Moment Calculator
Calculate force moments, couple moments, and resultant moments
Inputs
Formula Explanation
Formula ① — Force Moment (General)
The moment equals force multiplied by arm and sin of the angle . The arm is the distance from the rotation centre to the force's line of action.
Formula ② — Force Moment (θ = 90°)
When the force is perpendicular to the arm, sin 90° = 1 and the formula simplifies to .
Formula ③ — Couple Moment
A couple consists of two equal, opposite, parallel forces. Its moment equals one force times the couple arm (distance between the lines of action).
Formula ④ — Resultant Moment
The resultant moment is the algebraic sum of all individual moments. CCW moments are positive; CW moments are negative.
Key Concepts
Moment
A moment (or torque) is the tendency of a force to cause rotation about a point. Its magnitude equals the force times the perpendicular distance from the rotation centre to the line of action.
Sign Convention
Counterclockwise (CCW) moments are taken as positive (+); clockwise (CW) moments are negative (−). If the net moment is zero, the body remains stationary.
Couple
A couple is a pair of forces equal in magnitude, opposite in direction, and not sharing the same line of action. Its moment is independent of the chosen rotation centre.
Moment Equilibrium
For a body to be in rotational equilibrium, the sum of all moments about any point must equal zero: = 0.
Worked Example
A beam has two 83 N forces separated by . Find the couple moment.
Couple arm
Apply formula ③
The couple moment is (counterclockwise, positive).
Further Reading
Structural Analysis
Moment calculations are fundamental in determining bending moments in beams, frames, and trusses — the basis of structural design.
Steering Wheel
The car steering wheel applies a couple: two equal and opposite hand forces create a pure moment without net force on the column.
Torque Wrenches
A torque wrench measures the applied moment directly in N·m or lbf·ft, ensuring bolts are tightened to specification.
Equilibrium Design
Engineers use moment summation (ΣM = 0) alongside force equilibrium to solve for unknown reactions at beam supports.