Calculator
What the Combination Calculator does
Combination Calculator: calculates C(n,r) from n and r. Example: n 10 and r 3 gives c(n,r) 120.
The Combination Calculator takes n and r and returns C(n,r). You can nudge a single number and watch the effect straight away.
Most people who open the Combination Calculator are people who want the working shown. Checking a result a second way is the cheapest way to catch an arithmetic slip.
There is no account, no upload and no server round trip, because the page does the work itself.
Further down the page: what each field expects, how the result is derived, and one example worked from the defaults.
What do the Combination Calculator fields mean?
The Combination Calculator uses 2 inputs. Pre-filled inputs double as documentation: each one shows what a reasonable value looks like.
| Field | What to enter | Default |
|---|---|---|
| n | required | 10 |
| r | required | 3 |
How does the Combination Calculator work?
Each output is derived from the inputs above in a single pass; there is no hidden state carried between runs, so the same inputs always give the same calculation.
Nothing is computed until the inputs pass their checks, so you will not get a confident answer built on a typo.
Worked example
These are the values the Combination Calculator loads by default, and the result it produces from them. This is the worked example the page starts from, reproduced here so you can check the arithmetic.
| n | 10 |
|---|---|
| r | 3 |
| C(n,r) | 120 |
|---|---|
| What this means | C(10,3) = 120 |
Beyond the formula: combinations
A combination counts selections where order doesn’t matter (a lottery ticket, a committee), and the formula divides the permutation count by r! precisely to remove all the different orderings of the same chosen group.
Common mistakes and sanity checks
- C(n,r) always equals C(n, n−r): choosing which r items to include is mathematically identical to choosing which n−r items to leave out, a symmetry that’s a good way to double-check a result.
- Combinations grow fastest around r = n/2 and shrink toward the edges (r=0 or r=n both give exactly 1): this is the shape behind Pascal’s triangle and the bell-shaped binomial distribution.
- The most common mix-up with this calculator is using it for a problem where order actually does matter, like assigning distinct prizes to distinct winners. That calls for the permutation calculator instead: using combinations there undercounts.
How to use it
- Put n.
- Key in r.
- You will see the result move while you are still editing: that is expected.
- The results panel then shows C(n,r) and What this means.
- Copy Link puts the current inputs in the URL, so bookmarking it brings the same numbers back.
What this tool does not do
- Displayed values are rounded; the underlying calculation keeps full precision.
- Very large or very small numbers hit JavaScript floating-point limits (about 15 significant digits).
- The result reflects the moment you ran it; anything that changes over time is not tracked.
Frequently asked questions
Just n and r. Every box already holds a working value, which makes it easy to isolate the effect of a single variable.
With the values loaded when the page opens, c(n,r) comes out as 120. The figure is derived from the inputs above, so it updates whenever they do.
No. There is no upload step, no database, and nothing to delete afterwards.
No. There is no account, no usage cap and no trial period. The site is funded by advertising rather than by charging for the tools.
The output is deterministic. The same inputs always give the same answer, and the method is documented above so you can check it.