Cross Product Calculator

This Cross Product Calculator helps you find the cross product of two 3D vectors quickly and easily. The cross product is a vector that is perpendicular to both input vectors and is commonly used in physics, engineering, and 3D graphics.

How to Use the Calculator

• Enter each vector as 3 comma-separated numbers (e.g. 1, 2, 3).

• Click the “Calculate Cross Product” button.

• The result will display the resulting 3D vector.

Formula Used:

Let the two vectors be:

$$\vec{A} = [a_1, a_2, a_3], \quad \vec{B} = [b_1, b_2, b_3]$$

Then the cross product $\vec{A}\times \stackrel{}{B}$ is:

$$\vec{A}\times \vec{B}=\left[\begin{array}{c}{a}_2{b}_3-a_3{b}_2,\\ a_3{b}_1-a_1{b}_3,\\ a_1{b}_2-a_2{b}_1\end{array}\right]$$

Example:

Input:

$$\vec{A} = [1, 2, 3], \quad \vec{B} = [4, 5, 6]$$

Solution:

$$\vec{A}\times \vec{B}=\left[\begin{array}{c}(2)(6)-(3)(5),\\ (3)(4)-(1)(6),\\ (1)(5)-(2)(4)\end{array}\right]=\left[\begin{array}{c}-3,6,-3\end{array}\right]$$