Bell Number Calculator

About this calculator

The nth Bell number Bₙ counts the number of ways to partition a set of n distinct elements into non-empty, unordered subsets. B₀=1, B₁=1, B₂=2, B₃=5, B₄=15, B₅=52 … and they grow via the Bell triangle, a Pascal's-triangle-like construction where each row is built from the last entry of the previous row plus running sums.

Bell numbers show up throughout combinatorics and computer science: counting equivalence relations on a set, the number of ways to group items (e.g. distributing distinct objects into unlabeled boxes), and in the analysis of set-partition problems used in database theory and combinatorial optimization. Discrete math students and researchers use this calculator to check partition counts without enumerating every partition by hand. Enter n to get Bₙ.