Percentile rank estimate:
formula and worked example

What a percentile rank tells you

A percentile rank places one value within a group by counting how many fall below it. If your result has a percentile rank of 74, then about 74 out of every 100 in the group scored lower than you. It is a statement about order, with no information about how large the gaps between scores are.

It is the language of competitive exams, growth charts, test norms and performance benchmarks, where the raw score has little meaning unless you know how others did. A mark of 62 might be excellent on a hard paper and mediocre on an easy one, but a percentile rank travels across both.

The word percentile is also used for the value at a given rank, as in the 90th percentile income. That is the reverse question: here we are going from a score to its rank.

The formula and its inputs

Divide the number of observations below the value by the total number in the group, then multiply by 100.

• Below: how many observations are strictly lower than the value, 37 in the example.
• Total: the number of observations in the whole group, 50 in the example.
• Result: a percentage from 0 to 100, in the percent unit.

This is the simplest, strictly-below definition. A common alternative adds half of the observations that tie with the value, which treats equal scores as straddling the position.

Worked example: 37 below out of 50

In a group of 50, 37 people scored lower than a given person.

1. 1Divide the count below by the total: 37 ÷ 50 = 0.74.
2. 2Multiply by 100: 0.74 × 100 = 74.

The rank is 74%, so the person is above 74% of the group. Equivalently, 13 people, or 26%, scored the same or higher.

How to read a percentile rank honestly

The 50th percentile is the median: half the group is below. Ranks above 50 mean you are above the middle. A rank of 74 is just short of the top-quarter boundary, which sits at the 75th percentile.

Percentile rank is not the same as percentage correct. Someone scoring 40% on a very hard test might be at the 90th percentile, while 90% on an easy test can be at the 40th. Always check which of the two is being quoted.

The scale also compresses differences in the middle and stretches them at the ends. In a bell-shaped distribution, many people sit within a few marks of each other near the middle, so a tiny score gain moves the rank a lot there, and moves it very little near the extremes.

How the count below moves the rank

The rank rises one-for-one with the count below, scaled by 100 over the group size. In this group each additional person below adds 2 percentage points.

The 10% row uses 40.7 below, which is not a whole number of people. Treat it as a rough scenario: 41 below would give 82, and 40 below would give 80.

Errors that muddy percentile ranks

• Mistaking a percentile for a percentage score, so that rank 74 is taken to mean 74% correct.
• Counting the person themselves among those below, which inflates the rank by one position.
• Ignoring ties. In a coarse scale, such as marks out of 10, many people share a value, and the strictly-below rule and the mid-rank rule give different answers.
• Comparing ranks from groups of different composition, such as one cohort of all candidates and another of only those who passed.

Checking a rank report

A scorecard says a student is at the 74th percentile in a cohort of 50 and that 40 students scored below. Do these agree?

1. 1Convert the count: 40 ÷ 50 = 0.80, so 80%.
2. 2Compare with the stated 74: the figures disagree.
3. 3Likely explanations are a different tie convention, a different group, or a typing error.

Resolve the mismatch before using the figure, since an 80 and a 74 might fall on opposite sides of an admission cut-off.