How to use this calculator
Enter each force’s magnitude and its angle measured counterclockwise from the positive x-axis. Leave force 3 at 0 to add just two.
Formulas
ComponentsFx = F cos θ Fy = F sin θ
ResultantR = √(ΣFx² + ΣFy²) θR = atan2(ΣFy, ΣFx)
Worked example
400 N at 30°, 250 N at 135° and 150 N at 250° (the default)
- Rx = 346.4 − 176.8 − 51.3 = 118.3 N.
- Ry = 200 + 176.8 − 141.0 = 235.8 N.
- R = √(118.3² + 235.8²) = 263.8 N at 63.4°.
Frequently asked questions
What is the equilibrant?
The single force that balances the others: the same magnitude as the resultant, pointing the opposite way. In statics, the forces on a body in equilibrium have a resultant of zero.
Why use atan2 instead of arctan?
arctan(Ry/Rx) cannot tell a vector pointing up-right from one pointing down-left. atan2 uses both signs to give the right quadrant.