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Percentile Calculator
Paste a list of numbers to get the value at any percentile, the percentile rank of a score, the quartiles and the interquartile range. Choose the same method as Excel, Google Sheets or your textbook.
Numbers separated by commas, spaces or new lines. You can paste a spreadsheet column.
th
Enter your values to see the result.
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How to use the Percentile Calculator
- Paste your numbers, separated by commas, spaces or new lines.
- Enter the percentile you want, for example 90.
- Optionally enter a score to find its percentile rank.
- Pick a method to match Excel, your textbook or your software.
- Read the result, the quartiles, IQR, box plot and the full percentile table.
Percentile formulas
Sort the n values from smallest to largest, x₍₁₎ ≤ x₍₂₎ ≤ … ≤ x₍ₙ₎, then find the rank position r for percentile p:
- Inclusive / linear (Excel PERCENTILE.INC, Google Sheets PERCENTILE, R type 7): r = p/100 × (n − 1) + 1
- Exclusive (Excel PERCENTILE.EXC, R type 6): r = p/100 × (n + 1)
- Nearest rank: r = ⌈p/100 × n⌉, take that value directly
If r has a fractional part f, the percentile is x₍⌊r⌋₎ + f × (x₍⌊r⌋+1₎ − x₍⌊r⌋₎). Example with 1, 2, …, 10 and p = 25 (inclusive): r = 0.25 × 9 + 1 = 3.25, so P25 = 3 + 0.25 × (4 − 3) = 3.25.
Percentile rank of a score x: PR = (number below x + 0.5 × number equal to x) / n × 100.
Same data, different methods
Data: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 (n = 10).
| Percentile | Inclusive (INC) | Exclusive (EXC) | Nearest rank |
|---|---|---|---|
| 10th | 1.9 | 1.1 | 1 |
| 25th (Q1) | 3.25 | 2.75 | 3 |
| 50th (median) | 5.5 | 5.5 | 5 |
| 75th (Q3) | 7.75 | 8.25 | 8 |
| 90th | 9.1 | 9.9 | 9 |
Frequently asked questions
What is a percentile?
The pth percentile is the value below which about p% of the data falls. The 90th percentile of test scores is the score that 90% of students scored at or below.
How do you calculate a percentile?
Sort the data, then find the rank position. With the inclusive (Excel PERCENTILE.INC) method the rank is p/100 × (n − 1) + 1. If the rank is not a whole number, interpolate between the two neighbouring values.
What is the difference between a percentile and a percentile rank?
A percentile is a value in the data (the 90th percentile is 72). A percentile rank is the percentage of values below a given score (a score of 72 has a percentile rank of about 90%).
How is percentile rank calculated?
This calculator uses PR = (B + 0.5 × E) / n × 100, where B is the number of values below the score and E the number equal to it. It also shows the share strictly below and at or below.
Why do Excel's PERCENTILE.INC and PERCENTILE.EXC give different answers?
They use different rank formulas: INC uses p/100 × (n − 1) + 1 and EXC uses p/100 × (n + 1). EXC cannot compute very low or very high percentiles for small data sets. Both are valid conventions.
What are quartiles and the IQR?
Quartiles are the 25th (Q1), 50th (median) and 75th (Q3) percentiles. The interquartile range IQR = Q3 − Q1 covers the middle half of the data and is not affected by extreme values.
How are outliers found with the IQR?
A common rule, used in box plots, flags values below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR as outliers.
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