Percentile Calculator

A percentile tells you what share of a data set falls at or below a given value. If your score is at the 90th percentile, then 90% of the other values in the set are equal to or lower than yours. This percentile calculator finds any nth percentile you choose and also returns the four quartiles (Q1, Q2/Median, Q3) and the interquartile range (IQR), so you can describe the full spread of your data in one step.

How to use this calculator

1. Type your numbers into the Values box, separated by commas or spaces (for example, 2, 4, 4, 5, 7, 9).
2. Enter the Percentile you want — any number from 0 to 100 (for example, 90 for the 90th percentile).
3. Click Calculate. The tool shows the requested percentile value, then Q1, the median (Q2), Q3, and the IQR below it.

Worked example

Take the data set 2, 4, 4, 5, 7, 9 (six values) and find the 90th percentile.

The calculator uses the Hyndman-Fan Type 7 linear interpolation formula, which is the standard in R and NumPy. It locates the target between two adjacent sorted values:

position = (p / 100) x (n - 1)
         = 0.90 x (6 - 1)
         = 4.5

P90 = value[4] + 0.5 x (value[5] - value[4])
    = 7 + 0.5 x (9 - 7)
    = 8

The same method gives the quartiles automatically:

Q1  (P25) = 4.0   (25th percentile)
Q2  (P50) = 4.5   (median / 50th percentile)
Q3  (P75) = 6.5   (75th percentile)
IQR       = Q3 - Q1 = 6.5 - 4.0 = 2.5

The NIST/SEMATECH e-Handbook covers percentiles in its discussion of measures of location and order statistics, including how percentiles relate to the rank of each observation.

Frequently asked questions

What is a percentile rank?

Percentile rank is the percentage of values in a data set that fall at or below a particular score. If a test score sits at the 75th percentile, three-quarters of all scores in the group are equal to or lower than that score.

What is the nth percentile?

The nth percentile (sometimes written Pn) is the value below which n% of observations fall. The 50th percentile is the median; the 25th and 75th are the lower and upper quartiles. The 90th and 95th percentiles are common benchmarks in growth charts, performance testing, and quality control.

How is the IQR calculated?

The interquartile range is Q3 minus Q1 — the width of the middle 50% of your data. Because it ignores the lowest and highest quarters, the IQR is resistant to outliers and a reliable measure of spread when data is skewed or contains extreme values.

Which percentile formula does this calculator use?

This calculator uses the Hyndman-Fan Type 7 linear interpolation method. It computes a fractional index across the sorted list and blends two adjacent values using a weighted average. This is the default in R, NumPy, and most modern statistics packages, so results match those tools when you supply the same data.