Percentile Calculator
Paste your numbers to find the value at any percentile and the percentile rank of any value. Compare Excel’s inclusive and exclusive methods with nearest rank, and get quartiles, deciles, a full table, grouped data and bell-curve percentiles.
Separate them with commas, spaces or new lines. You can paste a column from a spreadsheet, and 15x3 means 15 three times.
Write “12, 4” for the value 12 four times, or a class like “10-20, 4” for grouped data.
Type 40 for the 40th percentile (0 to 100).
What percentile is this value at?
Percentile table
How your percentile is worked out
Sort the numbers, find the position for your percentile, then step part-way between the two values either side.
- 1
Sort the data
15, 20, 35, 40, 50
n = 5 - 2
Find the rank
1 + 0.4 × (5 − 1)
= 2.6 - 3
Values either side
2nd 20, 3rd 35
gap 15 - 4
Step part-way
20 + 0.6 × 15
= 29
Read more: the formula, a worked example, the three methods and percentile vs percentage
A percentile tells you where a value sits in a group. The 40th percentile is the value that 40% of the data is below. The 50th percentile is the median, and the 25th and 75th are the first and third quartiles. The percentile rank works the other way round: it takes a value and tells you what share of the data is below it.
The formula
Sort the n values from smallest to largest, and let P be the percentile as a decimal (40th → 0.40).
Inclusive (Excel PERCENTILE.INC, NumPy): rank = 1 + P × (n − 1)
Exclusive (Excel PERCENTILE.EXC): rank = P × (n + 1)
Nearest rank: rank = P × n, rounded up to a whole number
If the rank has a fraction: value = value below + fraction × (value above − value below)
Percentile rank of x = number of values below x ÷ n × 100
Midpoint version = (values below + ½ × values equal) ÷ n × 100
Grouped data: P value = L + ((P × N − CF) ÷ f) × w
Bell curve: z = (x − mean) ÷ SD, percentile = area below z; value = mean + z × SD
In the grouped-data line, L is the lower edge of the class that holds the P-th share, CF is the count of all classes before it, f is its own count, w is its width and N is the total count.
Worked example
Take the five numbers 15, 20, 35, 40, 50 (already sorted, so n = 5) and find the 40th percentile.
- Inclusive: rank = 1 + 0.40 × (5 − 1) = 1 + 1.6 = 2.6. That is 0.6 of the way from the 2nd value (20) to the 3rd value (35), so the 40th percentile is 20 + 0.6 × (35 − 20) = 20 + 9 = 29. Excel =PERCENTILE.INC(A1:A5, 0.4) gives 29 too.
- Exclusive: rank = 0.40 × (5 + 1) = 2.4, so the value is 20 + 0.4 × 15 = 20 + 6 = 26.
- Nearest rank: 0.40 × 5 = 2, which is already whole, so the answer is the 2nd value, 20.
Now the percentile rank of 35. Two values (15 and 20) are below it, so 2 ÷ 5 = 40% of the data is below 35. One value equals it, so the midpoint version is (2 + 0.5) ÷ 5 = 2.5 ÷ 5 = 50%, and 3 ÷ 5 = 60% of the data is at or below 35.
The quartiles by the inclusive method are Q1 at rank 1 + 0.25 × 4 = 2 (the value 20), the median at rank 3 (35) and Q3 at rank 1 + 0.75 × 4 = 4 (40), so the interquartile range is 40 − 20 = 20.
For a bell curve with a mean of 100 and an SD of 15, the value 130 is z = (130 − 100) ÷ 15 = 2, and the area below z = 2 is 0.97725, so 130 is at the 97.7th percentile. The 90th percentile is z = 1.2816, which is 100 + 1.2816 × 15 = 119.22.
The three methods compared
| Method | Rank | Used by | P40 of 15, 20, 35, 40, 50 |
|---|---|---|---|
| Inclusive | 1 + P(n − 1) | Excel PERCENTILE.INC and PERCENTILE, Google Sheets, NumPy, R type 7 | 29 |
| Exclusive | P(n + 1) | Excel PERCENTILE.EXC, Minitab, SPSS, R type 6 | 26 |
| Nearest rank | ⌈P × n⌉ | Many textbooks; always gives one of your own values | 20 |
The exclusive method cannot reach the very ends of small data sets: with 5 values, any percentile below 1 ÷ 6 (16.7%) or above 5 ÷ 6 (83.3%) gives a rank outside 1 to 5, and Excel shows #NUM!. The calculator then shows the smallest or largest value and flags it.
Percentile vs percentage
A percentage is a share of a total: 32 out of 40 questions right is 80%. A percentile is a position in a group: being at the 80th percentile means you did better than about 80% of the people who took the test. The two are not the same thing. On a hard exam, 60% correct might be the 90th percentile, and on an easy one 90% correct might only be the 50th.
Notes
- Percentile rank in Excel is PERCENTRANK.INC (values below ÷ (n − 1)) or PERCENTRANK.EXC ((values below + 1) ÷ (n + 1)), which are interpolated between data values. Advanced mode shows both next to the simple “% below” figures.
- Grouped data assumes the values are spread evenly inside each class, so the answer is an estimate.
- The bell-curve mode is only right when the data is roughly normal. For skewed data, such as incomes or house prices, paste the real numbers instead.
Common questions
How do I calculate a percentile?
Sort the numbers from smallest to largest. For the inclusive method (Excel PERCENTILE.INC) the position is 1 + P × (n − 1). For 15, 20, 35, 40, 50 and the 40th percentile that is 1 + 0.4 × 4 = 2.6, so the answer is 60% of the way from the 2nd value (20) to the 3rd (35): 20 + 0.6 × 15 = 29.
What is the difference between a percentile and a percentage?
A percentage is a share of a total, such as 80% of the questions right. A percentile is a position in a group: the 80th percentile means you did better than about 80% of people. You can score 60% on a hard test and still be at the 90th percentile if most people scored lower.
What is a percentile rank?
It is the percentage of values below a given value. In 15, 20, 35, 40, 50, two of the five values are below 35, so its percentile rank is 40%. Some books count half of the values equal to it as well, which gives (2 + 0.5) ÷ 5 = 50%.
Why does Excel give a different percentile from my textbook?
There are several methods. Excel PERCENTILE.INC (also Google Sheets and NumPy) uses 1 + P × (n − 1), PERCENTILE.EXC uses P × (n + 1), and many textbooks use the nearest rank ⌈P × n⌉ with no in-between values. For small data sets they can differ a lot. Advanced mode shows all three side by side.
Is the 50th percentile the median?
Yes. The 50th percentile is the median, the 25th is the first quartile (Q1) and the 75th is the third quartile (Q3). The gap between Q1 and Q3 is the interquartile range (IQR), which holds the middle half of the data.
How do I find a percentile from a mean and standard deviation?
If the data is roughly bell-shaped, work out z = (value − mean) ÷ SD and look up the area below z. An IQ of 130 with a mean of 100 and an SD of 15 is z = 2, which is the 97.7th percentile. Switch to Advanced and pick “Bell curve” to do this for any numbers.
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