Pascal's triangle generator
Each number in Pascal’s triangle is the sum of the two above it, and row n gives the coefficients of (a + b)^n.
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How to use it
- Enter number of rows.
- The result appears straight away and updates as you edit.
- Copy the result, or copy a link that keeps the same values to share it.
How it is calculated
Entry k of row n is C(n, k) = n! ÷ (k! × (n - k)!), with C(n, k) = C(n - 1, k - 1) + C(n - 1, k). Row n sums to 2^n.
Example
Inputs: Number of rows = 6. Result: Pascal's triangle: 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1; Sum of the last row: 32.
Limits and caveats
- Limited to 30 rows so the triangle stays readable; for later rows use the combination calculator.
Questions about this tool
How do I expand (a + b)^4 with it?
Row 4 is 1 4 6 4 1, so (a + b)^4 = a^4 + 4a^3b + 6a^2b^2 + 4ab^3 + b^4.
Why do rows start at 0?
The top row 1 stands for (a + b)^0 = 1, so the row number matches the exponent.
How does it relate to probability?
Row n divided by 2^n gives the chances of each number of heads in n fair coin flips.