A percentile tells you where a value stands within a data set. The 90th percentile is the value that 90% of the observations are at or below; the 50th percentile is the median; the 25th and 75th are the quartiles. Percentiles describe test scores, children’s growth, website response times (“95% of requests finish within 300 ms”) and incomes, because they work for any shape of distribution.
With a finite data set the requested percentage rarely falls exactly on an observation, so the value is interpolated between two neighbouring sorted values. The rank position depends on the convention. The NIST handbook and Excel’s PERCENTILE.EXC use r = p(n + 1); Excel’s PERCENTILE.INC, Google Sheets and R’s default use r = 1 + p(n − 1); the nearest-rank method simply rounds up p × n and returns an actual data value.
Choose the method that matches your course or software. The steps show the rank position and the interpolation, and the chart plots the cumulative percentage of the data with your percentile marked.
How to use the Percentile Calculator
- Data set
- Percentile (p): For example 90 for the 90th percentile.
- Percentile method
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How it works
Sort the data, compute the rank position for the chosen method, then interpolate linearly between the values at the neighbouring whole-number ranks (positions below 1 or above n use the minimum or maximum).
Worked example
Ten test scores: 55, 60, 62, 70, 71, 75, 80, 85, 88, 95. For the 90th percentile with the (n + 1) method the rank is 0.90 × 11 = 9.9, between the 9th value (88) and the 10th (95). P90 = 88 + 0.9 × (95 − 88) = 94.3. With Excel’s PERCENTILE.INC the rank is 1 + 0.9 × 9 = 9.1 and P90 = 88.7; the nearest-rank method gives the 9th value, 88.
Percentile methods compared
| Method | Rank position | Software | P90 of the example |
|---|---|---|---|
| (n + 1)·p | p(n + 1) | NIST, Excel PERCENTILE.EXC, Minitab | 94.3 |
| 1 + (n − 1)·p | 1 + p(n − 1) | Excel PERCENTILE.INC, Google Sheets, R type 7 | 88.7 |
| Nearest rank | ⌈p·n⌉ | Many textbooks, some grading systems | 88 |
Formula
Rank r = p/100 × (n + 1) (or 1 + p/100 × (n − 1)) · Pₚ = x₍⌊r⌋₎ + (r − ⌊r⌋) × (x₍⌊r⌋+1₎ − x₍⌊r⌋₎)
Worked example
Inputs: Data set: 55, 60, 62, 70, 71, 75, 80, 85, 88, 95; Percentile (p): 90; Percentile method: (n + 1)·p rank, interpolated (NIST, Excel PERCENTILE.EXC).
Results: Value at the percentile = 94.3; Rank position in the sorted data = 9.9; Share of data strictly below this value = 90 %; Q1, median and Q3 with the same method = 61.5, 73, 85.75; Number of values = 10; Step-by-step working = Sorted data: 55, 60, 62, 70, 71, 75, 80, 85, 88, 95
Rank position = (n + 1) × p = 11 × 0.9 = 9.9
Interpolate between value 9 (88) and value 10 (95): 88 + 0.9 × (95 − 88)
P90 = 94.3.
Key terms
- Percentile
- The value below which a given percentage of the data fall.
- Rank position
- The (possibly fractional) position in the sorted data at which the percentile is read.
- Interpolation
- Estimating a value between two known neighbouring values.
- Nearest rank
- A method that returns the data value at position ⌈p × n⌉.
Frequently asked questions
How do I calculate a percentile?
Sort the data, find the rank r = p/100 × (n + 1) and interpolate between the values at the ranks either side of r.
What is the 90th percentile of 55, 60, 62, 70, 71, 75, 80, 85, 88, 95?
r = 0.9 × 11 = 9.9, so P90 = 88 + 0.9 × (95 − 88) = 94.3. Excel's PERCENTILE.INC gives 88.7.
Is the 50th percentile the median?
Yes, with every method on this page.
What does it mean to be in the 90th percentile?
Your value is at or above 90% of the values in the group.
Why do Excel and my textbook give different percentiles?
They use different rank formulas. Choose the matching method in the menu; the differences shrink as the data set grows.
What is the difference between percentile and percentage?
A percentage is a proportion out of 100; a percentile is a value in the data below which a given percentage of observations fall.
What is the difference between a percentile and a percentile rank?
A percentile is a data value for a given percentage; a percentile rank is the percentage for a given data value. Use the percentile rank calculator for the latter.