Percentile Calculator
Find any percentile value from a data set, plus quartiles and IQR. See also Z-Score Calculator and Median Calculator.
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How to Calculate Percentiles
A percentile indicates the value below which a given percentage of data falls. The 75th percentile means 75% of the data is at or below that value. To calculate: sort the data, compute the rank position using L = (P/100) × (n−1), then interpolate between adjacent values if the position is not a whole number. Percentiles are widely used in standardized testing, growth charts, and data analysis.
Percentile Formula
Position L = (P / 100) × (n − 1)
If L is whole: Percentile = sorted[L]
If L is fractional: Interpolate between sorted[floor(L)] and sorted[ceil(L)]
Q1 = 25th percentile, Q2 = 50th (median), Q3 = 75th
IQR = Q3 − Q1
Example Calculation
Data: 15, 20, 35, 40, 50, 55, 60, 70, 75, 80, 90, 95
Find the 75th percentile (n = 12)
L = (75/100) × (12 − 1) = 8.25
Interpolate: sorted[8] = 75, sorted[9] = 80
P75 = 75 + 0.25 × (80 − 75) = 75 + 1.25 = 76.25
Common Percentiles Reference
| Percentile | Also Known As | Common Use |
|---|---|---|
| 25th (Q1) | First Quartile | Lower boundary of middle 50% |
| 50th (Q2) | Median | Central tendency |
| 75th (Q3) | Third Quartile | Upper boundary of middle 50% |
| 90th | Top 10% | Performance benchmarks |
| 95th | Top 5% | Outlier detection |
| 99th | Top 1% | Extreme values |
Frequently Asked Questions
What does the 90th percentile mean?
The 90th percentile is the value below which 90% of the data falls. If your test score is at the 90th percentile, you scored higher than 90% of test takers.
What is the difference between percentile and percentage?
Percentage is a fraction of 100 (e.g., 85% correct). Percentile is a ranking — it tells you what proportion of values fall below a given value in a data set.
Is the 50th percentile always the median?
Yes. The 50th percentile is the median by definition — the value where half the data is below and half is above.
How are percentiles used in real life?
Percentiles are used in standardized testing (SAT, GRE), child growth charts (height/weight), income distribution analysis, and performance benchmarking in technology (response times, latency).
What is the interquartile range (IQR)?
IQR = Q3 − Q1, the range of the middle 50% of data. It is a robust measure of spread that is not affected by outliers. Values below Q1 − 1.5×IQR or above Q3 + 1.5×IQR are often considered outliers.