Unit Vector Calculator
Enter a 2D or 3D vector to calculate its magnitude, normalized unit vector, direction angles, and verification instantly.
Vector components
Your result
Unit vector formulas
|v| = √(x² + y² + z²)
v̂ = v ÷ |v|
θ = cos⁻¹(component ÷ |v|)
Frequently asked questions
What is a unit vector?
A unit vector is a vector with magnitude 1. It is created by dividing every component of a non-zero vector by the vector's magnitude.
Can this calculator handle 2D and 3D vectors?
Yes. Leave the z component at zero for a 2D vector, or enter a non-zero z value for a 3D vector.
Why is the zero vector invalid?
The zero vector has magnitude 0, so dividing by its magnitude is undefined and no direction can be assigned.
Results are estimates generated locally in your browser using standard mathematical formulas. They are for informational and educational purposes only and are not a substitute for verification in coursework, examinations or professional contexts requiring certified accuracy. VisionVix accepts no liability for decisions based on this tool's output.
