Percentile Calculator
Calculate percentile values, percentile ranks, quartiles (Q1, Q2, Q3), interquartile range, deciles, and detect outliers in your data.
Percentile Calculator
Find the value at a specific percentile in your data set.
How to Use the Percentile Calculator
Enter your data values separated by spaces or commas. Choose the type of analysis: find a percentile value, calculate a percentile rank, analyze quartiles, or compute deciles.
Understanding Percentiles
Percentile Values
A percentile indicates the value below which a given percentage of data falls:
- 50th percentile: The median (50% of data is below)
- 25th percentile: First quartile (Q1)
- 75th percentile: Third quartile (Q3)
- 90th percentile: Only 10% of data exceeds this value
Percentile Rank
The percentile rank tells you what percentage of data falls at or below a specific value. Useful for comparing individual values to a distribution.
Quartiles and IQR
- Q1 (25th percentile): Lower quartile
- Q2 (50th percentile): Median
- Q3 (75th percentile): Upper quartile
- IQR = Q3 - Q1: Interquartile range (middle 50% spread)
Outlier Detection
Uses the 1.5 × IQR rule:
- Lower fence: Q1 - 1.5 × IQR
- Upper fence: Q3 + 1.5 × IQR
- Values outside these fences are considered outliers
Deciles
Deciles divide data into 10 equal parts:
- D1 (10th percentile): 10% below
- D5 (50th percentile): Median
- D9 (90th percentile): 90% below
Calculation Method
This calculator uses linear interpolation (similar to Excel's PERCENTILE.INC function). For a percentile p in a dataset of n values:
- Calculate index = (p/100) × (n-1)
- Interpolate between adjacent values if needed
Common Applications
- Academic grading and standardized testing
- Growth charts in pediatrics
- Income and wealth distribution analysis
- Performance benchmarking
- Quality control and process analysis
- Data exploration and summary statistics
Important Notes
- Different methods exist for calculating percentiles
- Results may vary slightly between statistical software
- More data points give more reliable percentile estimates
- Percentiles are useful for non-normal distributions
Worked Example
For the dataset 12, 23, 34, 45, 56, 67, 78, 89 (n = 8, already sorted), the 25th percentile index is (25/100) × (8 - 1) = 1.75, so Q1 interpolates 75% of the way from 23 to 34: 23 + 0.75 × 11 = 31.25. Similarly Q3 = 75.25, giving IQR = 44. Any value below Q1 - 1.5 × IQR = -34.75 or above Q3 + 1.5 × IQR = 141.25 would be flagged as an outlier — none here.
Frequently Asked Questions
What does it mean to be in the 90th percentile?+
It means the value is greater than or equal to 90% of the values in the dataset — only 10% score higher. For example, a test score in the 90th percentile beats nine out of ten test takers. Note that a percentile is a position in the distribution, not a percentage score on the test itself.
How is a percentile actually calculated?+
This tool sorts your data and uses linear interpolation, the same method as Excel's PERCENTILE.INC: the index is (p/100) × (n - 1), and if it falls between two data points the result is interpolated between them. Other conventions exist (nearest-rank, exclusive interpolation), which is why different software can give slightly different answers on small datasets.
What is the interquartile range (IQR) and why does it matter?+
The IQR is Q3 minus Q1 — the spread of the middle 50% of your data. Unlike the full range, it is not distorted by a single extreme value, which makes it a robust measure of variability. It also powers the standard outlier test: values below Q1 - 1.5 × IQR or above Q3 + 1.5 × IQR are flagged as outliers.
What is the difference between a percentile and a percentile rank?+
A percentile starts from a percentage and returns a value ('what value marks the 75th percentile?'), while a percentile rank starts from a value and returns a percentage ('what percent of the data falls at or below 82?'). This calculator has separate modes for each direction.
Is the percentile calculator free and is my data kept private?+
Yes. It is free with no sign-up, and your data never leaves your device — sorting, interpolation, quartiles, and outlier detection all run in your browser. It works on mobile and desktop, and accepts values separated by commas, spaces, or new lines.
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