📶 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.