A percentile tells you what percentage of a dataset falls at or below a particular value. If you scored in the 85th percentile on a test, it means you scored higher than 85% of all test-takers.
Percentile vs Percentage: Key Difference
These are often confused:
- Percentage — a ratio out of 100 (you answered 85% of questions correctly)
- Percentile — your position relative to others (you did better than 85% of people)
A student can score 60% on a test but be in the 90th percentile if it was a difficult exam and most people scored lower.
How to Calculate Percentile Rank
Percentile rank tells you where one value sits relative to the rest of the dataset.
Percentile rank = (number of values below X / total values) × 100
Example: In a class of 30 students, you scored 78. 21 students scored below 78.
Percentile rank = (21 / 30) × 100 = 70th percentile
You scored higher than 70% of the class.
Alternative Formula (inclusive)
Some sources include the score itself:
Percentile rank = ((number below + 0.5) / total) × 100
Using the example: ((21 + 0.5) / 30) × 100 = 71.7th percentile
Which formula you use depends on context. The inclusive version is common in educational testing.
Finding the Value at a Given Percentile
To find what value corresponds to a specific percentile (e.g., "what score is at the 75th percentile?"):
Step 1: Sort the data in ascending order.
Step 2: Calculate the index:
Index = (percentile / 100) × n
Where n = total number of values.
Step 3:
- If the index is a whole number, average the values at positions index and index + 1
- If not a whole number, round up and use that position
Example: Dataset (sorted): 12, 15, 18, 22, 25, 28, 31, 35, 40, 45. Find the 75th percentile (n = 10).
Index = (75 / 100) × 10 = 7.5
Round up to 8. The 8th value is 35.
The 75th percentile is 35.
Common Percentiles and Their Names
| Percentile | Also called |
|---|---|
| 25th | Lower quartile (Q1) |
| 50th | Median (Q2) |
| 75th | Upper quartile (Q3) |
| 90th | P90 |
| 95th | P95 |
| 99th | P99 |
Practical Applications
Test scores (SAT, GRE, IQ): A GRE score of 163 in verbal reasoning puts you in the 91st percentile — you scored higher than 91% of test-takers.
Child growth charts: A baby's height at the 60th percentile means 60% of babies that age are shorter. Neither high nor low percentiles indicate a problem on their own.
Income statistics: Earning above the 80th percentile means your income exceeds 80% of the population.
Web performance: P95 page load time means 95% of users experience that load time or faster. Engineers optimise P99 specifically to improve the worst-case experience.
Finance — Value at Risk (VaR): A 5th percentile outcome represents the worst 5% of scenarios — used in risk management.
Interquartile Range (IQR)
The IQR measures the spread of the middle 50% of data:
IQR = Q3 − Q1 = 75th percentile − 25th percentile
It's a robust measure of spread that's not affected by outliers — unlike range or variance.
Common Mistakes
Confusing percentile with percentage score — Your percentile depends on how everyone else did, not just you.
Assuming higher is always better — For response times, latency, and error rates, lower percentiles are better.
Off-by-one on the index — Particularly for small datasets. Always check your indexing method matches the convention being used.