Percentile Calculator
Paste your data and find the kth percentile by the three common methods side by side (Excel PERCENTILE.INC, PERCENTILE.EXC and the nearest rank), the percentile rank of any value, or the quartiles and deciles, with the working and a cumulative plot.
How to Use
- Paste or type your numbers, separated by commas, spaces or new lines (a spreadsheet column works).
- Choose percentile → value, value → percentile rank or quartiles and deciles.
- Type k (such as 90 for the 90th percentile) or the value whose rank you want.
- Read the answer by each method: Excel PERCENTILE.INC, PERCENTILE.EXC and the nearest rank often differ on small data sets.
- The plot shows the share of the data at or below each value, with the results marked; Show Work gives the positions used.
Worked Example
The 90th percentile of 1 to 10, three ways. PERCENTILE.INC puts it at position (10 − 1) × 0.9 + 1 = 9.1, a tenth of the way from the 9th value to the 10th: 9.1. PERCENTILE.EXC uses (10 + 1) × 0.9 = 9.9: 9.9. The nearest rank is the ⌈0.9 × 10⌉ = 9th value: 9. All three are correct under their own definition.
A percentile rank with ties. In 3, 5, 5, 5, 7, 8, 9, 10, 12, 15, the value 5 has 1 value below it and 3 equal to it. That is 1 ÷ 10 = 10% below and 4 ÷ 10 = 40% at or below; counting the ties half-way gives (1 + 1.5) ÷ 10 = 25%, the usual percentile rank.
The common mistake: reading a percentage as a percentile. A mark of 85 out of 100 is 85%, but in a class scoring 64, 69, 70, 72, 77, 78, 81, 85, 88, 90, 92 and 95, seven marks are lower and one is equal, so 85 is at the 62.5th percentile. A percentile always compares with the rest of the data.
Show Work
Formulas
Ranking Instead of Averaging
Francis Galton introduced the word “percentile” in 1885, while reporting on the thousands of visitors measured at his Anthropometric Laboratory. He preferred to describe a person by their place in the line-up of everyone measured, and championed the median and the quartiles, which a few extreme values cannot drag about the way they drag a mean.
No single definition of a sample percentile ever won. In 1996 Rob Hyndman and Yanan Fan catalogued nine in use across statistics packages, and Excel 2010 split its PERCENTILE function into PERCENTILE.INC and PERCENTILE.EXC, which is why two correct calculators can disagree on a small data set.
About This Calculator
This calculator works on up to 100,000 numbers. It gives the kth percentile by Excel’s PERCENTILE.INC and PERCENTILE.EXC and by the nearest rank side by side, so you can see whether the method matters for your data; the percentile rank of any value, below, at or below, with ties counted half, and as Excel’s PERCENTRANK.INC; and the quartiles by the inclusive, TI-84 and .EXC conventions, with all nine deciles. The exclusive (TI-84) quartiles match the Statistics Calculator’s.
Everything runs in your browser; nothing is sent anywhere.
Related tools: Statistics Calculator, Probability & Statistics Lab, and Z-Score Calculator.
Frequently Asked Questions
How do I calculate a percentile?
Sort the data, find the position of the percentile, and read off the value there, interpolating between neighbours if the position falls between two. In Excel’s PERCENTILE.INC the position is (n − 1)p + 1: for the 90th percentile of 1 to 10 it is 9 × 0.9 + 1 = 9.1, so the answer is 9 + 0.1 × (10 − 9) = 9.1.
Why do Excel, R and my textbook give different percentiles?
They use different definitions. PERCENTILE.INC (R’s default, type 7) uses position (n − 1)p + 1, PERCENTILE.EXC (R type 6) uses (n + 1)p, and the nearest-rank method takes the ⌈pn⌉-th value without interpolating. For the 20 response times in the presets, the 95th percentile is 930 ms, 1,470 ms or 900 ms. The gap shrinks as the data set grows.
What is a percentile rank?
The percentage of the data below a value, usually with ties counted half: (number below + ½ × number equal) ÷ n × 100. In 3, 5, 5, 5, 7, 8, 9, 10, 12, 15 the value 5 has 1 value below it and 3 equal to it, so it is 10% below, 40% at or below, and has percentile rank (1 + 1.5) ÷ 10 = 25%.
What is the difference between a percentile and a percentage?
A percentage is a score out of 100; a percentile compares a score with everyone else’s. A test mark of 85% in a class with scores 64, 69, 70, 72, 77, 78, 81, 85, 88, 90, 92 and 95 has 7 scores below it and 1 equal, so it is at the 62.5th percentile, not the 85th.
Are quartiles the same as percentiles?
Yes: Q1, the median and Q3 are the 25th, 50th and 75th percentiles, so they also depend on the method. For 1 to 10, Q1 is 3.25 inclusive (Excel QUARTILE.INC), 3 exclusive (TI-84, the median of each half) and 2.75 by Excel’s QUARTILE.EXC. Note that the TI-84’s exclusive method and Excel’s .EXC functions are not the same.
How do I use the Percentile Calculator?
Just type your numbers. The answer shows up right away — there is no button to press. Change anything and it updates by itself.
Does it cost anything or need an account?
No. The tool is completely free, there is no account to create, and it keeps working offline after the page first loads.
Is anything I type uploaded?
No. The tool works entirely on your device, so the values you enter never leave your browser.
Common Use Cases
Test scores
The 25th percentile of 12 class scores from 64 to 95 is 71.5 (INC), 70.5 (EXC) or 70 (nearest rank).
Response times
The 95th percentile of 20 page loads is 930 ms by PERCENTILE.INC but 900 ms by nearest rank.
Percentile rank
A score of 85 among those 12 sits at the 62.5th percentile.
Deciles
D9 of the same scores is 91.8, the line above which the top tenth sits.
Checking Excel
PERCENTRANK.INC of 5 in 1, 1, 1, 2, 3, 4, 8, 11, 12, 13 is 0.5833, which Excel shows as 0.583.
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