Moment Calculator
Compute force moment M = F·l·sinθ or couple moment M = F·d, and the algebraic sum of several moments.
Inputs
Formula
M = F l sinθ; couple M = F d
Fundamentals
Moment measures a force's turning effect about a point/axis — the basis of static equilibrium.
$M=F\times d$, $F$ force, $d$ lever arm (perpendicular distance from pivot to line of action). CCW positive, CW negative; equilibrium needs zero net moment.
History
The moment (lever) goes back to Archimedes; Varignon's theorem (1687) framed statics.
Engineering applications
Used for wrenches, levers, balances and overturning checks of structures.
Glossary
| Moment $M$ | Force × lever arm, N·m. |
| Lever arm $d$ | Perpendicular distance pivot to force line. |
| Direction | CCW/CW sets the sign of the moment. |
How to use
- Fill in Type, Force F, Lever arm l, Angle θ, Couple arm d in the Inputs section (watch the unit on each field).
- Click Calculate; the tool evaluates the formula shown above.
- Read Moment M in the results area.
Formula notesMoment M = F·d (F force, d perpendicular distance from pivot to line of action).
Formula · Worked Example · Knowledge
Formula
The moment of a force about point O equals the force times the perpendicular distance (lever arm) from O to the line of action:
$$M=F\cdot l\cdot\sin\theta$$
$F$ = force (N), $l$ = lever arm (mm), $\theta$ = angle between force and arm. Couple moment:
$$M=F\cdot d$$
$d$ = couple arm. CCW moment is positive, CW negative; zero net moment means rotational equilibrium.
$$M=F\cdot l\cdot\sin\theta$$
$F$ = force (N), $l$ = lever arm (mm), $\theta$ = angle between force and arm. Couple moment:
$$M=F\cdot d$$
$d$ = couple arm. CCW moment is positive, CW negative; zero net moment means rotational equilibrium.
Worked Example
Force $F=100\ \text{N}$, lever arm $l=500\ \text{mm}$, perpendicular ($\theta=90^{\circ}$):
$$M=100\times500=50000\ \text{N·mm}=50\ \text{N·m}$$
As a couple, two forces $F=83\ \text{N}$, couple arm $d=2.40\ \text{m}=2400\ \text{mm}$:
$$M=83\times2400=199200\ \text{N·mm}\approx199\ \text{N·m}$$
$$M=100\times500=50000\ \text{N·mm}=50\ \text{N·m}$$
As a couple, two forces $F=83\ \text{N}$, couple arm $d=2.40\ \text{m}=2400\ \text{mm}$:
$$M=83\times2400=199200\ \text{N·mm}\approx199\ \text{N·m}$$
Key Points
- Moment measures the turning effect of a force; units N·m or N·mm.
- A couple moment is independent of the chosen center of moments.
- Equilibrium requires $\sum M=0$, used to find support reactions of statically determinate structures.
Parameters
Inputs
| Parameter | Symbol | Unit | Default |
|---|---|---|---|
| Type | mode | force | |
| Force F (N) | F | N | 100 |
| Lever arm l (mm) | l | mm | 500 |
| Angle θ (°) | theta | ° | 90 |
| Couple arm d (mm) | d | mm | 0 |
Outputs
| Result | Symbol | Unit |
|---|---|---|
| Moment M | M | N·mm |
Applications
- Simply-supported/cantilever reactions
- Structural equilibrium analysis
- Shear & moment distribution
FAQ
What formula does this tool use?
This tool computes per ISO / AGMA / ASME standard formulas: M = F l sinθ; couple M = F d
How accurate are the results?
Results match input precision, based on SI units and common engineering approximations; for critical duty re-check with a safety factor.
Where is it used?
Simply-supported/cantilever reactions