Cross Product Calculator
Enter two vectors with three components each.
This result is an estimate only. Double-check important figures before relying on them.
How it is calculated
- x = a₂b₃ − a₃b₂
- y = a₃b₁ − a₁b₃
- z = a₁b₂ − a₂b₁
- Magnitude = √(x² + y² + z²)
For a number rather than a vector, use the dot product calculator.
Worked example
A = (1, 2, 3) and B = (4, 5, 6):
- A × B = (−3, 6, −3)
- Magnitude = 7.3485, the area of the parallelogram
Why your number may differ
The cross product exists only in 3D (and 7D). If your vectors have two components, add a 0 as the z value.
Frequently asked questions
What is the cross product?
For two 3D vectors, it is a new vector perpendicular to both, with a length equal to the area of the parallelogram they form.
What is the formula?
A × B = (a₂b₃ − a₃b₂, a₃b₁ − a₁b₃, a₁b₂ − a₂b₁).
Does the order matter?
Yes. B × A is the opposite of A × B, pointing the other way.