Percentile Rank Calculator

StatisticsLast updated: August 22, 2026

The percentile rank expresses the relative position of an observation within a data set as a percentage: "a score of 76 beats 54% of the class" is a percentile-rank statement. A raw score means little on its own, but its percentile rank places it against the group and makes results measured on different scales comparable.

This calculator works in both directions. It reports the percentile rank of the value you enter under three definitions (values below, values below plus half the ties, and values below or equal); in reverse, it finds the value corresponding to the percentile level you give, using both linear interpolation and the nearest-rank method. The sorted-data table also shows the percentile rank of every single observation.

You can separate the numbers with commas, spaces, or line breaks. At least 4 observations are required.
The relative position of this value within the data is reported as a percentage.
The reverse calculation: the value corresponding to this percentile is found. You may leave it blank.
Determines how tied values are counted. The results of all three definitions are shown as well.

Percentile Rank Formulas

Mid-rank definition:       PR = [(B + 0.5·E) / n] × 100
Strictly-below definition: PR = (B / n) × 100
Below or equal:            PR = [(B + E) / n] × 100
  B: number of observations below x,  E: number of observations equal to x
Reverse (interpolation):  rank = (p/100)·(n − 1),  Pₚ = x(⌊rank⌋) + fraction·[x(⌈rank⌉) − x(⌊rank⌋)]
Reverse (nearest rank):   Pₚ = x(⌈p·n/100⌉)
Standard position:         z = (x − x̄) / s
Quartiles:                 Q1 = P₂₅,  Md = P₅₀,  Q3 = P₇₅

The percentile rank gives the position of an observation as a percentage; a percentile gives the value corresponding to a stated percentage. The two are inverses of each other, and because the definitions differ they may not cancel out exactly.

How to Calculate

  1. Paste your data values into the box; commas, spaces, and line breaks are all accepted.
  2. Enter the value whose percentile rank you want (your own score, for example).
  3. If you like, enter a percentile level for the reverse calculation; the value corresponding to that percentile is returned.
  4. Choose the definition that decides how ties are counted; the results of all three are shown together.
  5. Find the marked row for your value in the sorted-data table and check the cumulative percentage.
  6. Read the z-score alongside the percentile rank: one describes distance, the other describes rank.

Worked Examples

Where an exam score sits within the class

In a class of 25, thirteen students scored below 76 and one scored exactly 76. The mid-rank definition gives a percentile rank of [(13 + 0.5) / 25]·100 = 54%; the strictly-below definition gives 52% and the below-or-equal definition 56%. In reverse, the 90th percentile corresponds to 92.20 by interpolation and to 93 by the nearest-rank method; the z-score of 76 is only 0.067.

Percentile rank of 76.00: 54.00% · Observations below: 13 / 25 · Observations equal to it: 1

How the definitions differ when values repeat

Four of the 12 observations equal 7, so the gap between definitions widens: strictly below gives 16.67%, mid-rank gives 33.33%, and below or equal gives 50%. Under the selected below-or-equal definition, someone scoring 7 is counted as having left 50% of the group behind. Because this value lands exactly on the Q1 line, the reverse calculation puts the 75th percentile at 10.

Percentile rank of 7.00: 50.00% · Observations below: 2 / 12 · Observations equal to it: 4

Strictly-below definition and the reverse of the 25th percentile

There are 7 observations below 175 and 7 above it, with one observation exactly at 175; the value therefore lands on the median line. The strictly-below definition gives 46.67%, the mid-rank definition 50%, and the below-or-equal definition 53.33%. In reverse, the 25th percentile is 157.50 by linear interpolation and 155 by the nearest-rank method (the 4th observation).

Percentile rank of 175: 46.67% · Observations below: 7 / 15 · Observations equal to it: 1

Frequently Asked Questions

What is the difference between a percentile rank and a percentile?
A percentile rank starts from a value and returns a percentage: "a score of 76 is at the 54% rank". A percentile starts from a percentage and returns a value: "the 90th percentile corresponds to 92.2 points". The two are inverses of each other, and this calculator computes both directions on the same screen.
Why are there three different percentile rank results?
The difference comes from how observations equal to the target value are counted. The strictly-below definition ignores ties entirely, the below-or-equal definition counts all of them, and the mid-rank definition counts half. When there are no repeated values the three results are almost identical; when many observations are tied the gap widens and you need to state which definition you used.
Can a percentile rank be 100%?
Under the mid-rank definition the result for the largest observation stays slightly below 100%, because that observation is itself part of the data. Under the below-or-equal definition the largest value gives exactly 100%. If you enter a value greater than the largest observation in the data set, every definition returns 100%.
How do I get the same result in Excel and SPSS?
In Excel, =PERCENTILE.INC(array, 0.9) performs the reverse calculation and =PERCENTRANK.INC(array, 76) gives the percentile rank; PERCENTRANK.INC uses an interpolation close to the strictly-below definition. In SPSS, the Cumulative Percent column of the Frequencies output corresponds to the below-or-equal definition. Small deviations caused by the differing definitions are normal.
How are the percentile rank and the z-score related?
The z-score tells you how many standard deviations you are from the mean; the percentile rank tells you how many people you passed. If the data is normally distributed the two can be converted into each other: z = 0 corresponds to about 50%, z = 1 to about 84%, and z = 2 to about 98%. When the distribution is skewed these correspondences break down and the percentile rank becomes the more reliable measure of position.
Is the percentile rank reliable on small samples?
Only to a limited extent. In a data set of 20 observations, each observation corresponds to a jump of roughly 5 percentile points, so intermediate values are rough estimates. With samples below 100 it is more honest to round the percentile rank to a whole number when reporting it, so as not to suggest a precision that is not there.
Do two people with the same score get the same percentile rank?
Yes. The percentile rank depends on the value, not on the person; equal values always receive the same rank. This is the "shared rank" logic of ranking, and the mid-rank definition handles it most fairly: tied observations share a single position averaged among themselves.