Pascal's Triangle Generator

Generate Pascal's triangle

Pascal's triangle is a triangular arrangement of numbers in which every entry is the sum of the two numbers directly above it, with ones running down both edges. This generator builds the triangle to as many rows as you choose. Each number is a binomial coefficient, the count of ways to choose a certain number of items from a set, so the triangle is a ready reference for combinations and for expanding expressions like one plus x raised to a power.

The tool uses exact big-integer arithmetic, so the large numbers deep in the triangle are shown precisely rather than being rounded, and it confirms that each row sums to a power of two.

Patterns and uses

Pascal's triangle is full of patterns. The rows give the coefficients of binomial expansions, the diagonals contain the counting numbers and triangular numbers, and the shallow diagonals sum to the Fibonacci sequence. It is widely used in probability, combinatorics and algebra, from working out the chance of a run of coin flips to expanding brackets quickly.

Students meet it when learning the binomial theorem, and it offers an intuitive way to see why combinations behave as they do. Generate up to thirty rows to explore the structure. All calculation runs locally in your browser.

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