Moment formula
A moment is the turning effect of a force about a point, equal to the force times its perpendicular distance from that point. It is the foundation of statics, beam analysis, and anything that pivots, balances, or bends.
Variables
| M | Moment (turning effect) | N·m or lb·ft |
| F | Applied force | N or lb |
| d | Perpendicular distance (lever arm) | m or ft |
Rearranged
d = M / F
Worked example
A force of 200 N acts at the end of a lever 0.5 m from the pivot.
Multiply force by the lever arm: 200 × 0.5 = 100.
Only the perpendicular distance counts, so a force pointing straight at the pivot creates no moment. In equilibrium the moments about any point sum to zero, which is the rule used to find support reactions and to size beams.
Working on a beam or a shaft?
See the Bending Stress Formula for beams, or the Torque Formula for shafts.
Moments and equilibrium
A body is in balance only when the moments about every point cancel out. Setting the sum of moments to zero, alongside the sum of forces, lets you solve for unknown support reactions on a beam or frame. This single principle, the lever turned into an equation, underlies almost all structural statics.
Moment vs torque
Moment and torque are the same quantity, force times distance, but the words are used in different settings. Moment usually describes bending or balancing about a point, as in a beam. Torque usually describes twisting about an axis, as in a shaft or a bolt. The formula and units are identical.
FAQ
What is the formula for a moment?
Moment equals force times the perpendicular distance from the pivot, M = F times d, in newton-metres or pound-feet.
Why does only perpendicular distance count?
Only the component of the force at right angles to the lever arm creates rotation. A force aimed through the pivot has no perpendicular distance and no turning effect.
What is the difference between moment and torque?
They are the same product of force and distance. Moment usually refers to bending about a point, torque to twisting about an axis.