Force Composition

Compute resultant magnitude and direction of two concurrent forces P, Q at angle α using the parallelogram law (law of cosines).

Inputs

Formula

R = √(P² + Q² + 2PQ cosα); β = atan(Q·sinα/(P + Q cosα))
F₁F₂R
Force Composition schematic

How to use

  1. Fill in Force P, Force Q, Angle α in the Inputs section (watch the unit on each field).
  2. Click Calculate; the tool evaluates the formula shown above.
  3. Read Resultant R, Direction β in the results area.
Formula notesForce composition (angle θ): R = √(F₁²+F₂²+2·F₁·F₂·cosθ); angle tanφ = F₂·sinθ/(F₁+F₂·cosθ).