs: 10, 20, 30, 40 and the 25th percentile. There are 4 values, so h = (25 ÷ 100) × (4 − 1) = 0.75. That is three quarters of the way from the first value (10) to the second (20): 10 + 0.75 × (20 − 10) = 17.5. Result: the 25th percentile is 17.5.
The method matters. For 10, 20, 30, 40 at the 25th percentile, taking the nearest value gives 10, this method gives 17.5, the exclusive method gives 12.5 and another common variant gives 15. All are legitimate; they answer a slightly different question, so compare a result only with a source that uses the same method.
How it works
The percentile is the value below which the stated percentage of the data falls. This calculator uses inclusive linear interpolation: when the position lands between two values it moves proportionally between them, so the result need not be one of your numbers. The 0th percentile is the smallest value, the 100th is the largest, and the 50th is the median. Any percentile from 0 to 100 is accepted, including decimals, and a single number is its own percentile.
The Quartiles & IQR Calculator uses a different method, the median of halves, so the 25th and 75th percentiles here can differ from Q1 and Q3 there. For 1, 2, 3, 4, 5, 6, 7 the 25th percentile is 2.5 while Q1 is 2. That is a difference between two approved methods, not an error. This tool finds the value at a percentage; it does not work out the percentile rank of a value.
What this result means
The percentile is the value at or below which the chosen percentage of your data falls. Because it interpolates between values, it need not be one of the numbers you entered.
Common mistakes
- Comparing the result with a source that uses a different percentile method. Nearest-rank, exclusive and inclusive methods give different answers for the same data; this tool uses inclusive interpolation, the method of the PERCENTILE.INC function in Excel.
- Expecting the 25th and 75th percentiles to equal Q1 and Q3 from the Quartiles & IQR Calculator. That tool uses the median-of-halves method, so they can differ: for 1 to 7 the 25th percentile is 2.5 and Q1 is 2.
Assumptions and limitations
- Finds the value at a percentage. It does not find the percentile rank of a value, group data, or list every percentile.
- Any percentile from 0 to 100 is accepted, and a single number is its own percentile.