What Is a Percentile?
A percentile is a measure that tells you what percentage of values in a data set fall below a given value. If your test score is at the 90th percentile, it means you scored higher than 90 percent of the people who took the same test. Percentiles are widely used in education, medicine, and statistics to compare an individual value against a distribution without relying on assumptions about the shape of that distribution.
There are two related but distinct calculations. The percentile rank of a value tells you where that value stands within a data set. The value at a given percentile tells you which data value corresponds to a particular percentage. Both are essential for interpreting standardized test scores, growth charts, and financial performance metrics. For normally distributed data, see our Z-score Calculator.
What This Calculator Does
This percentile calculator performs both operations. Enter a data set and a target value to find its percentile rank, and enter a percentile (0 to 100) to find the value at that percentile. It also displays the sorted data and key summary statistics including the minimum, maximum, median, and quartiles.
- Inputs: A data set (comma or space separated), a target value, and a percentile
- Outputs: Percentile rank of the target, value at the given percentile, and summary statistics
How the Calculation Works
Percentile Rank = (count below + 0.5 × count equal) / total × 100
Value at percentile p: linear interpolation between closest ranks
The percentile rank formula counts how many values fall below the target and how many equal it, then computes the percentage. When the target value is not in the data set, the calculator interpolates its position. For finding the value at a given percentile, the calculator uses linear interpolation between the two closest data points, which is the same method used by most statistical software. For broader statistical analysis, try our Statistics Calculator or Standard Deviation Calculator.
Example Calculation
Example: Consider the data set 15, 20, 35, 40, 50, 55, 60, 75, 80, 95. The value 50 has 4 values below it and no ties, so its percentile rank is (4 + 0) / 10 × 100 = 40. The 90th percentile value is found by interpolating: the 90th percentile position is 0.90 × 9 = 8.1, which falls between the 8th value (80) and the 9th value (95), giving 80 + 0.1 × (95 - 80) = 81.5.
Real-World Applications
Percentiles are used everywhere standardized comparisons are needed. Pediatricians use growth chart percentiles to track a child's height and weight relative to peers. College admissions offices report SAT and ACT scores in percentile bands. Financial analysts use percentiles to benchmark investment returns against a peer group. Human resources departments use salary percentiles to set competitive compensation bands. Unlike averages, percentiles are robust to outliers and work well with skewed distributions.