Pascal's Triangle Calculator

Generate Pascal's Triangle online up to 25 rows. Each row contains the binomial coefficients C(n, k). Shows the formula and explanation.

Number of rows (1–25)

1 1

1 2 1

1 3 3 1

1 4 6 4 1

1 5 10 10 5 1

1 6 15 20 15 6 1

1 7 21 35 35 21 7 1

1 8 28 56 70 56 28 8 1

1 9 36 84 126 126 84 36 9 1

Formula

C(n, k) = n! / (k! · (n − k)!)

Each entry is the sum of the two directly above it. Row n contains the binomial coefficients of (a + b)ⁿ.

How to Generate Pascal's Triangle

Enter the number of rows (1 to 25).
The triangle appears instantly with all binomial coefficients.
Use a value C(n, k) directly as a combination count or to expand (a + b)ⁿ.

Casi d'Uso

•Algebra — expand binomial powers like (x + y)⁵.
•Probability — count combinations without listing them.
•Competitive programming and number theory exercises.

Formula

C(n, k) = n! / (k! · (n − k)!). Each entry is the sum of the two entries directly above it.

Domande Frequenti

What is Pascal's Triangle used for?

Pascal's Triangle gives the binomial coefficients needed to expand (a + b)ⁿ, to count combinations C(n, k), and appears in probability, algebra and number theory.

How many rows can I generate?

Up to 25 rows. Beyond that, the numbers grow quickly and become harder to display, though the BigInt implementation can handle much more.

Are the rows zero-indexed?

Yes. Row 0 contains a single 1. Row n has n+1 entries: C(n, 0), C(n, 1), …, C(n, n).