Vector Magnitude Calculator

Calculate the magnitude (length) of a vector. Free online vector magnitude calculator for 2D and 3D vectors.

The Vector Magnitude Calculator finds the length of a vector in 2D, 3D, or higher dimensions. Using the formula |v| = √(x² + y² + z² + ...), this tool computes the Euclidean norm of any vector. Essential for physics (force, velocity), computer graphics, and any application involving vector quantities.

Common use cases

  • Physics force and velocity magnitudes
  • Distance calculations in coordinate systems
  • Normalizing vectors for graphics
  • Machine learning feature scaling
  • Signal strength calculations

How to use

  1. Select the number of dimensions
  2. Enter the vector components
  3. Click calculate for magnitude
  4. View the squared sum and root
  5. Use for unit vector calculation

FAQ

What is vector magnitude?

The length or norm of a vector. For v = (x, y, z), |v| = √(x² + y² + z²).

Is this the same as distance?

Yes, the magnitude of a position vector from origin equals the distance from origin to that point.

What is a unit vector?

A vector with magnitude 1. To normalize, divide each component by the magnitude: û = v/|v|.

What about higher dimensions?

The formula extends: |v| = √(v₁² + v₂² + ... + vₙ²) for n dimensions.