Cross Product Calculator
Calculate the cross product of two 3D vectors, which is perpendicular to both.
The magnitude is an area
|a × b| equals the area of the parallelogram the two vectors span, and half of it is the triangle they form — which is the most practical way to get the area of a triangle from three points in 3D space. The direction follows the right-hand rule, and reversing the operands reverses the result.
The formula
a × b = (a_y b_z − a_z b_y, a_z b_x − a_x b_z, a_x b_y − a_y b_x)
Every result on this page comes from this formula. Nothing is rounded until the final display, so figures match a spreadsheet to the cent.
How to use the Cross Product Calculator
- Fill in each field with your own figures — the defaults are only there as an example.
- The result updates as you type, so there is no button to press.
- Check the breakdown under the main result for the supporting numbers.
- Use the copy button to take the result with you, or share the link to reload the same inputs.
Cross Product Calculator — frequently asked questions
Is this cross product calculator free to use?
Yes. Every calculator on the site is free, needs no sign-up, and runs entirely in your browser, so your figures never leave your device.
How accurate is the result?
The maths is exact for the formula shown on the page. Accuracy in the real world depends on your inputs and on assumptions the formula cannot see, so treat the output as a well-grounded estimate rather than a quote.
Can I use it on my phone?
Yes. The page is responsive, weighs a few kilobytes and works offline once loaded, so it behaves the same on a phone as on a desktop.
What people search for
This page answers each of these searches. They are the exact phrases visitors use to find the cross product calculator.
- cross product calculator
About this calculator
Written and reviewed by The Samsung Calculator editorial team. Every calculator is written against a published formula, reviewed against at least one independent reference implementation, and dated when it changes.
Last reviewed August 23, 2026 · Calculation runs client-side · No data collected · Report an error