Cross Product Calculator
Cross product of 2-D or 3-D vectors, with exact fractions and the working.
Change the values and press Calculate to work out your own figures.
Enter the vector components (leave z blank for 2-D).
Show the working
- 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)
How to use it
Enter the vector components (leave z blank for 2-D).
Enter coordinates as whole numbers, decimals or fractions (3/4). Show the working gives the formula with your numbers.
Key facts
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)
Components
Enter the x-, y- and (optionally) z-components; leave z blank for vectors in a plane.
Questions
How is the cross product worked out?
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)
Can I use fractions?
Yes, such as 1/2 or -3/4.
Formulas
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)
Sources
Limitations
- Vectors have two or three components (leave z blank for 2-D).
- Earth distances assume the WGS 84 ellipsoid (sea level).