Vector Components Calculator

About this calculator

Any two-dimensional vector can be broken down into its horizontal (x) and vertical (y) components using basic trigonometry: given a magnitude |V| and a direction angle θ measured from the positive x-axis, the components are Vₓ = |V| × cos(θ) and Vᵨ = |V| × sin(θ). This decomposition is the foundation of vector algebra, since components in the same direction can be added or subtracted directly, unlike vectors at arbitrary angles.

Resolving vectors into components is a core skill in physics coursework covering forces, velocity, and projectile motion, as well as engineering fields like structural analysis and mechanics, where a single force or displacement at an angle needs to be split along perpendicular axes before it can be combined with other forces or used in equilibrium equations.

This calculator takes a vector's magnitude and angle and instantly returns its x and y components, saving physics and engineering students from working through the trigonometry by hand on every homework problem.