Calculator · Engineering Mechanics
Resultant Force Calculator
Add coplanar forces as components or as magnitude and direction. The resultant is the plain vector sum; the resultant moment is reported about the point you choose.
Forces
Moment reference point O
The resultant force never depends on O. Only the resultant moment does.
Diagram
- Name
- R
- Magnitude
- 435.9 N
- Direction
- 23.41°
- Components
- (400, 173.2) N
- Application point
- (0, 0) m
Results
Resultant force
435.89 N
23.413°
| Rx = ΣFx | 400 N |
|---|---|
| Ry = ΣFy | 173.21 N |
| |R| | 435.89 N |
| Direction θ (CCW from +x) | 23.413° |
| M_O = ΣM about O | 0 N·m |
| Sense of M_O | Negligible |
| System | Single resultant force through the reference point |
Technical reference
Rx = ΣFx, Ry = ΣFy
|R| = √(Rx² + Ry²)
θ = atan2(Ry, Rx)
M_O = ΣM about the chosen point O
- Rx, Ry
- components of the vector sum of the forces[N]
- |R|
- resultant magnitude[N]
- θ
- resultant direction, counter-clockwise from +x[°]
- M_O
- resultant moment of the whole system about O[N·m]
θ is undefined, not 0°, when Rx = Ry = 0: a zero vector has no direction, and this tool reports that honestly rather than defaulting to an arbitrary angle.
R never depends on O. Moving the reference point changes only M_O, which combines with R to describe the same force system at a different point.
Assumptions
- · Coplanar force system in the x–y plane: +x right, +y up, moments positive counter-clockwise.
- · Forces are added as vectors; no rigid body, support or material behaviour is assumed.
- · A zero resultant has no direction, so θ is reported as not defined rather than as 0°.
- · The resultant moment is taken about the stated point O; moving O changes M_O but never R.
Continue
Open in Statics & Equilibrium Lab
The same forces, with supports and an equilibrium solve available.