Calculator · Engineering Mechanics
Moment of a Force Calculator
The moment of a planar force about a point: M = r × F = rx·Fy − ry·Fx, positive counter-clockwise.
Force
x and y are the point of application P. Use the Statics Lab for several forces at once.
Moment centre O
Diagram
Results
Moment about O
Counter-clockwise (positive).
| Position vector r = P − O | (2, 0) m |
|---|---|
| |r| | 2 m |
| Force components | (0, 500) N |
| M_O = rx·Fy − ry·Fx | 1000 N·m |
| Sense | Counter-clockwise (positive) |
| Perpendicular lever arm d = |M| / |F| | 2 m |
Technical reference
M_O = r × F (vector form)
M_O = rx·Fy − ry·Fx (planar scalar form used here)
|M_O| = |F| · d_perp, d_perp = |M_O| / |F|
- r
- position vector from O to the point of application, r = P − O[m]
- F
- applied force[N]
- M_O
- scalar moment about O (out-of-plane z-component)[N·m]
- d_perp
- perpendicular lever arm from O to the line of action[m]
In the plane, the vector cross product r × F reduces to the single scalar rx·Fy − ry·Fx; that is exactly what this tool evaluates. The physical torque tendency it represents is the same quantity.
M_O is signed: its sign carries the sense of rotation, counter-clockwise positive. The lever-arm relation is a magnitude relation, |M_O| = |F|·d_perp, since d_perp is a non-negative distance and carries no sense.
d_perp = |M_O| / |F| is undefined for a zero force, since there is then no line of action to measure a distance from.
Assumptions
- · Planar problem: the moment is the scalar z-component of r × F.
- · Positive moment is counter-clockwise, the same convention as every Mechanics tool here.
- · The moment depends on the chosen centre O; the force itself does not.
- · A zero force gives no lever arm, which is reported as not defined rather than as 0 m.
Continue
Add more forces, supports and an equilibrium solve around the same point.
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