Percentiles describe where a value sits within a data set. The pth percentile is the value below which about p percent of the data fall, so the 90th percentile of commute times is the time that only one commute in ten exceeds. This calculator works both ways: give it a percentile and it returns the value, or give it a value and it returns the percentile rank.
How to use the percentile calculator
- Paste your data, separated by commas, spaces or new lines.
- Choose Value at a percentile or Percentile rank of a value.
- For a value, enter the percentile (0 to 100) and pick a method; for a rank, enter the score you want to place.
- Read the result on the tape and check the position or count in Show the work. In value mode a table lists the 5th through 95th percentiles with the same method.
Percentile formulas
Sort the data as x₁ ≤ x₂ ≤ … ≤ xₙ and let p be the percentile as a fraction (0.9 for the 90th).
Linear interpolation (PERCENTILE.INC). Find the position h = 1 + p(n − 1) and interpolate:
PERCENTILE.EXC uses h = p(n + 1) in the same expression. Nearest rank takes x at position ⌈p × n⌉ with no interpolation.
Percentile rank of a score with B values below it and E values equal to it:
Worked example
Twenty exam scores: 55, 61, 64, 68, 70, 72, 73, 75, 77, 78, 80, 81, 83, 85, 86, 88, 90, 92, 95, 98.
90th percentile (PERCENTILE.INC): h = 1 + 0.9 × 19 = 18.1. The 18th and 19th scores are 92 and 95, so P₉₀ = 92 + 0.1 × (95 − 92) = 92.3.
With PERCENTILE.EXC, h = 0.9 × 21 = 18.9, giving 92 + 0.9 × 3 = 94.7. With nearest rank, ⌈0.9 × 20⌉ = 18, giving 92.
Percentile rank of 85: thirteen scores are below 85 and one equals it, so PR = (13 + 0.5) ÷ 20 × 100 = 67.5. About two-thirds of the class scored lower.
Choosing a method
| Method | Used by | Notes |
|---|---|---|
| PERCENTILE.INC | Excel, Google Sheets, R (default), NumPy | Always defined; 0th = min, 100th = max |
| PERCENTILE.EXC | Excel, Minitab, SPSS | Spreads results further toward the extremes |
| Nearest rank | Many textbooks, service-level reports | Always returns an actual data value |
For large data sets the methods agree closely. For small ones, like the twenty scores above, they can differ by a few points, so use whichever your instructor, standard or software specifies. Service-level targets such as “95th-percentile response time” in IT monitoring are often computed with nearest rank so that the reported figure is a real measurement.
Percentiles in everyday life
- Growth charts. CDC growth charts place a child’s height or weight among U.S. reference data; the 75th percentile for weight means heavier than about 75% of children of the same age and sex.
- Standardized tests. Score reports for the SAT and ACT include percentile ranks so a raw score can be compared with other test takers.
- Income. Household income percentiles show inequality more clearly than an average, since the top percentiles stretch far above the median.
If your data are approximately normal and you know the mean and standard deviation, the z-score calculator converts a value to a percentile without the full data set. The quartile calculator covers the 25th, 50th and 75th percentiles in detail.
Frequently asked questions
What is the difference between a percentile and a percentile rank?
A percentile is a value: the 90th percentile of test scores might be 92 points. A percentile rank is a position: a score of 85 might sit at the 67.5th percentile rank, meaning about two-thirds of scores are below it.
Is the 50th percentile the same as the median?
Yes, with the interpolation methods the 50th percentile equals the median. The 25th and 75th percentiles are the first and third quartiles, although quartile conventions vary slightly between methods.
Which method does Excel use?
PERCENTILE.INC (and the older PERCENTILE) interpolates at position 1 + p(n − 1), counting from 1. PERCENTILE.EXC interpolates at position p(n + 1) and is undefined very close to 0% or 100%. Google Sheets and R's default match PERCENTILE.INC.
How is percentile rank calculated here?
With the mid-rank formula (B + 0.5E) ÷ n × 100, where B is the number of values below the score and E is the number equal to it. The tape also shows the percent strictly below and the percent at or below, the other two common definitions.
Does scoring in the 90th percentile mean I got 90% right?
No. A percentile compares you with other people, not with the maximum score. Scoring in the 90th percentile means you did as well as or better than about 90% of test takers, whatever your raw score was.