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Combination calculator (nCr)

Compute the number of combinations nCr of r items from n.

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Need nCr? The Combination calculator (nCr) derives it from n (total), r (chosen) in one step. For instance, with n (total) = 10 and r (chosen) = 3 it returns nCr = 120.

How to use it

  1. Enter your values: n (total), r (chosen).
  2. Read the result instantly: nCr.

Frequently asked questions

How does the Combination calculator (nCr) work?

It takes n (total) and r (chosen) and derives nCr from them. The calculation is live as you type, so the result updates on every change.

Which values does the calculator ask for?

2 values: n (total) and r (chosen). Nothing else is required — no account, no file upload.

What does a typical calculation look like?

With n (total) = 10 and r (chosen) = 3, the calculator returns nCr = 120. Those figures come from running this exact tool, so you can reproduce them by entering the same values.

How much does the result change with different inputs?

It moves a lot. Using n (total) = 20 and r (chosen) = 6 instead, nCr goes from 120 to 38,760 — which is why it is worth testing a few scenarios rather than trusting a single figure.

What does it give for smaller values?

Scaled down to n (total) = 5 and r (chosen) = 2, nCr comes out at 10. The relationship is worth checking at both ends before you rely on a single result.

When would I actually use this?

Counting possibilities before enumerating them: hands in a card game, passwords of a given shape, seatings around a table, or lottery odds.

What is the most common mistake?

Choosing a permutation when order does not matter. Picking three people from ten gives 720 arrangements but only 120 groups — the two differ by a factor of six here, and far more as the numbers grow.

What is the difference between the Combination calculator (nCr) and the Permutation calculator (nPr)?

This one returns nCr; the Permutation calculator (nPr) returns nPr. That is the whole difference — open the one whose figure you need.

Where do the figures come from, and how current are they?

Counting formulas are exact by definition. Large factorials are computed with arbitrary precision where needed, so a result is not silently rounded into scientific notation.

Further reading

All guides →
ExplainerCombinations vs Permutations: When Order MattersThe difference between combinations and permutations comes down to one question: does order matter? Learn the nCr and nPr formulas with clear worked examples.ExplainerWhat Is a Factorial? n! Explained SimplyA factorial multiplies every whole number down to 1. Learn what n! means, how fast it grows, and why it powers permutations and combinations.ExplainerOrdinal Numbers Explained: 1st, 2nd, 3rdOrdinal numbers show position, cardinal numbers show quantity. Learn the difference and how each language forms ordinals differently.ExplainerPoker Hand Probabilities, Derived Rather Than MemorisedEvery five-card poker probability is a counting argument over 2,598,960 hands, and each one fits on a single line. Here are all nine, with the check that proves them: the counts must sum to exactly C(52,5).GuideTournament Brackets: Byes, Seeds, and Why the Numbers Must Be Powers of TwoA knockout bracket halves its field every round, so it only closes on a power of two. The bye count, the round count, the seed order and the total number of matches all follow from that one fact — and each is a one-line derivation.ExplainerHow Exponents Work: Powers and the Laws of ExponentsAn exponent is repeated multiplication. Learn the laws of exponents, what negative and fractional powers mean, and why anything to the zero is one.