Resultant of Two Forces Calculator

About this calculator

When two forces act on the same point at an angle to each other, their combined effect — the resultant — is found geometrically with the parallelogram law: place the two force vectors as adjacent sides of a parallelogram, and the diagonal from their common origin is the resultant. Algebraically, its magnitude comes from the law of cosines applied to that triangle: R = √(F1² + F2² + 2·F1·F2·cos θ), where θ is the angle between the two forces.

The resultant’s direction relative to one of the original forces is then found with the law of sines (or an equivalent tangent formula) using the same triangle. This is fundamental to statics and engineering mechanics — anywhere multiple forces (cables, struts, applied loads, wind and gravity) act on a single point and need to be reduced to one equivalent force for equilibrium or structural analysis. This calculator takes the two force magnitudes and the angle between them and returns the resultant magnitude and direction.