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Formula
position = 1 + (P ÷ 100) × (n − 1); value = xₖ + f × (xₖ₊₁ − xₖ)
- P
- the percentile you want, from 0 to 100
- n
- the number of values
- k, f
- the whole-number and fractional parts of the position
- xₖ
- the kth value after sorting from smallest to largest
What a percentile is
The Pth percentile is the value below which about P% of the data falls. If the 75th percentile of commute times is 32 minutes, about three-quarters of commuters take 32 minutes or less. Percentiles describe position rather than size, which makes them useful for skewed data, such as incomes, response times and test scores, where an average can mislead.
The percentile calculator answers the question in either direction:
- Value at a percentile: “What score marks the 90th percentile?”
- Percentile rank of a value: “My score was 80. What percentile is that?”
How to use the percentile calculator
- Choose the tab for the question you’re asking.
- Paste your data. The order doesn’t matter; the calculator sorts it.
- Enter the percentile (0 to 100) or the value you want to rank.
- Read the answer at the top. The working shows the sorted data, the position and the interpolation.
How to calculate a percentile by hand
Take eight exam scores: 55, 61, 64, 70, 72, 78, 85 and 91. They’re already sorted. Find the 75th percentile.
- Find the position: 1 + (75 ÷ 100) × (8 − 1) = 1 + 5.25 = 6.25.
- Split it: the whole part, 6, points to the 6th value, 78. The fractional part is 0.25.
- Interpolate: go 0.25 of the way from the 6th value (78) to the 7th (85): 78 + 0.25 × (85 − 78) = 79.75.
So the 75th percentile is 79.75. If the position is a whole number, no interpolation is needed; the answer is that value.
Percentile rank of a score
Where does a score of 80 fall in the same list? It lies between 78 (6th value, rank 5 ÷ 7 = 71.43) and 85 (7th value, rank 6 ÷ 7 = 85.71). It’s 2 ÷ 7 of the way from 78 to 85, so its rank is 71.43 + (2 ÷ 7) × 14.29 ≈ 75.51. A score of 80 has a percentile rank of about 75.51, which agrees with the previous answer: the 75th percentile, 79.75, is just below 80.
Percentiles of the example scores
| Percentile | Position | Value |
|---|---|---|
| 10th | 1.7 | 59.2 |
| 25th (first quartile) | 2.75 | 63.25 |
| 50th (median) | 4.5 | 71 |
| 75th (third quartile) | 6.25 | 79.75 |
| 90th | 7.3 | 86.8 |
The interquartile range is 79.75 − 63.25 = 16.5 points, which means the middle half of the class spans 16.5 points.
Which percentile method is this?
Statisticians have published at least nine ways to calculate sample percentiles, catalogued by Hyndman and Fan in 1996. This calculator uses their type 7, linear interpolation with position 1 + p(n − 1). It’s the default in Excel’s PERCENTILE.INC (and the older PERCENTILE), Google Sheets, R and NumPy, so your answers will match the spreadsheet you’re likely to check them in.
The NIST handbook and Excel’s PERCENTILE.EXC use position p(n + 1) instead. For the 75th percentile of the eight scores above, that gives position 6.75 and a value of 83.25 rather than 79.75. Neither is wrong; they’re different conventions. On large data sets the methods converge.
Percentile rank: three common definitions
Ranking a value has its own set of conventions. The calculator’s main answer is the inclusive rank, the inverse of the interpolation above, so a value always lands back on the percentile that produced it. Below it, three simpler shares are listed:
- Share below: the percentage of values strictly less than yours. It never reaches 100.
- Share at or below: the percentage less than or equal to yours. It never falls to 0.
- Midpoint rank: values below plus half of those equal, divided by the count. Many education and health reports use this one, because it treats ties fairly.
For a score of 72 in the eight-score list, the inclusive rank is 57.14, the share below is 50%, the share at or below is 62.5%, and the midpoint rank is 56.25%. They all describe the same position, using slightly different rules, so quote the definition along with the number.
Real-life uses
- Test scores. Standardized tests report percentile ranks so students can see their standing in the group.
- Child growth. Pediatric charts show height and weight percentiles by age.
- Website and app performance. Engineers track the 95th or 99th percentile response time, because a mean hides the slow requests users notice.
- Pay and prices. Salary surveys quote the 25th, 50th and 75th percentiles to show a typical range.
If your data is roughly bell-shaped and you know only the mean and standard deviation, the z-score calculator estimates a percentile from those two numbers. For spread around the mean, use the standard deviation calculator.
Common mistakes
- Confusing percentile with percentage correct. They measure different things.
- Comparing results from different methods. Small data sets can give different answers in different software; check the method before comparing.
- Entering a decimal as the percentile. Enter 90 for the 90th percentile here, not 0.9 as in Excel.
- Forgetting to sort when working by hand. Positions refer to the sorted list.
For the mean, median and mode of the same data, use the average calculator.
Worked examples
40th percentile of five values
The value at the 40th percentile of a five-value data set, interpolated between the 2nd and 3rd values.
Inputs (Value at a percentile): Data values = 15, 20, 35, 40, 50; Percentile (P) = 40 th
Sorted: 15, 20, 35, 40, 50 Position = 1 + (P ÷ 100) × (n − 1) = 1 + (40 ÷ 100) × (5 − 1) = 2.6 Value = x₂ + 0.6 × (x₃ − x₂) = 20 + 0.6 × (35 − 20) = 29
Answer: The 40th percentile of the 5 values is 29 (linear interpolation, like Excel PERCENTILE.INC).
Percentile rank of a test score
Where a score of 10 ranks among ten quiz scores.
Inputs (Percentile rank of a value): Data values = 3 6 7 8 8 10 13 15 16 20; Value (x) = 10
Sorted: 3, 6, 7, 8, 8, 10, 13, 15, 16, 20 Values below 10: 5 Rank = 5 ÷ (10 − 1) × 100 = 55.5556
Answer: 10 is at the 55.56th percentile of the 10 values (inclusive linear interpolation, like Excel PERCENTRANK.INC).
The 100th percentile
Edge case: with the inclusive method, the 100th percentile is the largest value.
Inputs (Value at a percentile): Data values = 7.2, 3.1, 9.8, 4.4; Percentile (P) = 100 th
Sorted: 3.1, 4.4, 7.2, 9.8 Position = 1 + (P ÷ 100) × (n − 1) = 1 + (100 ÷ 100) × (4 − 1) = 4 Position 4 is a whole number, so the value is x₄ = 9.8
Answer: The 100th percentile of the 4 values is 9.8 (linear interpolation, like Excel PERCENTILE.INC).
Assumptions and limitations
- The value at a percentile uses linear interpolation between closest ranks, the inclusive method of Excel PERCENTILE.INC, Google Sheets PERCENTILE, NumPy's default and Hyndman and Fan's type 7.
- With this method the 0th percentile is the minimum, the 100th is the maximum and the 50th is the median.
- The percentile rank is the inverse of that method, matching Excel PERCENTRANK.INC (without Excel's truncation to 3 digits). A value that appears in the data gets rank = (values below it) ÷ (n − 1) × 100; a value between two data points is interpolated.
- The percentile rank also lists the plain shares of values below, and at or below, the value, because some textbooks and score reports use those definitions instead.
- The percentile rank needs at least two data values, and the value must lie between the smallest and largest of them.
- Up to 10,000 values can be entered. Results are shown to up to 6 decimal places.
Frequently asked questions
What is the difference between a percentile and a percentage?
A percentage is a share of a total, like scoring 80% of the points on a test. A percentile is a position in a group, like scoring higher than 80% of test takers. You can score 60% on a hard test and still be in the 90th percentile.
Why do different calculators give different percentiles?
There are at least nine published methods. They agree on large data sets but can differ noticeably on small ones. This calculator uses the inclusive linear interpolation method of Excel PERCENTILE.INC. Excel's PERCENTILE.EXC and the NIST handbook use a (n + 1)-based position instead, which spreads small samples further toward the extremes.
How do I find the 25th, 50th and 75th percentiles (quartiles)?
Enter 25, 50 and 75 as the percentile in turn. The 50th percentile is the median. The difference between the 75th and 25th percentiles is the interquartile range, a measure of spread that ignores outliers.
What does being in the 90th percentile mean?
It means about 90% of the values in the group are at or below yours, and about 10% are above. It says nothing about the absolute score, only about the position within the group.
Can a percentile be 100?
With the inclusive method used here, yes. The largest value is at the 100th percentile, because no value in the data exceeds it. Score reports that use the "share below" definition usually top out at 99.
How do I calculate a percentile in Excel?
Use =PERCENTILE.INC(range, 0.9) for the 90th percentile and =PERCENTRANK.INC(range, x) for the rank of x. Note that Excel takes the percentile as a decimal from 0 to 1, while this calculator takes 0 to 100.
Sources
- PERCENTILE.INC function — Microsoft Support. Checked October 12, 2026.
- PERCENTRANK.INC function — Microsoft Support. Checked October 12, 2026.
- Percentiles (NIST/SEMATECH e-Handbook of Statistical Methods, 7.2.6.2) — National Institute of Standards and Technology. Checked October 12, 2026.
- 2.3 Measures of the Location of the Data (Introductory Statistics 2e) — OpenStax, Rice University. Checked October 12, 2026.