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.

Anwendungsfälle

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

Formel

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

Häufig gestellte Fragen

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).