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Percentile Calculator

See where a number stands in a list: find the value at any percentile, or the percentile rank of a value you have.

Level: Grades 9–10

Printable worksheet

Percentile Calculator

Know the answer you need? Pick an input to work backward.

Inputs
Find

Separate with commas, spaces, or new lines. Don't use thousands separators.

Result

Value at the 40th percentile

29

The 40th percentile of 5 values is 29 (linear interpolation, as in PERCENTILE.INC).

Rank position r (1 = smallest)
2.6
Count (n)
5

See the step-by-step solution ↓

Step-by-step solution

  1. Put the 5 values in order from smallest to largest

    15, 20, 35, 40, 50

  2. Find the rank position r, the spot in the sorted list where the percentile falls. Rank 1 is the smallest value

    r=1+(5−1)×40100=2.6

  3. r falls between two spots, so start at value number 2 and move 0.6 of the way to value number 3

    value=20+0.6×(35−20)=29

Test yourself

20 quick questions built from this calculator's formula: work out results, predict what happens when an input changes, and work backward from an answer. Every answer comes with the working.

What this calculator does

Find out where a number stands compared with the rest of your list. A percentile tells you that position. The 90th percentile is the point that about 90% of the values fall below. The median, the middle value, is the 50th percentile. The quartiles are the 25th and 75th. Percentiles are used for test scores, growth charts, response times and anything else where position matters more than the raw number.

This calculator works in both directions. Give it a percentile, and it finds the matching value in your data. It uses the same method as the spreadsheet function PERCENTILE.INC, which fills in between values when needed. Or give it a value, and it tells you that value's percentile rank. It also shows the share of the data below your value, and at or below it.

Where it's used

Why this math matters outside the classroom:

  • Test scores. A student at the 90th percentile on a standardized test scored higher than about 90% of test takers.
  • Page load times. Engineers track the 95th percentile page load time, so they know 95% of visits loaded faster than that.
  • Salary benchmarks. Employers compare a $68,000 offer with the 25th, 50th and 75th percentiles of pay for the same role.
  • Race results. A runner who finished 50th out of 1,000 placed in roughly the 95th percentile of the field.
  • Storm drains. Engineers size storm drains for rainfall at a high percentile of past storms, such as the 99th.

How to use it

  1. Choose whether you want the value at a percentile, or the percentile rank of a value.
  2. Enter or paste your data, separated by commas, spaces or new lines. It doesn't need to be in order.
  3. Enter the percentile P (from 0 to 100) or the value x.
  4. Read the result. Open the working to see your data in order and how the answer was found.

What the inputs mean

Data set
Separate with commas, spaces, or new lines. Don't use thousands separators.
Percentile (P)
0 gives the smallest value, 100 the largest and 50 the median. Decimals such as 97.5 are allowed.
Value (x)
The value can be in your data or fall between two data values. Anything below the smallest value has a rank of 0%. Anything above the largest has a rank of 100%.

Formula and method

rank position r = 1 + (n − 1) × P ÷ 100
value = x⌊r⌋ + (r − ⌊r⌋) × (x⌊r⌋+1 − x⌊r⌋)
percentile rank = (B + 0.5 × E) ÷ n × 100

In the formulas, n is how many values you have and P is the percentile you want. r is the rank position, a spot in your sorted list. Rank 1 is the smallest value and rank n is the largest. ⌊r⌋ means r rounded down to a whole number, and x⌊r⌋ is the value sitting at that spot.

To find the value at a percentile, the calculator sorts your data and works out r. If r is a whole number, the answer is the value at that spot. If not, the answer falls between two neighboring values. It sits r − ⌊r⌋ of the way from the lower one to the upper one. This is called linear interpolation, and it's the inclusive method used by the spreadsheet function PERCENTILE.INC.

For the percentile rank of a value, B is how many data values are strictly below it. E is how many are equal to it. Counting half of the ties puts a repeated value in the middle of its group. That's why the median of a list with an odd count gets a rank of exactly 50%.

The results also show the share strictly below and the share at or below, the two simplest other definitions. You'll also see a filled-in rank that matches the spreadsheet function PERCENTRANK.INC. It's shown in full rather than cut off at three digits.

Worked example

Five values, 15, 20, 35, 40 and 50. What is the 40th percentile, and what is the percentile rank of 35?

  1. Rank position for P = 40: r = 1 + (5 − 1) × 0.4 = 2.6.
  2. The 2nd value in order is 20 and the 3rd is 35, so move 0.6 of the way between them: 20 + 0.6 × (35 − 20) = 29.
  3. For the rank of 35: two values (15 and 20) are below it, and one value equals it.
  4. Percentile rank = (2 + 0.5 × 1) ÷ 5 × 100 = 50%.

Result: The 40th percentile is 29, and 35 has a percentile rank of 50%.

Understanding the result

A value at the 80th percentile is higher than roughly 80% of the data. It doesn't tell you how much higher. For that, look at the gap in the original units, or at a z-score (how many standard deviations a value is from the average).

The value at a percentile doesn't have to be one of your data points. It can fall between two of them, as 29 does in the example.

A percentile rank isn't the percent you got right. Scoring at the 70th percentile on a test means you beat about 70% of test takers. It doesn't mean you answered 70% of the questions correctly.

Assumptions and limitations

  • Your data is treated as a complete list of observations, and each one counts once.
  • The value-at-percentile method fills in between the two closest ranks in a straight line (the PERCENTILE.INC method).
  • Other percentile definitions exist, including PERCENTILE.EXC and nearest-rank methods. They can give different answers, especially for small data sets.
  • With only a few data points, extreme percentiles such as the 1st or 99th are just filled-in guesses near the smallest or largest value. They don't tell you much.
  • It takes at most 10,000 values.

Frequently asked questions

Why does my spreadsheet give the same answer but my textbook doesn't?

This calculator follows the spreadsheet PERCENTILE.INC method. Many textbooks use a different rule. Some round the position up to the next whole rank, and some use (n + 1) × P ÷ 100 as the position. For large data sets, the methods give nearly the same answer.

What is the difference between a percentile and a percentile rank?

A percentile is a value. For example, the 90th percentile of incomes might be a dollar amount. A percentile rank is a position. A particular income might have a percentile rank of 90%. This calculator works in both directions.

Can a percentile rank be 0% or 100%?

Yes. A value below every data point has a rank of 0%, and one above every data point has a rank of 100%. A value equal to the single smallest data point gets a small rank above zero, because half of the tie is counted.

Is the 50th percentile always the median?

With the method used here, yes. For an even number of values, it's the average of the two middle values, exactly how the median is defined.

How this calculator is checked

Method: Linear-interpolation percentile equivalent to spreadsheet PERCENTILE.INC (Hyndman & Fan type 7); mid-rank percentile rank (B + 0.5E)/n; interpolated rank equivalent to PERCENTRANK.INC. Reference-tested against hand-worked spreadsheet results. The calculation is covered by automated tests with known reference values and edge cases. Last updated 2026-10-18. Found a problem? Tell us.

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