Enter a force (N), lever arm length (m), and an optional angle (°) to calculate the moment of force (torque) in Newton-meters. You can also solve for force or lever arm length by selecting what you want to calculate. The Moment of Force Calculator uses M = F × d × sin(θ) to find the turning effect of a force about a pivot point.
Result
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Moment of Force (N·m)
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Force (N)
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Lever Arm Length (m)
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Angle Used
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sin(θ)
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A moment of force (also called torque) is the turning effect produced when a force acts on an object about a pivot point or fulcrum. It measures how much a force tends to cause rotation. The greater the force or the longer the lever arm, the larger the moment.
The moment of force is calculated as M = F × d × sin(θ), where F is the applied force, d is the perpendicular distance (lever arm length) from the pivot to the line of action of the force, and θ is the angle between the force and the lever arm. When the force is perpendicular (θ = 90°), sin(θ) = 1 and the formula simplifies to M = F × d.
The SI unit of moment of force is Newton-meter (N·m). Other common units include kilonewton-meter (kN·m), pound-foot (lb·ft), and pound-force-foot (lbf·ft). This calculator lets you select your preferred unit for both inputs and output.
Moment of force and torque describe the same physical quantity — the rotational effect of a force. In engineering mechanics, 'moment' is often used for static situations (e.g. bending of beams), while 'torque' is more common in dynamics and rotational machinery. Both use the same formula: M = F × d.
The angle θ between the applied force and the lever arm determines the effective component of force causing rotation. A 90° angle produces the maximum moment because sin(90°) = 1. As the angle decreases toward 0° or 180°, sin(θ) approaches 0, meaning the force acts along the lever arm and produces no rotational effect.
The principle of moments states that for a body in rotational equilibrium, the sum of all clockwise moments about any point equals the sum of all anticlockwise moments about the same point. This principle is fundamental in analyzing levers, beams, and any structure subject to multiple forces.
Yes. Use the 'I want to calculate' dropdown to select what you need. If you know the moment and lever arm length, the calculator solves for force (F = M / (d × sin(θ))). If you know the moment and force, it solves for lever arm length (d = M / (F × sin(θ))).
Moment of force appears in many everyday and engineering contexts: tightening a bolt with a wrench, opening a door (the handle is placed far from the hinge to maximize moment), bridge and beam design, vehicle steering systems, biomechanics of human joints, and calculating the mechanical advantage of levers and pulleys.