Pascal's triangle arranges binomial coefficients in a triangular grid.
About this calculator
Pascal's triangle arranges binomial coefficients in a triangular grid. Row 5 reads 1, 5, 10, 10, 5, 1 — the coefficients in (a + b)⁵. Each number is the sum of the two above it.
Enter n to print the full row and its sum. The sum is always 2ⁿ because it counts all subsets of an n-element set.
Use this for binomial theorem homework and probability setups. For choosing r from n directly try the [[permutation-combination]] calculator. For n! values see the [[factorial]] calculator. For powers of two check the [[exponent]] calculator.
Common uses
- Print row n for binomial expansion homework
- Look up C(n,k) without a formula sheet
- Verify row sums equal 2ⁿ
- Connect triangle entries to probability problems
Frequently asked questions
What is row 5 of Pascal's triangle?
1, 5, 10, 10, 5, 1. These are C(5,0) through C(5,5), the coefficients of (a+b)⁵.
Why does each row sum to 2ⁿ?
Setting a = b = 1 in (a+b)ⁿ gives 2ⁿ, and the coefficients add to the same value.
How is Pascal's triangle related to combinations?
Entry k in row n equals C(n,k) — the number of k-subsets from n items.
What is the largest n supported?
Row index is capped at 30 so numbers stay readable on screen. Larger n still grows quickly — row 30