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Vector Magnitude Calculator
Find the magnitude (length) of a 2D or 3D vector from its components.
x
y
z
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How it works
|v| = √(x² + y² + z²)
A vector’s magnitude is its length, found by the Pythagorean theorem extended to as many dimensions as it has. Dividing each component by the magnitude gives the unit vector — same direction, length 1.
Worked example
(3,4,0) has magnitude √(9+16) = 5.
Frequently asked questions
How do I do a 2D vector?
Leave z at 0; the formula reduces to √(x² + y²).
What is a unit vector for?
It captures pure direction, useful in physics and graphics where length is handled separately.
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This calculator is for educational purposes. Double-check important results before acting on them.