What this calculator does
Percentile rank answers how a particular value compares with the rest of the data. In the set 55, 60, 63, 67, 70, 72, 75, 80, 85, 90, the value 72 has five values below it and one equal, giving a rank of 55%.
The half-credit for ties is what makes the formula behave sensibly. Counting the value itself as fully below would push every rank upward and make the highest value in any data set sit at the 100th percentile, which implies nothing can exceed it. Half credit keeps the ranks symmetric: here the lowest value lands at 5% and the highest at 95%.
The formula
The count of values strictly below the target, plus half the count equal to it, is divided by the total number of values and multiplied by 100. The half-weighting for ties is the standard convention and is what keeps the scale symmetric, so that the bottom and top values of a data set sit equally far from the ends.
| Term | Meaning |
|---|---|
| Percentile rank | The percentage of the data at or below a value, with ties counted at half. |
| Tied values | Values equal to the target, which contribute half their count. |
| Percentile | The reverse operation: the value at a given percentage position. |
The inputs explained
| Field | What to enter |
|---|---|
| Data (comma or space separated) | Your data, comma or space separated. It does not need to be sorted. |
| Value to rank | The value to rank. It does not have to appear in the data, in which case no values are counted as tied. |
When to use it
Interpreting a test score
A raw mark means little without knowing how it compares with everyone else, which is what a percentile rank reports.
Placing a measurement in context
Growth charts, benchmarks and reference ranges are all read as percentile ranks.
Reporting performance
Saying a result is in the top 10% is often more useful than quoting the number itself.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
What percentile rank does each value have?
Several values ranked against the same ten-point data set.
Questions
What does a percentile rank of 55 mean?
That roughly 55% of the data falls at or below that value, so it sits a little above the middle. It does not mean the value is 55, nor that it scored 55%: percentile rank is a position within the data, not a score.
Why is the highest value not the 100th percentile?
Because ties count at half weight. The top value has all others below it and itself as a tie, giving 95% in a ten-point set rather than 100%. This keeps the scale symmetric and avoids implying that nothing could ever exceed the largest value observed.
What is the difference between percentile and percentile rank?
They are inverse operations. Percentile rank starts from a value and returns its position as a percentage. A percentile starts from a percentage and returns the value at that position. One answers where does this value sit, the other what value sits here.
Can I rank a value that is not in the data?
Yes. The formula counts how many values fall below it and how many equal it, and if none are equal the tie term is simply zero. This is useful for placing a new observation against an existing reference set.
For the reverse operation, see the percentile value calculator. For standardising a value instead, see the z-score calculator.