Unit Vector Calculator

Calculate Normalized Vectors in 2D and 3D Space

Understanding Unit Vectors

A unit vector is a vector whose magnitude (length) is exactly 1 unit. Unit vectors are essential in mathematics and physics for describing directions without regard to magnitude.

How to Calculate a Unit Vector:

  1. Calculate the magnitude of the original vector using the formula: |v| = √(x² + y² + z²)
  2. Divide each component by the magnitude to get the unit vector components
  3. The resulting vector will have a magnitude of 1 while maintaining the original direction

Applications:

  • Physics: Describing force directions
  • Computer Graphics: Normalizing direction vectors
  • Navigation: Representing compass directions
  • 3D Modeling: Surface normal calculations