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The power set of a set is the collection of every possible subset, including the empty set and the set itself. This tool lists every one of them for a set with up to 10 elements.
How it works
Each of the 2ⁿ possible subsets corresponds to one binary pattern of "include/exclude" decisions for the n elements — the tool walks through every such pattern (via simple bitmasking) to build the complete list.
- Enter set elements (comma-separated).
- Click Calculate to see your results.
Examples
A 2-element set
The power set of {a, b} is {∅, {a}, {b}, {a,b}} — 4 subsets in total.
A 3-element set
The power set of {1,2,3} has 2³=8 subsets, from ∅ up to {1,2,3} itself.
Who should use it
- Set theory and discrete mathematics coursework.
- Combinatorics problems that require enumerating all possible subsets.
Industry applications
- Computer science education (combinatorics, algorithms)
- Discrete mathematics
Advantages
- Enumerates every subset explicitly, not just the count.
- Handles sets up to 10 elements (1024 subsets) instantly.
Limitations
- Capped at 10 elements to keep the subset list readable (2¹⁰=1024 is already a lot to display).
Common mistakes to avoid
- Forgetting to include the empty set or the full set itself when listing a power set by hand.
Best practices
- For larger sets, count subsets by size first (using combinations) as a sanity check that you haven't missed any in the full enumeration.
Tips
- The number of subsets of size k specifically is given by "n choose k" — the Subset Calculator on this site computes just those, if you don't need the full power set.