Percentile Rank Formula
Calculate percentile rank to find what percentage of values fall below a given score.
Used in test scores and data analysis.
The Formula
The percentile rank tells you the percentage of values in a dataset that fall at or below a particular value. If your test score is at the 85th percentile, 85% of test-takers scored at or below your score.
Variables
| Symbol | Meaning |
|---|---|
| L | Number of values BELOW the target value |
| S | Number of values EQUAL TO the target value (including the target itself) |
| N | Total number of values in the dataset |
Simplified Version
This simpler version is often used when there are no duplicate values in the dataset. Both formulas are widely accepted.
Example 1 — Test Score
A student scores 78 on a test. 30 students scored below 78, 3 students scored exactly 78, and there are 40 students total.
L = 30, S = 3, N = 40
Percentile = (30 + 0.5 × 3) / 40 × 100
Percentile = (30 + 1.5) / 40 × 100
Percentile = 78.75th percentile
Example 2 — Finding the Value at a Given Percentile
Find the 25th percentile (Q1) of the data: 12, 15, 18, 22, 25, 29, 33, 40
N = 8 values, target percentile = 25%
Index = (25/100) × (8 + 1) = 2.25
The 2nd value is 15 and the 3rd value is 18
Interpolate: 15 + 0.25 × (18 - 15) = 15 + 0.75
25th percentile = 15.75
Example 3 — Simple Ranking
You finish 12th out of 50 runners in a race. What is your percentile?
38 runners finished behind you (below you)
Percentile = (38 / 50) × 100
You are at the 76th percentile (faster than 76% of runners)
Common Percentiles
| Percentile | Name | Meaning |
|---|---|---|
| 25th | First Quartile (Q1) | 25% of values are below this |
| 50th | Median (Q2) | The middle value — 50% above, 50% below |
| 75th | Third Quartile (Q3) | 75% of values are below this |
| 90th | 90th percentile | Top 10% of values |
| 99th | 99th percentile | Top 1% — exceptional performance |
When to Use It
- Interpreting standardized test scores (SAT, GRE, IQ tests)
- Tracking child growth percentiles (height, weight by age)
- Analyzing survey results and data distributions
- Comparing performance rankings (sales, athletics, academics)
- Setting thresholds in data science (e.g., filtering outliers above the 99th percentile)