Math & Scientific
Combination Calculator
Combination: it counts selections where order does not matter using C(n, r) = n! / (r!·(n−r)!). Worked through below with real figures, and the calculator repeats the working on your own inputs — free, on-device, instant.
Enter your n and r and Combination Calculator works out the result with the standard method — fast, free and private, with no sign-up or uploads.
About this calculator
Combination is easiest to get wrong in the setup, not the arithmetic. It counts selections where order does not matter using C(n, r) = n! / (r!·(n−r)!). It matters when you need the exact relationship checked quickly rather than worked through by hand. The worked example on this page (Choose 2 from 5: C(5,2) = 5! ÷ (2! × 3!) = 120 ÷ 12 = 10 combinations.) shows the full substitution; the calculator above runs the same working on your own numbers, in your browser, with nothing uploaded.
How to use
- Enter n, the total number of items.
- Enter r, how many you choose.
- Press Calculate to compute C(n, r).
- Read the number of combinations, with permutations shown for comparison.
Why use Combination Calculator
Fast
Calculations run in your browser. No round trip to a server.
Private
Your inputs never leave your device. Nothing is uploaded.
Free
No signup, no paywall, no ads-in-results, no watermarks.
Accurate
Uses standard, well-established formulas; check critical results independently.
Mobile-ready
Optimised for phones, tablets, and desktops alike.
Transparent
Honest disclaimers wherever browser limits or regional rules apply.
Common uses
Use it for understanding a formula's behaviour
Use it for verifying answers from a textbook
Use it for quick mental-math cross-checks
Use it for science-fair and project numbers
Combination in competitive-exam practice
Combination in statistics and data coursework
Technical notes
Combination Calculator counts selections where order does not matter using C(n, r) = n! / (r!·(n−r)!).
Inputs are taken exactly as entered, so check for typos before trusting an answer.
The tool works offline once loaded, since every computation is client-side.
FAQ
What is the difference between a combination and a permutation?
A combination counts selections where order does not matter; a permutation counts arrangements where order does matter, so P(n, r) is always at least as large as C(n, r).
Are large results exact?
Yes. Combinations are computed with exact integer arithmetic, so even very large values like C(60, 30) are returned precisely rather than rounded.
Do n and r have to be whole numbers?
Yes. You are counting whole items, so both n and r must be non-negative whole numbers with r no greater than n.
Does the Combination Calculator send my data to a server?
No. The Combination Calculator runs entirely in your browser, so nothing you enter is uploaded, stored, or shared.
Worked example
Choose 2 from 5: C(5,2) = 5! ÷ (2! × 3!) = 120 ÷ 12 = 10 combinations.