Unit Vector Calculator
Normalize a nonzero 2D or 3D vector and find its magnitude. Use z = 0 for 2D.
Formula
|v| = √(x²+y²+z²); u = v/|v|.
Unit x ≈ (0.75)÷(1.25) · Unit y ≈ (1)÷(1.25) · Unit z ≈ (0)÷(1.25) · Original magnitude ≈ (4)×(1.25)
How to use
- Enter x, y and z components.
- Use a common unit for every component.
- Read the unit vector and original magnitude.
Examples
- (3,4,0) has magnitude 5 and unit vector (0.6,0.8,0).
Frequently asked questions
What is a unit vector?
It has length 1 and keeps the direction of the original vector.
Why is the zero vector rejected?
It has no unique direction and cannot be divided by its zero magnitude.
Do the outputs have units?
The unit vector is dimensionless. The magnitude keeps your input unit.
Sources
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