Percentile Calculator
Find percentile ranks and values from a dataset.
Find the value at a given percentile in a dataset
What Is the Percentile Calculator?
The Percentile Calculator finds the value below which a given percentage of data falls. For example, the 75th percentile is the value below which 75% of the data lies. The tool uses linear interpolation for accurate results and also computes the full five-number summary (Min, Q1, Q2, Q3, Max).
Formula
How to Use
Enter your data values separated by commas or spaces in the text area. Enter the percentile you want to compute (0–100). Click Calculate to get the percentile value, all quartiles, the IQR, and the five-number summary.
Example Calculation
Data: 4, 7, 13, 16, 21, 24, 28, 30 N = 8 values, sorted: 4 7 13 16 21 24 28 30 50th percentile (median): Rank = 0.5×7+1 = 4.5 → between index 3 and 4 P50 = 16 + 0.5×(21−16) = 16 + 2.5 = 18.5 Q1 = 10, Q3 = 25, IQR = 15
Understanding Percentile
Percentiles are one of the most important tools for interpreting data in context. A raw score of 75 on a test means nothing without knowing the distribution; a percentile rank of 90 tells you exactly where you stand relative to your peers.
The five-number summary and box plot are standard tools in exploratory data analysis (EDA). The IQR is used to detect outliers: a value is often flagged as an outlier if it falls more than 1.5 × IQR below Q1 or above Q3 (Tukey's fences).
Percentiles differ from percentages: a percentage is a raw proportion (75%), while a percentile is a rank in a distribution (75th percentile). A student scoring 75% might be at the 60th or 90th percentile depending on how others performed.
Frequently Asked Questions
What is a percentile?
The Pth percentile is the value below which P% of the data falls. If your test score is at the 90th percentile, you scored higher than 90% of other test-takers.
What is the IQR?
The Interquartile Range (IQR = Q3 − Q1) measures the spread of the middle 50% of the data. It is a robust measure of variability, unaffected by extreme outliers.
What is the five-number summary?
The five-number summary (Min, Q1, Median, Q3, Max) provides a complete picture of a dataset's distribution and is the basis for box plots.
Why is median the 50th percentile?
The median splits the data in half: 50% of values fall below it and 50% above it. It equals the 50th percentile by definition.
How are percentiles used in practice?
Standardized test scores (SAT, GRE), pediatric growth charts, income distributions, and performance benchmarks all use percentiles to compare individuals to a reference population.