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Binomial Coefficient Calculator
Work out n choose k and see the whole matching row of Pascal's triangle.
Binomial coefficient
C(n, k): —
Pascal row n: —
How to use the Binomial Coefficient Calculator
- Enter n, the total number of items you can choose from.
- Enter k, the number of items you want to choose.
- Read C(n, k) and the whole matching row of Pascal's triangle.
Features
- n choose k from 0 to 30
- Shows the full Pascal's triangle row
- Handles k larger than n correctly
- Runs locally, no uploads
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Frequently Asked Questions
Common questions about the free online binomial coefficient calculator.
It is the number of ways to choose k items from n without regard to order, written as n
choose k.
It is 15, because there are fifteen different pairs you can pick from six items.
Row n of Pascal's triangle lists n choose k for every k from 0 up to n.
It equals 1, because there is exactly one way to choose nothing at all.
The coefficient is 0, since you cannot choose more items than are available.
No. The tool works with whole numbers from 0 to 30, and negatives are clamped to 0.
Yes. A combination is exactly the same count, and it ignores the order of the chosen items.
No. Every coefficient is computed locally in your browser and nothing is sent anywhere.
Yes. The calculator is fully responsive and works on phone, tablet and desktop.
Yes. It is completely free and unlimited, with no account or sign-up required.
Last updated: October 10, 2026