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Catalan Number from n Calculator

C_n = (2n)! / ((n+1)! · n!) — counts many combinatorial objects.

Compute the n-th Catalan number C_n = (2n)! / ((n+1)! · n!). C_n counts non-crossing handshakes of 2n people, balanced parenthesisations of n+1 factors, monotonic lattice paths, and triangulations of a convex (n+2)-gon.

Daniel Oh By Daniel Oh
Published Last reviewed 1 min read

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How to use this calculator

  1. Fill in the inputs above using the units you already have.
  2. Values update automatically as you type — no submit button needed.
  3. Hover any result row for the underlying formula and intermediate values.

Formula

C_n = (2n)! / ((n+1)! · n!)

In depth

Compute the n-th Catalan number C_n = (2n)! / ((n+1)! · n!). C_n counts non-crossing handshakes of 2n people, balanced parenthesisations of n+1 factors, monotonic lattice paths, and triangulations of a convex (n+2)-gon.