Calculate the magnitude (length, norm) of a vector in 2D or 3D space. Enter coordinates to find the distance from origin to the point.

Magnitude: 5.00

Formula: |v| = √(x² + y² + z²). The magnitude represents the distance from the origin (0,0,0) to the point (x,y,z).

What is Vector Magnitude?

The magnitude (or norm, length) of a vector is the distance from the origin to the point represented by the vector in Euclidean space. It is a measure of the vector's size or length, regardless of its direction.

|v| = √(x² + y² + z²)

For a 2D vector v = (x, y), the magnitude is √(x² + y²). For a 3D vector v = (x, y, z), the magnitude is √(x² + y² + z²).

Key applications of vector magnitude:

• Physics — calculating speed, force, and acceleration magnitudes
• Engineering — stress analysis, displacement calculations
• Computer graphics — determining distances between points and scaling
• Mathematics — vector operations, normalization

The unit vector (or direction vector) is obtained by dividing each coordinate by the magnitude, giving a vector of length 1 in the same direction.

How to Use This Calculator

1. Select dimension: Choose between 2D (x, y) or 3D (x, y, z) vector space.
2. Enter coordinates: Input the x, y (and z if 3D) coordinates of your vector.
3. Calculate: Click the “Calculate Magnitude” button or press Enter.
4. Reset: Use the “Reset” button to restore default values (x=3, y=4, 2D).
5. Interpretation: The result shows the magnitude (length) and the unit vector (direction). For example, vector (3, 4) has magnitude 5 and unit vector (0.6, 0.8).