Quick answer
A percentile is found by interpolating: rank = p ÷ 100 × (n − 1), value = x[⌊rank⌋] + frac(rank) × (x[⌈rank⌉] − x[⌊rank⌋]). The 90th percentile of 1 to 10 is 9.1.
Enter the data and a percentile. The calculator returns the value at that percentile.
Related tools: IQ Percentile Calculator: Percentile of an IQ score on a normal scale. Standard Deviation Calculator: Sample or population standard deviation with variance and mean. Z-Score Calculator: Standardize a value using a mean and standard deviation.
How to use the Percentile Calculator
- Type data set, for example 4, 8, 15, 16, 23, 42.
- Enter percentile (%) (between 0 and 100). It starts at 90.
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Data set | Text, such as 4, 8, 15, 16, 23, 42 | — |
| Percentile | A number, in % | ≥ 0, ≤ 100, starts at 90 |
Formula and method
Formula
rank = p ÷ 100 × (n − 1); value = x[⌊rank⌋] + frac(rank) × (x[⌈rank⌉] − x[⌊rank⌋])
IEEE-754 double precision; shown to at most 6 decimal places.
Linear interpolation between closest ranks (Excel PERCENTILE.INC, NumPy default).
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Data set = 1,2,3,4,5,6,7,8,9,10; Percentile = 90.
| Result | Value |
|---|---|
| 90th percentile | 9.1 |
Example 2
Inputs: Data set = 1,2,3,4,5,6,7,8,9,10; Percentile = 50.
| Result | Value |
|---|---|
| 50th percentile | 5.5 |
Example 3
Inputs: Data set = 3, 1, 2; Percentile = 100.
| Result | Value |
|---|---|
| 100th percentile | 3 |
The first line is the headline result (90th percentile). IEEE-754 double precision; shown to at most 6 decimal places.
Worked example
For ten values, rank = 0.9 × 9 = 8.1. The 9th value is 9 and the 10th is 10, so the value is 9 + 0.1 × 1 = 9.1. 0 gives the minimum and 100 the maximum.
Methods differ
There are several definitions of percentiles; this uses linear interpolation (the same as Excel's PERCENTILE.INC). Other software may give slightly different answers. The 50th percentile is the median.
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Percentile: entering "101" shows "Percentile must be at most 100." beside that field and no result.
Choosing between the Percentile Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [IQ Percentile Calculator](/statistics/iq-percentile/) | iQ score, mean and standard deviation | Percentile |
| [Standard Deviation Calculator](/statistics/standard-deviation-calculator/) | data set and data type | Population standard deviation (σ) |
| [Z-Score Calculator](/statistics/z-score-calculator/) | value, mean and standard deviation | Z-score |
| [Mean Median Mode Range Calculator](/statistics/mean-median-mode-range-calculator/) | data set | Mean |
| [Median Calculator](/statistics/median-calculator/) | data set | Median |
Background: descriptive statistics
Population statistics divide by n and sample statistics divide by n − 1 (Bessel's correction), because a sample tends to understate variability. Use the population version when your data is every value in the group, and the sample version when it is a subset.
Defaults differ between tools, and so do quartile conventions, which can give slightly different values for small data sets; this page states the method it uses.
Assumptions and limitations
- 0 gives the minimum; 100 gives the maximum
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for percentile to confirm this.
Frequently asked questions
What is the 25th percentile?
The 25th percentile is the first quartile Q1: a quarter of the values lie below it.
Is it a percentage?
No, it's a value in the data.
What does being at the 90th percentile mean?
Higher than 90% of values.
What does the Percentile Calculator calculate?
The value at a given percentile of a data set. It returns 90th percentile.
What formula does the Percentile Calculator use?
rank = p ÷ 100 × (n − 1); value = x[⌊rank⌋] + frac(rank) × (x[⌈rank⌉] − x[⌊rank⌋]). Linear interpolation between closest ranks (Excel PERCENTILE.INC, NumPy default).
What do I need to enter in the percentile Calculator?
You enter Data set and Percentile (%).
How is the result rounded or limited?
IEEE-754 double precision; shown to at most 6 decimal places. 0 gives the minimum; 100 gives the maximum.
What is an example of a percentile result?
With data set 1,2,3,4,5,6,7,8,9,10 and percentile 90, the 90th percentile is 9.1.
Related calculators
- IQ Percentile Calculator — Percentile of an IQ score on a normal scale.
- Standard Deviation Calculator — Sample or population standard deviation with variance and mean.
- Z-Score Calculator — Standardize a value using a mean and standard deviation.
- Mean Median Mode Range Calculator — Mean, median, mode and range of a data set.
- Median Calculator — Median of a data set.
- Relative Standard Deviation Calculator — Relative standard deviation (RSD) as a percentage.
Sources
- Standard statistics definition (e.g. NIST/SEMATECH e-Handbook of Statistical Methods)
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.