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Percentile Calculator
Find a percentile rank with (number of values below the score ÷ n) × 100, or the value at a percentile by linear interpolation.
Commas, spaces, or new lines. Do not put a comma inside a number. Negatives can use a hyphen or a minus sign.
Percentile rank is (number of values below this score ÷ n) × 100. Equal values are not counted as below.
Enter a data list and a score to see the percentile rank.
Enter a data list and a score to see the percentile rank.
This percentile calculator answers two different questions about a data list. Percentile rank uses (number of values below the score ÷ n) × 100 and reports how many values are below the score, how many equal it, and n. The value at a percentile is a separate question. Spreadsheet linear interpolation, the default and the Excel PERCENTILE and PERCENTILE.INC formula, uses the rank (p ÷ 100) × (n − 1) + 1. Exclusive linear interpolation, Excel PERCENTILE.EXC, uses (p ÷ 100) × (n + 1). A whole-number rank is that position in the sorted list. A rank between two positions is filled by linear interpolation. The result names the formula it used.
How to find the percentile of a data set
A percentile calculator has to answer two different questions, and the formulas are not interchangeable. Percentile rank starts from a score and returns a percent: what share of the data is below that score? The other question starts from a percent, such as the 90th percentile, and returns a data value. A percentile rank of 40 does not mean the score is the 40th percentile.
How to calculate a percentile rank: count the values strictly below the score, divide by n (how many values are in the list), and multiply by 100. A percentile rank calculator uses that percent, not the data value at a chosen percentile. The percentile formula on this page is (number of values below the score ÷ n) × 100. Values equal to the score are part of n and are reported, but they are not counted as below. In the list 15, 20, 35, 40, 50, the score 35 has 2 values below it and n is 5, so (2 ÷ 5) × 100 = 40. Another formula adds half the ties, (number below + 0.5 × number equal) ÷ n × 100, which would give 50 for that same score. This page does not use that formula.
The value at a percentile
Finding the value at a percentile turns p into a rank in the sorted list, counting the first position as 1. Spreadsheet linear interpolation, the default, is what Excel PERCENTILE and PERCENTILE.INC use: (p ÷ 100) × (n − 1) + 1. Exclusive linear interpolation, Excel PERCENTILE.EXC and many textbooks, uses (p ÷ 100) × (n + 1). If the rank is a whole number, the value is the number in that position. If the rank falls between two positions, linear interpolation adds the fractional part of the rank times the gap between those two values. Some textbooks instead average the two neighboring values and ignore the fraction, or round the position up and take that single data value. This page does not mix those rules in. The switch keeps the spreadsheet rank and the exclusive rank apart, and the result names the one it used.
For 15, 20, 35, 40, 50, the 50th percentile has spreadsheet rank (50 ÷ 100) × (5 − 1) + 1 = 3. Position 3 is 35, the middle of an odd list, which is the median. The exclusive rank is also 3, so it is 35 as well. The 90th percentile is where the two ranks split. Spreadsheet rank (90 ÷ 100) × (5 − 1) + 1 = 4.6, and linear interpolation gives 40 + 0.6 × (50 − 40) = 46. Exclusive rank (90 ÷ 100) × 6 = 5.4, which is past the last position, so that formula has no value in the list.
What the result is showing
An exact whole number or a short exact decimal is shown with an equals sign, such as 40 or 12.5. A result that does not come out evenly is shown to 8 significant figures with an about sign, and the line under it says it was rounded. Lists of 40 numbers or fewer are printed in order. A longer list still uses every value, and the result shows n and the rank instead of every number. A percentile below 0 or above 100 is rejected, and so is a list with no numbers. Negatives can be typed with a hyphen or a minus sign.
Frequently Asked Questions
How do you find the percentile of a value in a data set?
Count the values strictly below the score, divide by n, and multiply by 100. The formula is (number of values below the score ÷ n) × 100. For 15, 20, 35, 40, 50, the score 35 has 2 values below it and n is 5, so the percentile rank is 40. That is not the same question as the value at the 40th percentile.
What is the percentile formula for the value at the 90th percentile?
Spreadsheet rank, the default here and the one used by Excel PERCENTILE and PERCENTILE.INC, is (90 ÷ 100) × (n − 1) + 1. Exclusive rank, Excel PERCENTILE.EXC, is (90 ÷ 100) × (n + 1). A whole-number rank is that position in the sorted list. A rank between two positions uses linear interpolation. For 15, 20, 35, 40, 50, the spreadsheet rank is 4.6, and the interpolated value is 46. The exclusive rank is 5.4, past the end of the list, so there is no value.
How is percentile rank different from the value at a percentile?
Percentile rank starts with a score and returns the percent of the data below it. The value at a percentile starts with a percent and returns a data value, such as the number at the 90th percentile. A percentile rank of 40 means 40 percent of the values are below the score. It does not mean the score is the 40th percentile.
Why do percentile calculators disagree?
There is more than one definition. Percentile rank on this page counts only values below the score. Another formula counts those plus half of the values that equal the score. For the value at a percentile, Excel PERCENTILE and PERCENTILE.INC use the rank (p ÷ 100) × (n − 1) + 1, while Excel PERCENTILE.EXC and many textbooks use (p ÷ 100) × (n + 1). Both of those then use linear interpolation. The result names which formula was used.
What is the 50th percentile of 15, 20, 35, 40, and 50?
It is 35, the median. With five numbers, the middle value is the third one. Spreadsheet rank (50 ÷ 100) × (5 − 1) + 1 = 3, and the exclusive rank is also 3, so both methods land on 35. For an even count, both ranks fall halfway between the two middle numbers, and linear interpolation averages them, which is the usual median.