Percentile Calculator (Percentile and Percentile Rank)
Find the value at any percentile (Excel PERCENTILE.INC, EXC or nearest rank), the percentile rank of a value, quartiles and IQR, or a percentile from a z-score.
| Percentile | Inclusive (PERCENTILE.INC) | Exclusive (PERCENTILE.EXC) | Nearest rank |
|---|---|---|---|
| 0 | 3 | — | 3 |
| 5 | 4.35 | — | 3 |
| 10 | 5.7 | 3.3 | 3 |
| 25 | 7.25 | 6.75 | 7 |
| 50 | 9 | 9 | 8 |
| 75 | 14.5 | 15.25 | 15 |
| 90 | 16.4 | 19.6 | 16 |
| 95 | 18.2 | — | 20 |
| 99 | 19.64 | — | 20 |
| 100 | 20 | — | 20 |
A percentile tells you where a value sits in a data set: the 90th percentile is the value below which 90% of the data fall. This calculator finds the value at any percentile, the percentile rank of a given value, the quartiles and interquartile range, and the percentile of a score in a normal distribution. Because spreadsheets and textbooks use different rules, it lets you choose the inclusive, exclusive or nearest-rank method.
How to use this tool
- Paste your numbers, separated by commas, spaces or new lines.
- Choose whether you want the value at a percentile, or the percentile rank of a value.
- Pick the method that matches your course or software (Excel PERCENTILE.INC is the common default).
- For test scores with a known mean and SD, use the z mode instead of raw data.
Formula
Inclusive: rank r = (n − 1)p + 1 · Exclusive: r = (n + 1)p · Nearest rank: r = ⌈pn⌉ · value = x⌊r⌋ + (r − ⌊r⌋)(x⌊r⌋+1 − x⌊r⌋)
The data are sorted, p is the percentile as a fraction and n the number of values; fractional ranks are interpolated between neighbours. The exclusive method needs 1/(n + 1) ≤ p ≤ n/(n + 1). Percentile rank = (number below + ½ × number equal) ÷ n × 100. The z mode uses the normal distribution: percentile = Φ((x − mean) ÷ SD).
Example
For 3, 6, 7, 8, 8, 10, 13, 15, 16, 20 (n = 10), the inclusive 25th percentile has rank 9 × 0.25 + 1 = 3.25, so it lies a quarter of the way from 7 to 8: 7.25. The median is 9, Q3 is 14.5 and the IQR is 7.25. The value 8 has a percentile rank of (3 + ½ × 2) ÷ 10 = 40%. An IQ of 130 (mean 100, SD 15) is z = 2, the 97.7th percentile.
Frequently asked questions
Why do Excel and my textbook give different percentiles?
There are several accepted definitions. Excel's PERCENTILE.INC and NumPy's default interpolate with rank (n − 1)p + 1; PERCENTILE.EXC and many statistics textbooks use (n + 1)p; others take the nearest rank. With large data sets they nearly agree.
Is the 50th percentile the median?
Yes, with the inclusive and exclusive methods it equals the usual median. The nearest-rank method gives the lower of the two middle values for an even count.
What is a percentile rank?
It is the percentage of values below a score, counting ties as half. A score at the 40th percentile rank beat 40% of the group.
Sources
Last updated:
Page address with these inputs: https://kakao.mobile/tools/percentile-calculator/
Cite or embed this tool
kakaoCalc. (2026, November 8). Percentile Calculator (Percentile and Percentile Rank). https://kakao.mobile/tools/percentile-calculator/
“Percentile Calculator (Percentile and Percentile Rank).” kakaoCalc, 8 Nov. 2026, kakao.mobile/tools/percentile-calculator/.
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