# Set Calculator - Union, Intersection, Difference and Symmetric Difference

> Free online set calculator: union, intersection, differences and symmetric difference of two groups, with subset and disjoint checks and Jaccard similarity.

- URL: https://qilingtools.com/en/math/set
- Category: Math Tools (https://qilingtools.com/en/math)
- Tags: [Math](https://qilingtools.com/en/tags/math), [Education](https://qilingtools.com/en/tags/education), [Algorithms](https://qilingtools.com/en/tags/algorithm)
- Last updated: 2026-10-26
- Price: Free, no sign-up
- Privacy: Runs locally in the browser; files are never uploaded

Paste two groups of elements — numbers or words — to get the union, intersection, A−B, B−A and the symmetric difference, together with subset, superset, equality and disjoint checks, the Jaccard similarity, the power set size and the size of the Cartesian product. Duplicates are removed automatically.

## How to use

1. Enter the elements of set A and set B in the two boxes
2. Separate elements with spaces, commas or line breaks
3. Read the results and choose whether to sort them numerically

## Features

- Union, intersection, both differences and the symmetric difference at once
- Subset, superset, equality and disjoint checks
- Jaccard similarity to measure the overlap
- Power set size 2^|A| as an exact big integer, and the Cartesian product size
- Duplicates removed, with a note saying how many

## FAQ

### What is the difference A−B?

The elements of A that are not in B. A−B and B−A are generally different, so both are listed.

### What is the symmetric difference?

A △ B holds the elements in exactly one of the sets: (A−B) ∪ (B−A), equivalently the union minus the intersection.

### Why are there fewer elements than I typed?

Sets contain no duplicates, so repeated entries are merged — the tool tells you how many were removed.

### What does the Jaccard similarity mean?

The size of the intersection divided by the size of the union, from 0 to 1. It measures how similar two sets are and is widely used in text and data deduplication.

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