Vector Magnitude Calculator (3D)

Enter the x, y and z components of a vector to calculate its magnitude (length).

Vector Magnitude Calculator (3D)

Calculate the magnitude (length) of a 3D or 2D vector from its components.

This calculator provides an estimate for general informational purposes only. It is not a substitute for professional financial, mechanical or engineering advice.

A vector's magnitude is found by applying the Pythagorean theorem to its components — squaring each one, summing them, and taking the square root.

Example

  • With the default values shown above, this calculator returns: Vector Magnitude ≈ 13.00.

Frequently Asked Questions

What is the formula?

Magnitude = √(x² + y² + z²), a direct extension of the Pythagorean theorem into three dimensions.

What if I have a 2D vector?

Enter 0 for the z-component, and the formula reduces to the standard 2D magnitude, √(x² + y²).

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3D Vector Dot Product CalculatorCalculate the dot product of two 3D vectors from their x, y and z components.Vector Cross Product Calculator (3D)Calculate the cross product of two 3D vectors, producing a new vector perpendicular to both.3D Distance CalculatorCalculate the straight-line distance between two points in 3D space.
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