Vector Components Calculator

About this calculator

Resolving a vector into its x and y components means splitting a single magnitude-and-angle description into two perpendicular pieces: horizontal (x = magnitude × cos θ) and vertical (y = magnitude × sin θ). This is the standard first step in nearly every mechanics problem, because forces, velocities and displacements are far easier to add together axis by axis than at arbitrary angles.

Physics students use component resolution to solve projectile motion, inclined-plane friction problems and equilibrium questions where several forces act at different angles — you cannot simply add two forces of 10 N and 15 N unless they point the same way, but you can always add their x-components together and their y-components together. Engineers rely on the same decomposition when analyzing truss loads, wind forces on a structure, or thrust vectors in aerospace design, and the reverse operation (recombining x and y back into magnitude and angle via the Pythagorean theorem and arctangent) is just as common.

Enter a vector’s magnitude and its angle from the x-axis, and this calculator returns the exact x and y components along with the angle’s quadrant, so you can move straight to the next step of your problem.