Magnitudes, dot product, cross product vector, and angle between two 3D vectors.. 3D Vector Calculator is a free online tool from the ToolsRift Math Calculators collection. It runs entirely in your browser — nothing to install, no signup, and your data never leaves your device.
Enter the x, y and z components of both vectors and the calculator returns magnitudes, dot product, cross product and the angle.
The cross product is a vector: (y₁z₂−z₁y₂, z₁x₂−x₁z₂, x₁y₂−y₁x₂), perpendicular to both inputs.
It measures alignment: positive means a similar direction, zero means perpendicular, negative means opposite directions.
θ = arccos((a · b) / (|a| |b|)), using the dot product and both magnitudes.