Power Set Calculator

About this calculator

The power set of a set with n elements is the collection of all its possible subsets, including the empty set and the set itself, and its size is always exactly 2 raised to the power of n — a result that follows because each of the n elements independently can either be included in a given subset or excluded from it, giving two choices per element. The count of proper subsets, which excludes the full set itself, is one less: 2^n − 1.

This result is foundational in set theory and combinatorics, and it shows up constantly in computer science: algorithms that enumerate all subsets of a set of items (as in brute-force solutions to the knapsack or subset-sum problems) commonly use a bitmask from 0 to 2^n − 1, where each bit represents whether one element is included.

Enter the number of elements n in your set, and this calculator returns the total number of subsets and the number of proper subsets.