# Power Set Calculator

URL: https://speedycalculator.com/calculators/math/power-set/
Last updated: 2026-10-30

> The power set calculator lists every subset of a set of up to 10 elements, grouped by size, and counts them (2ⁿ in total).

## Inputs

- Set elements (separate with commas)

## Results

- Number of subsets
- All subsets
- Subsets by size
- Number of elements

## Formula

```
|P(S)| = 2ⁿ,  number of k-element subsets = C(n, k)
```

## Explanation

The power set of S is the set of all its subsets, including the empty set and S itself. Power sets appear in probability (events), logic, computer science (bit masks) and combinatorics.

### How to use the Power Set Calculator

- **Set elements (separate with commas)**

Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.

### How it works

Each element is either in or out of a subset, so n elements give 2ⁿ subsets. The calculator generates them with binary counting and sorts them by size.

## Worked example

Inputs — Set elements (separate with commas): a, b, c.

Results — **Number of subsets = 8**; All subsets = ∅, {a}, {b}, {c}, {a, b}, {a, c}, {b, c}, {a, b, c}; Subsets by size = 0 elements: 1
1 element: 3
2 elements: 3
3 elements: 1; Number of elements = 3.

## Key terms

- **Power set**: The set of all subsets of a set.
- **Cardinality**: The number of elements in a set.

## FAQ

**How many subsets does a set with 4 elements have?**
2⁴ = 16.

**Is the empty set a subset?**
Yes, of every set.

**What is the power set of the empty set?**
{∅} – it has one element.

**Why 2ⁿ?**
Each of the n elements can independently be in or out of a subset.


## Sources

- [OpenStax – Contemporary Mathematics](https://openstax.org/details/books/contemporary-mathematics)
- [Wolfram MathWorld – Power set](https://mathworld.wolfram.com/PowerSet.html)