Catalan Number Calculator

About this calculator

This calculator finds the nth Catalan number: Cn = (2n)! / ((n+1)! · n!), a sequence (1, 1, 2, 5, 14, 42, 132, …) that counts a surprising number of unrelated-looking combinatorial structures of size n, including the number of ways to correctly match n pairs of balanced parentheses, the number of distinct binary search trees with n nodes, and the number of ways to triangulate a convex polygon with n+2 sides.

Computer science students and researchers use it to count valid expression trees, parsing possibilities, and recursive data structures, while math enthusiasts use it as a classic example of how one recurrence relation reappears across many different combinatorics problems. Enter n to get Cn.