Force & Arm
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Calculate torque from force and lever arm, power and RPM, or moment of inertia and angular acceleration. Supports multiple calculation methods with unit conversions.
90° = perpendicular (maximum torque)
Enter values above to see results.
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Rotational Mechanics
Calculate torque from force and lever arm, power and RPM, or moment of inertia and angular acceleration for mechanical design.
Force-Arm
τ = F × r
Power-Speed
τ = P / ω
Inertia-Accel
τ = I × α
Unit
N·m (SI)
Reviewed by: CalculatorApp Mechanical Engineering Team
Torque is the rotational equivalent of linear force — it causes or resists angular acceleration. Every rotating machine involves torque: engines and motors produce it, gearboxes transmit and transform it, fasteners require it for proper clamping, and brakes oppose it. Understanding torque is essential for sizing motors, designing drive trains, specifying fasteners, and analyzing mechanical failures.
Force & Arm
τ = F × rPower & Speed
τ = P / ω (ω = 2πn/60)Inertia
τ = I × αPower Link
P = τ × ω| Application | Typical Torque Range | Design Focus |
|---|---|---|
| Threaded fasteners | 1 N·m – 2000 N·m | Clamp load, yield limit |
| Electric motors | 0.1 N·m – 10 kN·m | Starting torque, efficiency |
| Automotive engines | 100 – 2000 N·m | Peak torque vs RPM curve |
| Wind turbines | 10 kN·m – 10 MN·m | Gearbox ratio, shaft design |
Antiquity: Archimedes formalizes the lever principle — the geometric foundation of torque.
1687: Newton's laws of motion establish the rotational analogs: τ = Iα follows from F = ma.
1800s: Steam engines make torque a central practical engineering quantity for power transmission.
1882: De Laval's steam turbine demonstrates high-speed rotational torque in continuous operation.
1900s: Automotive and aerospace industries drive precise torque standards for fasteners and driveshafts.
Modern era: Torque sensors, dynamometers, and smart wrenches enable real-time torque control in manufacturing.
Standard mechanical design and power transmission codes.
Torque rating standards for electric motors.
Bolt tightening torque specifications from ISO.
Rotating equipment guarding and safety standards.
Myth: Higher torque always means a more powerful machine.
Fact: Power = torque × speed. A high-torque, low-speed motor can have the same power as a low-torque, high-speed motor.
Myth: Tightening a bolt harder always improves joint strength.
Fact: Over-torquing yields the bolt shank, reducing or eliminating clamp load and causing premature failure.
Myth: Torque and moment are different quantities.
Fact: Torque and moment are both force × distance; torque specifically applies to a rotational axis.
Myth: Gear reduction reduces power.
Fact: Ideal gears preserve power; torque increases as speed decreases by the gear ratio (minus friction losses).
Torque (τ) is a rotational force: τ = F × r. It is measured in Newton-meters (N·m) in SI units.
P = τ × ω, where ω is angular velocity in rad/s. For rpm: P = τ × 2πn/60.
τ = I × α, where I is moment of inertia (kg·m²) and α is angular acceleration (rad/s²).
1 N·m = 0.7376 ft·lb. Multiply Newton-meters by 0.7376 to get foot-pounds.
Torque wrenches apply a specified tightening torque to fasteners, preventing over- or under-tightening that can cause joint failure.
A gear reduction multiplies torque by the gear ratio while reducing speed proportionally, maintaining constant power (minus losses).
At constant power, torque decreases as RPM increases: τ = P / ω. High-torque motors run at low RPM.
Bolt tightening torque depends on bolt size, grade, and lubrication. Typical M10 8.8 bolt: ~45-50 N·m dry.
Both describe rotational force × distance; torque specifically refers to a twisting force about a rotational axis.
L = I × ω. Torque equals the rate of change of angular momentum: τ = dL/dt, analogous to force = dp/dt.
τ = P/ω from the shaft power required; then select a motor with torque rating exceeding this with a service factor.
Excess torque stresses the bolt beyond its yield strength, causing permanent stretch or fracture of the threaded section.
Pair torque analysis with motor sizing, gear ratio, and kinetic energy calculators for complete drive system design.
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