Math
Vector dot product
Compute the scalar dot product of two three-dimensional vectors.
Calculators / Math / Vector cross product
Vector cross product calculator
Calculate the components and magnitude of the cross product of two vectors.
On this page
Cross product x-3
Cross product y6
Cross product z-3
Cross product magnitude7.35
Calculator controls
How to calculate
Calculate the components and magnitude of the cross product of two vectors.
Cross product x = ay*bz-az*by; Cross product y = az*bx-ax*bz; Cross product z = ax*by-ay*bx; Cross product magnitude = sqrt((ay*bz-az*by)^2+(az*bx-ax*bz)^2+(ax*by-ay*bx)^2)
Worked example
Vector A x: 1; Vector A y: 2; Vector A z: 3; Vector B x: 4; Vector B y: 5; Vector B z: 6.
Cross product x: -3 ; Cross product y: 6 ; Cross product z: -3 ; Cross product magnitude: 7.35 .
Assumptions and limits
Uses a right-handed Cartesian basis and the order A × B. Reversing the order reverses the sign.
Results are rounded for display; calculations use unrounded values. Read our calculation methodology.
Understanding the result
Calculate the components and magnitude of the cross product of two vectors.
When this tool is useful
Cross product x = ay*bz-az*by; Cross product y = az*bx-ax*bz; Cross product z = ax*by-ay*bx; Cross product magnitude = sqrt((ay*bz-az*by)^2+(az*bx-ax*bz)^2+(ax*by-ay*bx)^2)
Understanding your inputs
| Input | What to enter |
|---|---|
| Vector A x | Enter a number of at least -1000000000000 and no more than 1000000000000. |
| Vector A y | Enter a number of at least -1000000000000 and no more than 1000000000000. |
| Vector A z | Enter a number of at least -1000000000000 and no more than 1000000000000. |
| Vector B x | Enter a number of at least -1000000000000 and no more than 1000000000000. |
| Vector B y | Enter a number of at least -1000000000000 and no more than 1000000000000. |
| Vector B z | Enter a number of at least -1000000000000 and no more than 1000000000000. |
Frequently asked questions
What assumptions does this calculation use?
Uses a right-handed Cartesian basis and the order A × B. Reversing the order reverses the sign.
How is the result calculated?
Cross product x = ay*bz-az*by; Cross product y = az*bx-ax*bz; Cross product z = ax*by-ay*bx; Cross product magnitude = sqrt((ay*bz-az*by)^2+(az*bx-ax*bz)^2+(ax*by-ay*bx)^2)