Calculate the magnitude of a 2D or 3D vector with squared magnitude, unit vector, and direction angles.
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Dimension
What is vector magnitude?
The magnitude of a vector is its length in Euclidean space, calculated as the square root of the sum of its squared components.
Unit vectors
A unit vector points in the same direction but has a magnitude of exactly 1. It is found by dividing each component by the magnitude.
Result
The magnitude of vector [3, 4] is 5.
Steps
Components: x=3, y=4
Squared: x²=9 + y²=16
Sum of squares: 25
Magnitude: √25 = 5
Unit vector: [0.600000, 0.800000]
Direction angles: α=53.1301°, β=36.8699°
Also in Linear Algebra
Linear Algebra
A vector magnitude calculator computes the length (norm) of a 2D or 3D vector using the Euclidean distance formula. It also provides the unit vector and direction angles.
The magnitude of vector v = (x, y, z) is |v| = √(x² + y² + z²). For 2D vectors, omit the z component.
The unit vector is v/|v|, pointing in the same direction with magnitude 1. Direction angles give the angle to each coordinate axis.
|v| = √(x² + y² + z²)
Euclidean vector magnitude.
Frequently asked questions
No — magnitude is always non-negative. It is zero only for the zero vector.
For Euclidean vectors, magnitude and norm (specifically the L2 norm) are the same thing.
Related
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