Vector Magnitude Calculator
Calculate the magnitude (length) and unit vector of a 2D or 3D vector.
Magnitude
5.000000
Formula
## Vector Magnitude ### Formula **|v| = sqrt(x² + y² + z²)** For 2D vectors (z = 0): **|v| = sqrt(x² + y²)** ### Unit Vector A unit vector has magnitude 1 and points in the same direction: **v_hat = v / |v| = (x/|v|, y/|v|, z/|v|)** ### Direction (2D) The angle from the positive x-axis: **theta = arctan(y/x)**
Exemplo Resolvido
Find the magnitude and unit vector of (3, 4, 0).
- 01|v| = √(9 + 16 + 0) = √25 = 5
- 02Unit vector = (3/5, 4/5, 0) = (0.6, 0.8, 0)
- 03Direction = arctan(4/3) ≈ 53.13°
Perguntas Frequentes
What is vector magnitude?
The magnitude (or length) of a vector is the distance from the origin to the point it represents. It is always non-negative.
What is a unit vector?
A unit vector has a magnitude of exactly 1. It indicates direction only. Any nonzero vector can be normalized to a unit vector by dividing by its magnitude.
How do I find the distance between two points?
Form a vector from one point to the other by subtracting coordinates, then find the magnitude. distance = √((x₂-x₁)² + (y₂-y₁)² + (z₂-z₁)²).
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