Percentile Calculator — Find Percentile Rank & Value
Enter a list of numbers to instantly find the percentile rank of any value, or look up the exact data value at any given percentile. Uses the midpoint formula for ranks and linear interpolation for values — the same method used by Excel and NumPy. Supports commas, spaces, semicolons, and newlines as delimiters.
Enter Your Data
Enter numbers separated by commas, spaces, semicolons, or newlines.
Enter a value to find what percentile rank it occupies in your dataset.
Frequently Asked Questions
What is a percentile?
A percentile is a value below which a given percentage of observations fall. For example, if your score is at the 75th percentile, it means 75% of all values in the dataset are at or below your score. Percentiles are used in test scores, growth charts, salary surveys, and many other fields.
How do you calculate percentile rank?
Use the formula: PR = ((B + 0.5 × E) / N) × 100, where B is the number of values strictly below the score, E is the number of values equal to the score, and N is the total number of values. This midpoint method is the most widely used approach and accounts fairly for tied values.
What is the difference between percentile rank and percentile score?
Percentile rank is a percentage (0–100) that tells you where a score stands relative to others. Percentile score (or value at percentile) is the actual data value that corresponds to a given percentile rank. For example, a rank of 90 means you scored higher than 90% of the group; the 90th percentile score is the specific number that marks that boundary.
What is linear interpolation in percentile calculation?
Linear interpolation is used when the desired percentile falls between two data points. The calculator computes a fractional index position in the sorted dataset and blends the two neighboring values proportionally. For example, the 50th percentile of [10, 20, 30, 40] is 25, because it lies halfway between the 2nd and 3rd values (20 and 30).
What is the 50th percentile?
The 50th percentile is the median — the middle value of the dataset when sorted. Half of all values fall below it and half above. It is a robust measure of central tendency because, unlike the mean, it is not affected by extreme outliers.
What do Q1, Q2, and Q3 mean?
Q1 (first quartile) is the 25th percentile, Q2 (second quartile) is the 50th percentile (the median), and Q3 (third quartile) is the 75th percentile. The interquartile range (IQR) is Q3 − Q1 and represents the spread of the middle 50% of the data. Together with the minimum and maximum, they form the five-number summary.
How is percentile different from percentage?
A percentage is a ratio of a part to a whole (e.g., you answered 80% of questions correctly). A percentile is a positional measure that compares your score to others in a distribution (e.g., your score is higher than 80% of all scores). Percentages describe absolute performance; percentiles describe relative standing.
What does it mean to be in the 99th percentile?
Being in the 99th percentile means your value is higher than 99% of all values in the dataset. It is the top 1%. This term is common in standardized testing (e.g., SAT, IQ scores), income distributions, and system performance benchmarks (P99 latency).
Percentile Rank Formula
A percentile rank tells you what percentage of values in a dataset fall at or below a given score. The most widely-used formula — known as the inclusive or midpoint method — is:
Percentile Rank Formula
PR = ( (B + 0.5 × E) / N ) × 100
- B — number of values strictly below the score
- E — number of values exactly equal to the score
- N — total number of values in the dataset
Example
Dataset: 15, 20, 35, 40, 50 — finding the rank of 35:
B = 2 (values 15, 20 are below) | E = 1 (value 35 equals 35) | N = 5
PR = ((2 + 0.5 × 1) / 5) × 100 = (2.5 / 5) × 100 = 50th percentile
Percentile Rank vs Percentile Score
These two terms are often confused. Understanding the difference is essential for interpreting results correctly.
| Term | Definition | Example |
|---|---|---|
| Percentile Rank | The percentage of values at or below a given score | Score 35 has rank 50 → 50% of scores are ≤ 35 |
| Percentile Score (Value at Percentile) | The value that corresponds to a given percentile rank | The 75th percentile value is 40 |
Practical tip:When a test result says you scored in the “85th percentile,” it means your score (the percentile score) was higher than 85% of all test takers. The percentile rank is 85.
Linear Interpolation for Value at Percentile
When finding the value at a given percentile, the requested percentile often falls between two data points. Linear interpolation is used to estimate the exact value:
Interpolation Formula
index = (p / 100) × (N − 1)
value = data[floor(index)] + (data[ceil(index)] − data[floor(index)]) × (index − floor(index))
Example
Dataset: 10, 20, 30, 40 — finding the 50th percentile:
index = (50 / 100) × (4 − 1) = 1.5
value = 20 + (30 − 20) × 0.5 = 20 + 5 = 25
This is the same method used by NumPy's np.percentile() with the default linear interpolation setting.
Common Percentiles and Their Names
Certain percentiles have special names because of their frequent use in statistics and data analysis:
| Percentile | Name | Common Use |
|---|---|---|
| 25th | Q1 (First Quartile) | Lower bound of the IQR |
| 50th | Q2 / Median | Middle value, robust to outliers |
| 75th | Q3 (Third Quartile) | Upper bound of the IQR |
| 90th | P90 | Performance benchmarks (latency, income) |
| 95th / 99th | P95 / P99 | Tail latency in systems engineering |
Related Tools
- Standard Deviation Calculator — Calculate population or sample standard deviation, variance, and mean.
- Z-Score Calculator — Convert raw scores to standard deviations from the mean.
- Five Number Summary Calculator — Find min, Q1, median, Q3, max, and IQR in one step.