Paste a list of numbers and pick a question. The page finds the percentile rank of a value in your list, the value that sits at a percentile, or the percentile that goes with a z-score. It shows the steps and says which method it used, because books and software differ.
Pick a question and enter the numbers
Everything is worked out in your browser. Nothing you type is sent anywhere.
Your answer
Your answer shows up here once you fill in the boxes.
What to enter
- Your list of values
- The numbers in your data set, such as test scores. They can be in any order and can repeat.
- The value to rank
- The score you want to place in the list. It does not need to be in the list.
- The percentile
- A number from 0 to 100. The 50th percentile is the median.
- The z-score
- How many standard deviations a value sits above (positive) or below (negative) the mean.
Worked examples
Where does a score of 60 sit?
Five students scored 55, 60, 60, 70 and 80. What is the percentile rank of a score of 60?
- Count the values below 60: 1. Count the values equal to it: 2.
- Add the values below and half of the values equal: 1 + 0.5 × 2 = 2.
- Divide by the number of values and multiply by 100: 2 ÷ 5 × 100 = 40.
One score is below 60 and two are equal to it, so the percentile rank is (1 + half of 2) ÷ 5 × 100 = 40. Counting half of the ties puts tied scores in the middle of their range.
What score marks the 90th percentile?
For the list 1, 2, 3, 4, 5, what value sits at the 90th percentile?
- Sort the values from smallest to largest.
- Find the position: (90 ÷ 100) × (5 – 1) = 3.6, counting the smallest value as position 0.
- That falls between 4 and 5. Go 0.6 of the way across: 4 + 0.6 × (5 – 4) = 4.6.
The 90th percentile is 4.6. It falls between 4 and 5, and the page goes 60% of the way across.
A z-score of 1.96
A value has a z-score of 1.96. What percentile is it?
- Find the area under the standard normal curve to the left of z = 1.96.
- That area is 0.975002. Multiply by 100 to get the percentile: 97.500217.
It is at the 97.500217 percentile, which is why 1.96 shows up in so many confidence interval tables.
Common z-scores and their percentiles
Here are the z-scores you see most often, with the percentile the page gives for each. The values come from the standard normal curve.
| Z-score | Percentile |
|---|---|
| -2 | 2.275 |
| -1.645 | 4.9985 |
| -1 | 15.8655 |
| 0 | 50 |
| 1 | 84.1345 |
| 1.282 | 90.0079 |
| 1.645 | 95.0015 |
| 1.96 | 97.5002 |
| 2 | 97.725 |
| 2.576 | 99.5002 |
| 3 | 99.865 |
Percentile or percent?
A percent is a share of a total. A percentile is a position in a ranked list. A student who scores 80% on a test might be at the 50th percentile, if half the class scored higher, and at the 95th percentile if almost everyone scored lower. The percentile says how you compare with others, and the percent says how much of the test you got right.
Test-score percentiles
Percentiles on tests like the SAT, the ACT or the ATAR come from the test maker’s own data about everyone who sat the test. This page ranks the list you give it, so it cannot tell you where you sit among all test takers. For that, use the percentile table the test maker publishes.
Methods differ, so answers can differ
There is more than one accepted way to work out a percentile. This page uses two common ones. For percentile rank, it counts the values below yours and half of the values equal to it. For the value at a percentile, it sorts the list and goes a fraction of the way between two neighbours, the same as the inclusive method in Excel. Other tools may count differently and give a slightly different answer, especially for small lists. If your course names a method, follow it.
How it is calculated
- For a rank, count the values in your list that are below the value, and the values equal to it.
- Add the values below and half of the values equal, divide by the number of values, then multiply by 100.
- For the value at a percentile, sort the list, then work out the position from the percentile and the number of values.
- If the position falls between two values, go that fraction of the way from the lower one to the higher one.
- For a z-score, find the area under the standard normal curve to the left of it and multiply by 100.
Percentile rank = (values below + 0.5 × values equal) ÷ number of values × 100
Position = percentile ÷ 100 × (number of values – 1), counting the smallest value as position 0
Assumptions to keep in mind
- The z-score mode assumes a normal (bell curve) distribution. Real data is not always normal.
- The answers use the methods named above. Other textbooks and tools use other methods and can differ.
- A small list gives a rough percentile. With 5 values, each one is worth 20 percentile points.
- The page does the arithmetic only. It does not check your data for typing mistakes.
Mistakes that give the wrong answer
Calling a percent a percentile
A score of 80% is not the 80th percentile. The percentile depends on how everyone else did.
Forgetting the ties
If several values equal yours, count half of them. Counting all of them or none of them moves the answer.
Not sorting the list by hand
To find the value at a percentile by hand, sort first. The page does it for you.
Using a z-score with data that is not normal
The percentile from a z-score is only right if the data follows a bell curve. For a skewed list, use the rank mode.
Questions students ask
How do I calculate a percentile?
Count the values below yours, add half of the values equal to it, divide by the number of values, then multiply by 100. For a score of 60 in the list 55, 60, 60, 70, 80, that is (1 + 1) ÷ 5 × 100 = 40.
What is the difference between percentile and percentage?
A percentage is a share of a total, like 80% of the marks. A percentile is a position in a ranked group, like beating 80% of the other students.
What is the 50th percentile?
It is the median, the middle value of a sorted list.
How do I find the percentile of a z-score?
Look up the area to the left of the z-score on the standard normal curve and multiply by 100. The third mode does it. A z-score of 0 is the 50th percentile and 1.96 is about the 97.5th.
Why does another tool give a different percentile?
There are several accepted methods, and small lists show the differences most. This page names its methods so you can match your course.
