# Subset Calculator

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

> The subset calculator counts the subsets and proper subsets of a set, the number of subsets of a given size, and lists all subsets for small sets.

## Inputs

- Enter
- Set elements (separate with commas)
- Number of elements n
- Subset size k

## Results

- Number of subsets
- Number of proper subsets
- Subsets with k elements
- All subsets

## Formula

```
Subsets = 2ⁿ,  proper subsets = 2ⁿ − 1,  k-element subsets = C(n, k)
```

## Explanation

A subset contains some (or none, or all) of the elements of a set. Counting subsets answers questions like "how many pizza topping combinations are there?" – with 8 toppings, 256, including the plain pizza.

### How to use the Subset Calculator

- **Enter**
- **Set elements (separate with commas)**
- **Number of elements n**
- **Subset size k**

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

### How it works

Enter the elements, or just the number of elements for large sets. Proper subsets exclude the set itself; the number of subsets of size k is the binomial coefficient.

## Worked example

Inputs — Enter: Set elements; Set elements (separate with commas): 1, 2, 3, 4; Subset size k: 2.

Results — **Number of subsets = 16**; Number of proper subsets = 15; Subsets with k elements = 6; All subsets = ∅, {1}, {2}, {3}, {4}, {1, 2}, {1, 3}, {2, 3}, {1, 4}, {2, 4}, {3, 4}, {1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}, {1, 2, 3, 4}.

## Key terms

- **Subset**: A set whose elements all belong to another set.

## FAQ

**What is a proper subset?**
A subset that is not equal to the original set.

**How many subsets does {1, 2, 3} have?**
8: ∅, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}.

**Is every set a subset of itself?**
Yes, but not a proper subset.

**How many 2-element subsets does a 10-element set have?**
C(10, 2) = 45.


## Sources

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