Percentile Rank Calculator
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.
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
- Paste your data values into the box; commas, spaces, and line breaks are all accepted.
- Enter the value whose percentile rank you want (your own score, for example).
- If you like, enter a percentile level for the reverse calculation; the value corresponding to that percentile is returned.
- Choose the definition that decides how ties are counted; the results of all three are shown together.
- Find the marked row for your value in the sorted-data table and check the cumulative percentage.
- 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