Vector Magnitude Calculator
Calculate vector magnitude, unit vectors, and angles with coordinate axes
Magnitude Formulas
2D Vector
|v| = √(x² + y²)
For a 2D vector v = <x, y>, the magnitude is the square root of the sum of squared components.
3D Vector
|v| = √(x² + y² + z²)
For a 3D vector v = <x, y, z>, the magnitude extends the 2D formula with an additional z-component.
Unit Vector
û = v/|v|
The unit vector has magnitude 1 and points in the same direction as the original vector. It's calculated by dividing each component by the vector's magnitude.
Applications
Physics
- Force and velocity calculations
- Momentum and acceleration
- Electric and magnetic fields
- Wave propagation
Engineering
- Structural analysis
- Fluid dynamics
- Computer graphics
- Robotics and navigation
What is Vector Magnitude?
Vector magnitude (or length) represents the size or length of a vector in space. It's calculated using the Pythagorean theorem extended to multiple dimensions and is essential for understanding the scale of vector quantities in physics and engineering.