2D Vector Calculator

About this calculator

This calculator finds a 2D vector's magnitude, |v| = √(x² + y²) (from the Pythagorean theorem), and its direction angle, θ = arctan(y/x) (adjusted for the correct quadrant), given its x and y components. Together, magnitude and angle describe the same vector in polar form instead of Cartesian form — the two representations are mathematically interchangeable.

Physics and engineering students use this to convert between component and polar notation for forces, velocities and displacements, and it's a basic building block in computer graphics, robotics and game development for representing direction and speed. Enter the x and y components to get the magnitude and angle.