Pascal's Triangle Calculator
Discover Pascal's triangle patterns and find any triangle level you need with our Pascal's triangle calculator. Fast and accurate results.
Row 51, 5, 10, 10, 5, 1
Entries in that row6
Row sum32always 2^5
Largest entry10the central binomial coefficient
Pascal’s triangle
| Row 0 | 1 |
| Row 1 | 1 1 |
| Row 2 | 1 2 1 |
| Row 3 | 1 3 3 1 |
| Row 4 | 1 4 6 4 1 |
| Row 5 | 1 5 10 10 5 1 |
| Row 6 | 1 6 15 20 15 6 1 |
| Row 7 | 1 7 21 35 35 21 7 1 |
| Row 8 | 1 8 28 56 70 56 28 8 1 |
| Row 9 | 1 9 36 84 126 126 84 36 9 1 |
The formula
each entry is the sum of the two above it
What the rows are
Row n holds the binomial coefficients "n choose k" — the coefficients of (a + b)ⁿ, and the number of ways to pick k things from n. Each row sums to 2ⁿ, because that counts every possible subset.
The diagonals hold the counting numbers, then the triangular numbers, then the tetrahedral numbers — and shallow diagonals sum to the Fibonacci sequence.