Moment of Force (Torque) Calculator
Formula
What is Moment of Force?
The moment of a force (torque) is its turning effect about a pivot. It is the product of the force and the perpendicular distance from the pivot to the force's line of action. Maximum torque occurs when the force is perpendicular to the lever arm (θ = 90°). The SI unit is the newton‑meter (N·m); the direction follows the right‑hand rule (CCW positive, CW negative).
Core equations
τ = F · r · sin(θ) | τ = F × d⊥ | Couple: M = F · d | Rotation: τ = I · α | Power: P = τ · ω, ω = 2π·RPM/60
τ(N·m) ≈ 9550 · P(kW)/RPM | τ(lbf·ft) = 5252 · HP/RPM
τ(N·m) ≈ 9550 · P(kW)/RPM | τ(lbf·ft) = 5252 · HP/RPM
Seven Engineering Models Included
Torque (F·r·sinθ)Solve for torque, force, distance or angle; multi‑unit; direction; live lever diagram.
Resultant MomentSum of signed moments from multiple forces about a pivot (CW/CCW).
CouplePure moment M = F·d from two equal, opposite, parallel forces.
Power · Torque · RPMRotational power with HP/kW and the 5252 & 9550 constants; solve any variable.
Dynamics τ = I·αMoment‑of‑inertia shape library (cylinder, sphere, rod, plate, ring, point mass).
Beam Bending MomentCantilever & simply‑supported standard cases (point load, UDL) with reactions.
Torque Unit ConverterConvert across N·m, lbf·ft, lbf·in, kgf·m, ozf·in, N·cm/mm, dyne·cm and more.
Multi‑Unit I/OForce (N, kN, lbf, kgf, tf, ozf, pdl, dyn), length (m, cm, mm, in, ft, yd, mi), power (W, kW, HP, PS).
Torque Unit Reference
| Unit | Symbol | Equals (N·m) |
|---|---|---|
| Newton‑meter | N·m | 1 |
| Kilonewton‑meter | kN·m | 1000 |
| Pound‑force foot | lbf·ft | 1.35581795 |
| Pound‑force inch | lbf·in | 0.11298483 |
| Kilogram‑force meter | kgf·m | 9.80665 |
| Kilogram‑force centimeter | kgf·cm | 0.0980665 |
| Ounce‑force inch | ozf·in | 0.00706155 |
| Newton‑centimeter | N·cm | 0.01 |
| Newton‑millimeter | N·mm | 0.001 |
| Dyne‑centimeter | dyn·cm | 1×10⁻⁷ |
Frequently Asked Questions
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