A percentile rank turns a raw value into a position within a group. If your test score has a percentile rank of 67, you did as well as or better than 67% of the people who took the test. It is the reverse of a percentile: instead of asking “which score cuts off the top 10%?”, it asks “where does this particular score stand?”. Percentile ranks are used on standardised test reports, in child growth charts and in salary benchmarking.
The basic formula counts how many values are at or below your value and divides by the total number of values. A popular alternative, used for many standardised tests, counts all values below plus half of the values equal to yours (the mid-rank formula), which treats ties more evenly; a strict version counts only the values below.
Enter the data and the value to rank. The value does not have to appear in the data set. The result explains the percentage at or below and above the value, and the working shows exactly what was counted.
How to use the Percentile Rank Calculator
- Value to rank (x)
- Data set
- Formula
Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.
How it works
Sort the data and count the values below (B), equal to (E) and above the value. The percentile rank is (B + E) ÷ N × 100 by default, (B + E/2) ÷ N × 100 for the mid-rank formula, or B ÷ N × 100 for the strict version.
Worked example
Fifteen students’ scores: 52, 58, 61, 64, 66, 70, 72, 75, 78, 78, 81, 84, 86, 90, 95. For a score of 78: 8 scores are lower, 2 are equal and 5 are higher. PR = (8 + 2) ÷ 15 × 100 = 66.7: the student did as well as or better than two thirds of the class. The mid-rank formula gives (8 + 1) ÷ 15 × 100 = 60, the strict formula 8 ÷ 15 × 100 = 53.3.
Percentile rank versus percentile
The two are inverse operations. The percentile calculator answers “what score is at the 67th percentile?”; this calculator answers “what percentile is a score of 78?”. Because of interpolation and tie handling the round trip is not always exact for small data sets.
Formula
PR = L ÷ N × 100, where L = number of values ≤ x · mid-rank version: PR = (B + ½E) ÷ N × 100
Worked example
Inputs — Value to rank (x): 78; Data set: 52, 58, 61, 64, 66, 70, 72, 75, 78, 78, 81, 84, 86, 90, 95; Formula: Values at or below x ÷ N (most common).
Results — Percentile rank = 66.67; What it means = A value of 78 has a percentile rank of 66.7: 66.7% of the data are at or below it and 33.3% are above it.; Values below x = 8; Values equal to x = 2; Values above x = 5; Number of values (N) = 15.
Key terms
- Percentile rank
- The percentage of values at or below a given value.
- Mid-rank
- Counting tied values as half below and half above.
- Percentile
- The value corresponding to a given percentile rank.
Frequently asked questions
How do I calculate percentile rank?
Count the values at or below your value, divide by the total number of values and multiply by 100.
What is the percentile rank of 78 in the example data?
10 of the 15 values are 78 or lower, so PR = 10 ÷ 15 × 100 = 66.7. With the mid-rank formula it is (8 + 1) ÷ 15 × 100 = 60.
What does a percentile rank of 95 mean?
The value is at or above 95% of the values in the group – only 5% are higher.
Is percentile rank the same as percentage score?
No. Scoring 80% on a test is about the marks; a percentile rank of 80 means you did as well as or better than 80% of the test takers.
Can the value be outside the data?
Yes. A value below every data point has a rank of 0; a value at or above every point has a rank of 100.
Which formula do standardised tests use?
Many use the mid-rank formula (below plus half of the ties), which avoids rewarding ties.
How do I find percentile rank in Excel?
=PERCENTRANK.INC(range, x) uses a slightly different scale; =COUNTIF(range,"<="&x)/COUNT(range) matches the default formula here.