Vector Magnitude & Direction Calculator

How to calculate vector magnitude and direction?

Magnitude is found using the Pythagorean theorem, while the direction angle is calculated using the inverse tangent of the components.

Formula: Magnitude = √(x² + y²) | Angle (θ) = tan⁻¹(y/x)

Using the Vector calculator: an example

Example: A vector with an X-Component of 3 and a Y-Component of 4.

Step-by-step calculation:

• Square the components: 3² = 9 and 4² = 16
• Add them and take the square root: √(9 + 16) = 5 (Magnitude)
• Calculate the angle: tan⁻¹(4/3) ≈ 53.13° (Direction)

Frequently Asked Questions

What coordinate system is used?

This calculator uses the standard Cartesian coordinate system where 0° is the positive x-axis.

How are quadrants handled?

The calculator uses the atan2 function to ensure the angle correctly identifies the vector's quadrant (0° to 360°).