A rank expressed as a percentage
A percentile rank answers: what percentage of the group falls below this score, with ties split fairly? The formula counts three things in the data: scores strictly below yours (B), scores equal to yours (E), and the total (n). PR = (B + ½E) ÷ n × 100. The half-credit for ties is the standard convention; without it, a big tied group at the same score would all claim the rank of the person below the tie, or all jump above it, depending on the direction chosen.
Quiz scores: 58, 65, 67, 69, 72, 72, 74, 76, 80, 91. For a score of 72: four scores sit below, two equal it (including your own), so PR = (4 + 1) ÷ 10 × 100 = 50. Dead average, exactly as a median score should be. The top score, 91, earns (9 + 0.5)/10 = 95, and the lowest, 58, earns 5: percentile ranks in a finite group never quite reach 0 or 100, because you are always tied with yourself.
Percentile rank versus percentile
The two get confused constantly, and the grammar gives them away. A percentile is a score: "the 90th percentile is 81.1" names a value on the mark scale. A percentile rank is a percentage: "her rank is 90" names a position in the group. One starts from a percentage and returns a score; the other starts from a score and returns a percentage. This page runs the second direction; the percentile calculator runs the first. Norm-referenced tests (the SAT family, IQ tests) report ranks and scaled scores precisely because raw marks mean nothing across different test forms, while positions in a reference group travel well.
Reading a percentile rank of 75 as "scored 75%". The rank says 75% of the group scored below, nothing about the share of questions answered correctly. A brutal exam can put a 40%-correct script at rank 95.
Frequently asked questions
Can a percentile rank be 100?
Not under the standard formula: you are always tied with yourself, so the maximum is (n - 0.5)/n x 100, which approaches 100 only in huge groups.
What does a percentile rank of 50 mean?
The middle of the group: half the scores fall below yours (with ties split). It coincides with the median score's rank.
Why split the ties in half?
Fairness and convention. Crediting all tied scores with the full count below plus all the ties would inflate ranks in lumpy data; crediting none would deflate them. Half is the neutral middle, and it is what testing agencies use.