A percentile rank tells you what percentage of a data set falls below a score. The standard percentile rank formula is (B + 0.5E) ÷ N × 100. Paste your data and the score above to get the percentile rank under four common definitions: mid-rank, at-or-below, strictly-below and Excel’s PERCENTRANK.INC. You also see the below, tied and above counts, the arithmetic, and a dot plot marking the score. Switch modes to find the value at any percentile using the NIST or Excel method, with a full percentile table.
This works on your actual data, with no bell curve assumed. That is what separates it from a z-score to percentile calculator, which reads a percentile off the normal distribution.
How to use the percentile rank calculator
- Paste the reference data: class scores, times, measurements, or a spreadsheet column.
- Enter the score you want to rank.
- Pick the definition your course, test or software uses. Mid-rank is the default textbook method.
- Read the percentile rank and check the counts. The dot plot colours values below, tied with and above the score.
- To go the other way, choose “Value at a given percentile” and enter p.
Percentile rank formula (three definitions plus Excel)
Let N be the number of values, B the number strictly below the score, and E the number exactly equal to it. The definitions differ only in how they treat E:
| Definition | Formula | Used by |
|---|---|---|
| Mid-rank | 100 × (B + 0.5E) ÷ N | OpenStax Introductory Statistics |
| At or below (weak) | 100 × (B + E) ÷ N | College Board SAT percentile ranks |
| Strictly below | 100 × B ÷ N | “Percent of the group you beat” |
| Excel PERCENTRANK.INC | B ÷ (N − 1), interpolated between values | Microsoft Excel |
OpenStax §2.3 gives the mid-rank formula as (x + 0.5y)/n × 100, where x is the number of values below and y the number equal. It then rounds to the nearest integer. Counting half of the tied values places a group of equal scores at the middle of its block. This is why it is the usual choice when many people share the same score. The College Board instead defines a student’s percentile rank as the percentage of students with scores equal to or lower than theirs, which is the “at or below” version. Microsoft’s PERCENTRANK.INC divides by N − 1, so the lowest value gets 0 and the highest gets 1.
Worked example with ties
Fifteen quiz scores: 55, 60, 62, 70, 71, 75, 78, 80, 80, 80, 84, 88, 90, 93, 97. Rank the score 80. Seven values are below it (B = 7), three equal it (E = 3) and 5 are above, with N = 15.
- Mid-rank: 100 × (7 + 0.5 × 3) ÷ 15 = 56.67, which OpenStax would round to the 57th percentile.
- At or below: 100 × (7 + 3) ÷ 15 = 66.67.
- Strictly below: 100 × 7 ÷ 15 = 46.67.
- Excel: 7 ÷ (15 − 1) = 0.5.
Four defensible answers span 46.67 to 66.67, all because of the three tied 80s. With no ties, the first three differ by only 100 ÷ N. Always say which one you used.
Checking against Excel
Microsoft’s documentation uses the data 13, 12, 11, 8, 4, 3, 2, 1, 1, 1. PERCENTRANK.INC gives 0.333 for 2, 0.555 for 4, 0.666 for 8, and 0.583 for 5, which is not in the data and so is interpolated between 4 and 8. The calculator reproduces all four, before Excel’s default truncation to three digits.
Finding the value at the Pth percentile
The reverse question is which score sits at the 90th percentile. The NIST e-Handbook defines the pth percentile as a value such that at most 100p% of the measurements are below it and at most 100(1 − p)% are above it. Its default recipe sorts the data and sets p(N + 1) = k + d, where k is an integer and d the fractional part. It then interpolates: Y(p) = Y[k] + d × (Y[k+1] − Y[k]). When k = 0 the answer is the minimum, and when k ≥ N it is the maximum. Hyndman and Fan call this method R6. Excel’s PERCENTILE.INC uses 1 + p(N − 1) instead (R7). NIST notes that the methods give similar but not identical results, especially for small samples. These are the same two methods the box plot maker offers for quartiles, so its Q1 and Q3 match the 25th and 75th percentiles here.
For the 15 quiz scores, the 90th percentile position is 0.9 × 16 = 14.4 under NIST, which gives 94.6. Under Excel it is 1 + 0.9 × 14 = 13.6, which gives 91.8. OpenStax uses the same i = k(n + 1)/100 position as NIST, but when i is not a whole number it averages the two neighbouring values instead of interpolating. That gives (93 + 97) ÷ 2 = 95. None of these is wrong. They are different conventions, so match the one your class or software uses.
| Percentile | NIST p(N+1) (R6) | Excel 1+p(N−1) (R7) |
|---|---|---|
| 10th | 58 | 60.8 |
| 25th | 70 | 70.5 |
| 50th | 80 | 80 |
| 75th | 88 | 86 |
| 90th | 94.6 | 91.8 |
Percentile vs percentile rank vs rank
These are easy to confuse. A rank is a position in the sorted list, such as 3rd of 20. A percentile rank converts a score into a percentage of the group, such as the 85th percentile. A percentile goes the other way and names the score at a given percentage, such as “the 85th percentile is 91 points”. OpenStax adds a key point: low percentiles always correspond to low data values. Whether that is good depends on the context. A low percentile for a race time is good, and a low percentile for a test score usually is not. If your ranking puts 1 as best, flip the order or work with the underlying scores before you convert.
Empirical percentile rank or z-score percentile?
Use this calculator when you have the actual group’s data, such as a class’s scores, a team’s sales or a lab’s measurements. It makes no assumption about the shape of the distribution, so it is correct for skewed data and small groups. Use the z-score percentile calculator when you only know the mean and standard deviation and the data are known to be close to normal. You can get both of those from raw data with the average and standard deviation calculator. When both are available, comparing them is a quick normality check: big gaps mean the bell-curve model is off.
Interpreting and reporting a percentile rank
- It is relative to one group. A 90th-percentile score in an honours class may be a 99th-percentile score nationally. Name the reference group.
- Small groups move in big steps. With N = 10, each person is worth 10 percentile points, so do not read meaning into a change of 5.
- Percentile ranks are not equal-interval. In a bell-shaped distribution, going from the 50th to the 60th percentile takes a much smaller score gain than going from the 89th to the 99th.
- Say the method. “PR = 57 (mid-rank, N = 15)” is reproducible, while “57th percentile” alone may not be.
Common mistakes
- Forgetting to sort before finding a percentile value.
- Counting the score itself as “below” when it is part of the data. It is a tie, so it belongs in E.
- Mixing definitions, for example quoting a mid-rank next to an SAT percentile that is at-or-below.
- Treating percentile rank as percent correct. For points earned out of points possible, use the grade calculator.
Frequently asked questions
What is the percentile rank formula?
The textbook formula is PR = (B + 0.5E) ÷ N × 100, where B is the number of values below the score, E the number equal to it and N the total. OpenStax gives it as (x + 0.5y)/n × 100, rounded to the nearest integer. Other conventions drop the 0.5 or the E term.
How do I calculate percentile rank from a data set?
Sort the data, count the values below your score (B) and the values tied with it (E), then apply the formula. The calculator does this for four definitions at once and marks your score on a dot plot.
What is the difference between a percentile and a percentile rank?
A percentile is a value in the data, such as “the 90th percentile is 95 points”. A percentile rank is a percentage attached to a score, such as “a score of 80 has a percentile rank of 57”. This calculator does both: switch the mode to “Value at a given percentile”.
How are tied scores handled?
It depends on the definition. The mid-rank counts half of the ties as below, “at or below” counts all of them, and “strictly below” counts none. With many ties the three can differ by a lot, so the calculator shows them side by side.
What does it mean to be in the 75th percentile?
Under the College Board’s definition, about 75% of the comparison group scored at or below you. Under the mid-rank definition, 75% scored below you once half of the people tied with you are counted. In a large group with few ties, the two are almost the same.
Can a percentile rank be 100?
Under the “at or below” definition the top score always gets 100, because every value is at or below it. Under the mid-rank definition it can only reach 100 − 50/N, and under “strictly below” the maximum is 100 × (N − 1)/N. Excel’s PERCENTRANK.INC gives 1 (100%) to a maximum that is not tied.
How do I find the value at the 90th percentile?
Sort the data and compute a position. NIST’s default is p(N + 1), and Excel’s PERCENTILE.INC uses 1 + p(N − 1). Interpolate between the two sorted values around that position. For the example data here, NIST gives 94.6 and Excel gives 91.8.
Why do different percentile calculators give different answers?
NIST’s e-Handbook says there is no standard, universally accepted way to interpolate percentiles. Tools differ in how they count ties (for ranks) and in which position formula they interpolate from (for values). State the method alongside your answer.
Is percentile rank the same as percent correct?
No. Percent correct is points earned divided by points possible. Percentile rank compares your score with other people’s scores. An 80% test score can be anywhere from the 10th to the 99th percentile depending on the group.
What is the Excel formula for percentile rank?
PERCENTRANK.INC(range, x) returns B ÷ (N − 1) for a value in the data and interpolates between data values otherwise. Microsoft documents only values inside the data range, so this calculator leaves it undefined outside that range. By default it shows three digits, cut off rather than rounded: 0.555 for 5/9.
Sources & method
- OpenStax Introductory Statistics 2e §2.3 — Measures of location: percentile of a value (x + 0.5y)/n and the kth percentile i = k(n+1)/100
- NIST/SEMATECH e-Handbook §7.2.6.2 — Percentiles (p(N+1) method, boundary rules, R6/R7/R8)
- College Board — SAT User Percentiles (percentile rank = percentage scoring equal to or lower)
- Microsoft Support — PERCENTRANK.INC function (definition and worked examples)
- Microsoft Support — PERCENTILE.INC function (k-th percentile, inclusive)
Results are estimates for general information. Found an error? It helps everyone — see our methodology.