Pascal’s Triangle Calculator

This Pascal's triangle calculator generates any single row of Pascal's triangle instantly, without you having to build the whole triangle by hand from the top down. You enter one number, the row you want, counting the lone 1 at the very top as row 0, and the calculator lists every entry in that row, separated by commas, along with two supporting figures: the sum of the row, which always works out to 2 raised to the power of that row number, and the number of entries in the row, which is always one more than the row number itself. These figures matter beyond curiosity. Each row of Pascal's triangle is exactly the set of binomial coefficients, written as n choose k, so the row you generate tells you the coefficients you would use to expand an expression like (a + b) raised to that power, and the same numbers count combinations in probability and statistics problems. The tool accepts any whole row number from 0 to 30, which comfortably covers school algebra, university combinatorics papers and most probability work, and it updates the result the moment you change the number, so you can step through consecutive rows to see the pattern build. A worked example below shows row 4 confirmed against the calculator, and the FAQ section explains how each row is constructed from the one above it.

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Row number n (0 to 30)

1, 4, 6, 4, 1

Sum of row (2^n)16

Number of entries5

The formula

Row n of Pascal’s triangle is the list of binomial coefficients n choose 0, n choose 1, up to n choose n. Each entry equals the sum of the two entries above it, and the whole row sums to 2 to the power n.

Worked example

Row 4 is 1, 4, 6, 4, 1. These add to 16, which is 2 to the power 4, and they are the coefficients of (a + b) to the fourth. Enter 4 to confirm.

Frequently asked questions

How is Pascal’s triangle built?

Start each row with 1, and every inner number is the sum of the two numbers above it. The ends are always 1.

What is row n?

The binomial coefficients n choose 0 through n choose n, the coefficients of (a + b) to the n.

Why does each row sum to a power of 2?

Because the sum of n choose k over all k equals 2 to the n, the number of subsets of an n element set.

Who this calculator is for

This calculator is for algebra students and anyone needing a quick, reliable result.

What this calculator assumes

You enter valid numbers.
The standard method is applied.
Results are rounded for display.

Formula and sources

Related calculators

Quadratic Formula Calculator: solve a quadratic.
Scientific Calculator: general maths.
Matrix Calculator: matrix operations.

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