Quick guide
How to use this calculator
- Enter a nonzero vector.
- Inspect its exact squared magnitude.
- Read exact or explicitly approximate normalized components.
Calculation method
Divide by the magnitude
A unit vector in the direction of a is a/‖a‖. The zero vector is rejected because it has no direction.
Worked example
Normalize a 3–4 vector
The vector ⟨3,4⟩ has magnitude 5.
a/‖a‖ = ⟨3/5,4/5⟩
Supported inputs
Precision and limits
Vector size
General vectors may contain 2–8 components; three-dimensional products require exactly three.
Entry precision
Each signed decimal may contain up to 30 digits and 15 decimal places.
Square roots
Squared magnitudes remain exact. Irrational roots and normalized components are explicitly labelled approximations.