Percentile Calculator

What is a percentile calculator?

A percentile calculator answers two related questions about a list of numbers. First, where does one value stand? — its percentile rank tells you the percentage of the data that falls at or below it. Second, what value marks a given cut-off? — the kth percentile is the data value beneath which a chosen percentage of observations lie. The 90th percentile of a set of exam marks, for example, is the score that 90% of the group scored at or below.

This tool handles both directions. Paste your numbers, pick a mode, and it returns either a percentile rank as a percentage or an interpolated value at the percentile you ask for. Nothing is rounded away from your inputs, and the calculation runs entirely in your browser, so your data never leaves your device.

How does the percentile calculator work?

The tool uses two standard methods, one for each mode.

Percentile rank of a value. It counts how many numbers sit strictly below your value, adds half of any that equal it, divides by the total count n, and multiplies by 100:

rank = (count below + 0.5 × count equal) ÷ n × 100

The half-count for ties places your value fairly in the middle of any group of equal scores rather than at the top or bottom — this is the standard “mid-rank” definition of percentile rank.

Value at the kth percentile. It sorts the data from smallest to largest, then finds a fractional position:

index = k / 100 × (n − 1)

If that index is a whole number, the answer is the value sitting exactly there. If it falls between two positions, the tool linearly interpolates between the two surrounding values. This is the same linear-interpolation method used by spreadsheet functions like PERCENTILE.INC.

Here n is the count of values, k is the percentile you want (0 to 100), and index is counted from 0, so the first value is at index 0 and the last at index n − 1. Percentile rank is reported as a percentage; the kth percentile is reported in the same units as your data.

Examples

Each example uses the verified data set 5, 8, 12, 15, 16, 18, 20, 25, 30, 40 (already sorted, n = 10). Type the same numbers into the tool above to confirm.

Example 1: percentile rank of 18

Count the values below 18 — that is 5, 8, 12, 15, 16, so 5 values. One value equals 18, so count equal = 1.

rank = (5 + 0.5 × 1) ÷ 10 × 100 = 5.5 ÷ 10 × 100 = 55%

So 18 sits at the 55th percentile: 55% of the data is at or below it.

Example 2: the 50th percentile (the median)

index = 50 / 100 × (10 − 1) = 0.5 × 9 = 4.5

Index 4.5 lies halfway between index 4 and index 5 — the values 16 and 18. Interpolating at the midpoint:

16 + 0.5 × (18 − 16) = 16 + 1 = 17

The 50th percentile is 17, which is exactly the median of this ten-value set.

Example 3: the 90th percentile (high cut-off)

index = 90 / 100 × (10 − 1) = 0.9 × 9 = 8.1

Index 8.1 lies between index 8 and index 9 — the values 30 and 40. Interpolating one-tenth of the way:

30 + 0.1 × (40 − 30) = 30 + 1 = 31

The 90th percentile is 31, so 90% of the data falls at or below 31.

Example 4: percentile rank of 25

Seven values fall below 25 (5, 8, 12, 15, 16, 18, 20) and one equals it:

rank = (7 + 0.5 × 1) ÷ 10 × 100 = 7.5 ÷ 10 × 100 = 75%

So 25 lands at the 75th percentile — the upper quartile of this set.

Percentile reference table

This table lists several percentiles of the same data set 5, 8, 12, 15, 16, 18, 20, 25, 30, 40 (n = 10), each found with index = k/100 × 9 and linear interpolation.

Percentile (k)	Index = k/100 × 9	Surrounding values	Interpolated value
0th (minimum)	0	5	5
25th (Q1)	2.25	12 and 15	12.75
50th (median)	4.5	16 and 18	17
75th (Q3)	6.75	20 and 25	23.75
90th	8.1	30 and 40	31
100th (maximum)	9	40	40

The 25th, 50th and 75th percentiles are also called the first quartile, median and third quartile. Notice the 0th percentile equals the smallest value and the 100th equals the largest, because the index lands exactly on the end positions.

Common uses for percentiles

• Test scores. Standardized exams report a percentile rank so a student knows what share of test-takers they outperformed.
• Child growth charts. Pediatricians plot height and weight against age-based percentiles to track development.
• Salary benchmarking. HR teams compare a pay figure to the 25th, 50th and 75th percentiles of a market band.
• Performance monitoring. Engineers track response-time percentiles such as the 95th or 99th to capture worst-case behaviour rather than just the average.
• Describing spread. Quartiles (the 25th, 50th and 75th percentiles) summarise a distribution and feed box plots and the interquartile range.

Tips and common mistakes

• Rank and value are opposites. A percentile rank turns a score into a percentage; the kth percentile turns a percentage into a score. Pick the mode that matches your question.
• Different tools, different methods. Spreadsheets offer both PERCENTILE.INC (the inclusive interpolation this tool uses) and PERCENTILE.EXC; small data sets can give noticeably different answers, so state which method you used.
• Sort first for the kth value. The index formula assumes sorted data — the tool sorts for you, but if you compute by hand, order the numbers before indexing.
• Mind the tie handling. Because equal values count as half, a percentile rank for a repeated score lands in the middle of that group, not at its top.
• Check the count n. A stray comma or typo changes n and shifts every result; confirm the tool read the same number of values you intended.

Limitations and notes

Percentiles are most informative when you have enough data — with only a handful of points, a single value can swing a percentile sharply, and the interpolated kth value depends heavily on the two neighbours it sits between. The linear-interpolation method used here (equivalent to PERCENTILE.INC) is one of several accepted conventions; another common one excludes the endpoints, so a result may differ slightly from a textbook or a different statistics package. Percentiles also describe position, not the shape of a distribution: two very different data sets can share the same median yet behave quite differently in their tails. Everything is computed locally in your browser, and results display rounded for readability. This tool is for educational and general analytical use and is not a substitute for professional statistical advice.

Related tools

Keep exploring the statistics category: find the centre of your data with the mean, median & mode calculator, measure its spread with the standard deviation calculator, or see how far a single value sits from the mean with the z-score calculator.