Vector Resolution into Components Calculator

About this calculator

Resolving a vector into components means breaking a single quantity that has both magnitude and direction — like a force, velocity, or displacement — into two perpendicular parts that add back up to the original vector. For a vector of magnitude V pointing at angle θ from the horizontal axis, the horizontal component is Vx = V·cos(θ) and the vertical component is Vy = V·sin(θ), derived directly from right-triangle trigonometry with the vector as the hypotenuse.

This is one of the most-used steps in physics and engineering because most real problems are easier to solve one axis at a time: summing horizontal and vertical forces separately in statics, finding the range of a projectile, or combining multiple velocity or force vectors that don’t point in the same direction. Physics students, engineers and anyone working with mechanics, ballistics, or navigation use component resolution to turn a diagonal vector into two independent, addable pieces.