How to Use the 3D Vector Calculator
This calculator takes two 3D vectors and instantly returns the four values used most often in vector math. The dot product is a scalar that tells you how much two vectors point in the same direction — it's used to calculate work in physics and to check whether two vectors are perpendicular.
The cross product produces a new vector that is perpendicular to both input vectors, and its magnitude equals the area of the parallelogram the two vectors form. It's widely used to find surface normals in 3D graphics and to compute torque in physics.
The magnitude of a vector is its Euclidean distance from the origin, and the angle is derived by inverting the dot-product formula and converting the result from radians to degrees. Just enter the x, y, z components — as long as neither vector is the zero vector (0,0,0), you'll get instant results. This tool is handy for quickly verifying vector math in game development, 3D modeling, physics simulations, and robotics.
Frequently Asked Questions
The cross product follows the right-hand rule. If you curl the fingers of your right hand from vector A toward vector B, your thumb points in the direction of the cross product, which is always perpendicular to the plane containing both vectors.
A dot product of zero means the two vectors are perpendicular (90 degrees) to each other. If the dot product equals the product of the two magnitudes, the vectors point in the same direction (0 degrees).