Percentile Calculator
Find the value at any percentile in a data set, plus quartiles and rank.
Enter numbers separated by commas, spaces or new lines.
Computed using the linear-interpolation method.
Quartiles & Range
| Statistic | Value |
|---|---|
| Minimum | |
| First Quartile (Q1, 25th) | |
| Median (Q2, 50th) | |
| Third Quartile (Q3, 75th) | |
| Maximum | |
| Interquartile Range (IQR) |
What Is a Percentile?
A percentile is a value below which a given percentage of observations in a data set fall. For example, the 90th percentile is the value below which 90% of the data lie. Percentiles are widely used to interpret test scores, growth charts, salaries and other rankings because they describe relative standing within a group rather than an absolute amount.
The Linear-Interpolation Method
This calculator uses the linear-interpolation method. The data are first sorted in ascending order. For a percentile p and n values, a fractional rank is computed and the result is interpolated between the two nearest data points:
- Step 1: Sort the values ascending.
- Step 2: Compute the rank:
rank = (p / 100) × (n − 1). - Step 3: Let
i = floor(rank)andf = rank − i(the fractional part). - Step 4: Interpolate:
value = sorted[i] + f × (sorted[i+1] − sorted[i]), clamping at the ends of the data.
Quartiles and the IQR
Quartiles are simply the 25th (Q1), 50th (median, Q2) and 75th (Q3) percentiles, dividing the sorted data into four equal parts. The interquartile range (IQR = Q3 − Q1) measures the spread of the middle 50% of the data and is a robust indicator of variability that is not distorted by extreme outliers.