What a percentile means, and how it differs from a percentage
What a percentile really measures, how to get one from an exam rank, how it differs from a percentage of marks, and how percentiles and quartiles are found for a list of numbers.
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In short
- A percentile compares you with other people. A percentage compares your marks with the maximum.
- Exam percentile = (total candidates − your rank) ÷ total candidates × 100. Rank 250 out of 50,000 is the 99.5 percentile.
- The 99 percentile means about 1 percent of candidates are ahead of you, not that you scored 99 percent.
- For a list of numbers, the 50th percentile is the median and the 25th and 75th are the quartiles.
- Different methods for lists give slightly different answers on small data sets. This page uses the same method as Excel's PERCENTILE.INC.
Few words cause as much confusion among students and parents as percentile. A score of 90 percentile can be excellent, and it can also come with only 40 percent of the marks. Percentiles appear in entrance exam results, in children's growth charts, in salary surveys and in website speed reports. They all mean the same thing, and once you see it, the rest is simple arithmetic. This page explains the idea, shows the formula used for ranks, and shows how to find percentiles in a list of numbers.
Percentile and percentage are different things
A percentage is your own score out of the maximum. If you got 180 out of 300, that is 60 percent, and it would be 60 percent whatever anyone else did.
A percentile is your position in a group. If you are at the 95 percentile, you did as well as or better than 95 percent of the group. It says nothing directly about your marks.
So in a very hard exam, 60 percent of the marks may put you at the 95 percentile. In an easy one, 60 percent may put you at the 40 percentile. The percentage calculator handles marks. This one handles position.
The formula for exam ranks
If you know your rank and the number of candidates:
percentile = (total − rank) ÷ total × 100
Rank 250 out of 50,000 gives (50,000 − 250) ÷ 50,000 × 100 = 99.5. Rank 5,000 out of 50,000 gives 90.
Going the other way, for a given percentile:
rank = total × (1 − percentile ÷ 100)
A 99 percentile among 12,00,000 candidates is a rank of about 12,000. That shows why percentile gaps matter more at the top. Between 99 and 99.9 lie 10,800 candidates in this example, as many as lie between 90 and 90.9.
| Percentile | Ahead of you in 12 lakh | Share ahead |
|---|---|---|
| 80 | 2,40,000 | 20% |
| 90 | 1,20,000 | 10% |
| 95 | 60,000 | 5% |
| 99 | 12,000 | 1% |
| 99.5 | 6,000 | 0.5% |
| 99.9 | 1,200 | 0.1% |
Real exam bodies use their own exact rules, so treat a result from here as a close estimate. An exam held over several sessions can also calculate percentiles within each session and then combine them, because one paper may be harder than another. That is why the rank published for a given percentile can differ a little from this formula.
Reading common uses
Entrance exams. A percentile score tells a college how you compare with everyone who sat the paper. Check the exact method in the official bulletin of your exam, since these change.
Children's growth charts. A child at the 75th percentile for height is taller than about 75 percent of children of the same age and sex. It is not a grade. What a paediatrician usually watches is whether a child stays near the same line over time.
Salaries. Survey reports often give the 25th, 50th and 75th percentiles. The 50th is the median, the middle salary, which is usually a better guide than the average because a few very high salaries pull the average up.
Website speed. Reports on page load often use the 75th percentile, meaning three out of four visits were this fast or faster.
Percentiles of a list of numbers
Sometimes you have the data and want the value at a certain percentile. Take ten test scores:
45, 52, 58, 61, 67, 70, 72, 78, 84, 91
First put them in order, as above. To find the percentile p in a list of n numbers:
position = p ÷ 100 × (n − 1)
Count positions from 0. If the position falls between two values, move proportionally between them.
For the 50th percentile, the position is 0.5 × 9 = 4.5, which is halfway between the fifth and sixth values, 67 and 70. The result is 68.5, which is also the median.
For the 25th percentile, the position is 0.25 × 9 = 2.25. That is a quarter of the way from 58 to 61, which gives 58.75.
For the 75th percentile, the position is 6.75, three quarters of the way from 72 to 78, which gives 76.5.
For the 90th percentile, the position is 8.1, a tenth of the way from 84 to 91, which gives 84.7.
This is known as linear interpolation. It is the method of PERCENTILE.INC in Excel. Other software offers alternatives, and on a short list they can give somewhat different answers. On long lists, the choice hardly matters.
Quartiles and the spread of data
The 25th, 50th and 75th percentiles have their own name, the quartiles, because they split the data into four equal parts. The gap between the first and third quartiles is called the interquartile range. For the scores above, it is 76.5 − 58.75 = 17.75, which means the middle half of the class spans about 18 marks.
The interquartile range is less affected by extreme values than the full range. One student scoring 100 changes the range but hardly moves the quartiles. For the average and standard deviation of the same data, use the average calculator.
Percentile rank of a value
You can also ask the reverse question: where does a given value stand in the list? The calculator counts the values below it, adds half of any that are equal, and divides by the size of the list.
percentile rank = (values below + half of equal values) ÷ n × 100
In the list above, 72 has six values below it and one equal, which is itself. So its rank is (6 + 0.5) ÷ 10 × 100 = 65. That differs from what the formula for exam ranks would give, since that formula counts everyone at or below your rank. Both are accepted conventions, and the difference fades as the group grows.
Common mistakes
Reading a percentile as marks. A 90 percentile does not mean 90 percent of the marks.
Rounding away the top. The difference between 99.9 and 99.99 is tiny as a number, but it is a tenfold difference in how many are ahead of you.
Comparing across exams. A percentile only has meaning within its own group. A 95 percentile among all applicants and a 95 percentile among selected students are very different results.
Forgetting to sort. Percentiles of a list only work on sorted values. The calculator sorts your numbers first, so you can paste them in any order.
Averaging percentiles. You cannot find an overall percentile by averaging those from two papers, because the two groups and their score spreads differ.
A worked example from start to finish
Suppose 8,00,000 candidates sit a paper, and you get rank 24,000. Your percentile is (8,00,000 − 24,000) ÷ 8,00,000 × 100 = 97. So 3 percent of candidates, the 24,000 ranked above you, finished ahead, and 97 percent are at or behind you.
To reach the 99 percentile in the same exam, you would need a rank of about 8,000. Your rank would have to improve threefold for two more points of percentile.
What this calculator assumes
- Exam percentile is calculated as (total − rank) ÷ total × 100, which counts the candidates behind you.
- Ties in rank are not handled, because you enter one rank.
- List percentiles use linear interpolation, as in Excel's
PERCENTILE.INC. - Percentile rank of a value counts half of any ties.
- An estimate from this page is not an official score. Your exam's own published result always decides.