This vector calculator normalizes 2D and 3D vectors and solves both positive and negative solutions for a missing component at a target magnitude.
Math
Unit Vector Calculator
Normalize 2D and 3D vectors or solve both signs of a missing component.
Calculator
About this calculator
Formula notes
magnitude = sqrt(x^2 + y^2 + z^2); unit components are each component divided by the magnitude; missing component = +/-sqrt(target^2 - known^2).
Worked examples
- Example: normalizing (3, 4) gives a magnitude of 5 and a unit vector of (0.6, 0.8).
- Normalizing (6, 8) gives magnitude 10 and unit vector (0.6, 0.8).
How to use it
- Choose normalize or find a missing component.
- Choose 2D or 3D and enter the vector components.
- Read the magnitude, unit vector, and direction angle or the missing-component solutions.
Frequently asked questions
Can a zero vector be normalized?
No. A vector with zero magnitude has no defined direction and is rejected.
What if the known components exceed the target magnitude?
The missing-component mode rejects the input because the radicand would be negative.
Limits and interpretation
- The calculator uses exact Euclidean magnitude; floating-point rounding may produce tiny trailing differences.
- A zero vector cannot be normalized and is rejected.