📶 Percentile Calculator
P40 of your data, three ways at once: linear interpolation (Excel's PERCENTILE.INC), nearest rank, and exclusive interpolation (PERCENTILE.EXC), because they genuinely disagree, and knowing which one your course or spreadsheet uses is the whole game.
29
Linear interpolation
Excel PERCENTILE.INC · R-7 · NumPy default
20
Nearest rank
classic textbook definition
26
Exclusive interpolation
Excel PERCENTILE.EXC · R-6 · Minitab
Working (linear interpolation shown)
- Sort the 5 values: 15, 20, 35, 40, 50
- Rank position = (p/100)·(n − 1) = (40/100)·4 = 1.6 (zero-based)
- Interpolate between positions 1 (20) and 2 (35): 29
The three methods disagree on small datasets by design. This is the #1 source of "my answer doesn't match Excel" confusion. Match the method your course or spreadsheet uses.
Method stated on every answer, percentile definitions differ between textbooks, and knowing which one you're using is half the mark. Runs locally.
How the percentile calculator works
There is no single definition of "percentile", statisticians catalogue nine, and the three that matter in practice disagree visibly on small datasets. This calculator computes all three, labeled by their common names: linear interpolation over (n−1) intervals (R-7, Excel's PERCENTILE.INC and the NumPy default), the classic nearest-rank definition (value at position ⌈p·n/100⌉), and exclusive interpolation over (n+1) (R-6, Excel's PERCENTILE.EXC and Minitab). The working is shown for the interpolation path: sort, compute the rank position, interpolate between the straddling values. The rank tab answers the reverse question, what percentile is this value at? Using the midpoint convention (below + half of equal).
The "my answer doesn't match Excel" confusion that fills statistics forums is almost always a method mismatch, not an arithmetic error, INC and EXC can differ by whole points on a class-sized dataset, and textbook nearest-rank differs from both. Showing the three side by side turns the gotcha into a lesson: percentiles below 1/(n+1) or above n/(n+1) don't even exist under EXC, which is why Excel returns #NUM! there and this tool clamps with a note.
Frequently asked questions
Why do different calculators give different percentiles?
Because "percentile" has multiple standard definitions. Excel alone ships two (PERCENTILE.INC and .EXC), textbooks often use nearest-rank, and they disagree on small datasets. This tool shows all three, named, so you can match yours.
Which method should I use?
Whichever your context uses: INC (linear interpolation) for Excel defaults, NumPy and most software; nearest-rank for classic textbook and percentile-of-score definitions; EXC for Minitab and some statistics courses. When reporting, name the method.
How is percentile rank calculated?
The midpoint convention: (number below + half the number equal) ÷ n × 100. A value equal to the median of 5 points ranks at the 50th percentile.
What's the difference between percentile and percentage?
A percentage is a fraction of a total; a percentile is a position in a distribution. Scoring 80% on a test says how many answers you got right; being at the 80th percentile says you beat 80% of the takers.
Are quartiles just percentiles?
Yes, Q1 = P25, median = P50, Q3 = P75 (method caveats apply here too). For the full quartile/IQR table, the statistics calculator on this site computes them alongside variance and standard deviation.