Bell Number Calculator

The Bell Number Calculator is a free online tool for finding out the number of ways to divide a set into subsets.

Bell Number Calculator

B_n = ?

Calculate Reset

What is a Bell number?

Bell number is the number of ways a set of n numbers can be partitioned into subsets.

Bell number is indicated as B_n, where n is the integer for which the number of subsets is calculated.

For example

B₀ = 1 because empty set only one subset can be created.

B₁ = 1 as only one subset can be created for a single integer.

B₂ = 2 as 2 partitions can be created for 2 integers.

The bell number for set of integers {3, 4} is 2. The subsets are {{3}, {4}} and {3,4}.

First 20 Bell numbers

B₀ = 1
B₁ = 1
B₂ = 2
B₃ = 5
B₄ = 15
B₅ = 52
B₆ = 203
B₇ = 877
B₈ = 4140
B₉ = 21147
B₁₀ = 115975
B₁₁ = 678570
B₁₂ = 4213597
B₁₃ = 27644437
B₁₄ = 190899322
B₁₅ = 1382958545
B₁₆ = 10480142147
B₁₇ = 82864869804
B₁₈ = 682076806159
B₁₉ = 5832742205057

How to use the Bell number calculator

The procedure to use the Bell number calculator is as follows:

1Please enter an integer n between 0-100.
2Click the Calculate button to calculate the number of ways to divide into subsets.
3Click the Reset button to start a new calculation.

Solved examples using the Bell number calculator

Example 1: How many ways of Bell number 8?

Enter 8 into the input box and click Calculate button, as shown in the figure, there are 4140 ways to divide a set of 8 numbers into subsets.

B₈ = 4140

Example 2: How many ways are there to divide a set of 50 numbers into subsets?

Enter 50 into the input box and click Calculate button, as shown in the figure, there are 185724268771078270438257767181908917499221852770 ways to subset a set of 50 numbers.

B₅₀ = 185724268771078270438257767181908917499221852770

How many ways are there to divide a set of 50 numbers into subsets

Bell Number Calculator