Power Set Calculator

Generate the power set of a set and review every subset in a clean visual layout.

Last updated: March 2026 | By ForgeCalc Engineering

Power Set Solver

Subset generation

Enter Set Elements

Set Info

Total Subsets: 8

1.Original set: {a, b, c}

2.Number of elements: 3

3.Number of subsets: 2^3 = 8

4.Power set contains the empty set and every subset of the original set.

Subsets

Empty Set

{ a }

{ b }

{ a, b }

{ c }

{ a, c }

{ b, c }

{ a, b, c }

What a Power Set Means

The power set of a set is the set of all possible subsets, including the empty set and the set itself.

How to Generate a Power Set

List the elements of the set.
Start with the empty set.
For each element, duplicate the current subsets and add the new element.
Continue until every subset is included.

|P(S)| = 2^n

Worked Example

Example: The power set of {a, b} has 4 subsets.

Empty set, {a}, {b}, {a, b}

Frequently Asked Questions

Does the order of elements matter?

The order of listing does not change the set of subsets.

Why limit the size?

Power sets grow exponentially, so large sets become expensive to render.

Does this include the empty set?

Yes. The empty set is always included.

What is the size of the power set?

If the original set has n elements, the power set has 2^n subsets.

Related Tools

Set Builder Calculator

Set builder notation.

Subset Calculator

Find subsets of sets.

Sum Of Products Calculator

Boolean sum of products.

Truth Table Generator

Generate truth tables.

Union Intersection Calculator

Set operations.

Venn Diagram Calculator

Visualize set relationships.

Browse all Math Tools →