What is a Cartesian product?

Given sets A and B, A × B is the set of all ordered pairs (a, b) with a ∈ A and b ∈ B. For three sets A × B × C it extends to ordered triples (a, b, c), and so on.

How many results will I get?

The result size equals |A| × |B| × … (the product of the sizes of every set). Two sets with 3 and 4 elements produce 12 tuples.

Are duplicate elements in a set removed?

Yes. Each set is de-duplicated before computing the product, so repeated elements count only once.

Is the result a set (no duplicate tuples)?

Yes. Because each set is de-duplicated first, every output tuple is unique.

What is the maximum number of sets?

This tool supports up to 4 sets. To keep the browser responsive, the total result count is capped at 10,000 tuples.

Cartesian Product Calculator

Enter two or more sets and instantly see every ordered tuple in their Cartesian product.

Define Sets

Define your sets and click Compute to see all ordered tuples.

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Summary

The Cartesian product A × B of two sets is the set of all ordered pairs (a, b) where a belongs to A and b belongs to B. This tool extends that to up to four sets, computing every possible ordered tuple instantly in your browser.

How it works

Enter elements of each set separated by commas (e.g. 1, 2, 3).
Add up to four sets using the "+ Add Set" button.
Click "Compute" to generate all ordered tuples.
The result table lists every combination with tuple notation.
Copy the full result as text or as a JSON array.

Use cases

Generate all possible combinations of two or more finite sets.
Enumerate test case inputs when each parameter has a fixed set of values.
Illustrate Cartesian product concepts in discrete math coursework.
Build a truth table skeleton by crossing boolean sets.
Explore sample spaces in probability problems.
Map every (row, column) coordinate pair in a grid.

Frequently Asked Questions

Last updated: 2026-06-11 · Reviewed by Nham Vu