Vector Magnitude Calculator
Calculate the magnitude (length) and unit vector of a 2D or 3D vector.
Magnitude
5.000000
Unit X0.600000
Unit Y0.800000
Unit Z0.000000
Direction Deg53.1301 deg
Vector Magnitude
Formula
For 2D vectors (z = 0): A unit vector has magnitude 1 and points in the same direction: v_hat = v /v = sqrt(x² + y² + z²) v = sqrt(x² + y²) Unit Vector
v = (x/ v , y/ v , z/ v
Direction (2D)
The angle from the positive x-axis: theta = arctan(y/x)
Example Calculation
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°
Frequently Asked Questions
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