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.
1
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.
Casos de Uso
- •Algebra — expand binomial powers like (x + y)⁵.
- •Probability — count combinations without listing them.
- •Competitive programming and number theory exercises.
Fórmula
C(n, k) = n! / (k! · (n − k)!). Each entry is the sum of the two entries directly above it.
Preguntas Frecuentes
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).