Torque Calculator
Torque (N⋅m)
50
How it works
Torque is the rotational equivalent of force: τ = F × d × sin(θ), where F is the applied force, d is the distance from the pivot (moment arm), and θ is the angle between the force and the moment arm. When force is perpendicular to the moment arm (θ = 90°), τ = F × d.
**Units and conversions** SI unit: Newton-meter (N·m). US customary: foot-pound (ft·lb) and inch-pound (in·lb). 1 ft·lb = 1.356 N·m. 1 N·m = 8.851 in·lb. Fastener torque specs are often given in N·m or ft·lb — use the correct unit to avoid under-tightening (loose joint) or over-tightening (stripped threads, cracked components).
**Torque vs. work** Although torque and energy share the same units (N·m = joule), they are different quantities. Torque is a rotational moment (force × distance vector), while work is force × displacement scalar. The distinction matters when analyzing rotating systems.
**Angular velocity and power** Power in a rotating system: P = τ × ω, where ω is angular velocity in radians/second. A motor producing 100 N·m at 1000 RPM (104.7 rad/s) outputs 10.47 kW. This relationship connects torque specifications to actual power requirements.
**Fastener torque and clamping force** Torque applied to a fastener creates clamping force through thread mechanics. The relationship: F = T / (K × D), where K is the nut factor (~0.2 for dry steel threads) and D is the bolt diameter. A ½-inch bolt torqued to 75 ft·lb develops approximately 13,500 lb of clamping force. Lubricated threads reduce K, increasing clamping force at the same torque — a reason why torque specs should specify lubrication condition.
Frequently Asked Questions
- Torque = (F × lead) / (2π × efficiency), where F is axial force, lead is distance traveled per revolution. For a 5 mm lead screw lifting 50 kg (490 N) with 40% efficiency: T = (490 × 0.005) / (2π × 0.4) = 0.976 N·m. Lead screws have low efficiency (20–50%) due to sliding friction. Ball screws have much higher efficiency (85–95%) and require much less torque for the same load — critical for CNC machines and precision motion systems where holding torque and backdrivability also matter.
- Power (W) = Torque (N·m) × Angular velocity (rad/s). Angular velocity ω = 2π × RPM / 60. For horsepower: HP = Torque (ft·lb) × RPM / 5252 (US formula). A motor producing 50 ft·lb at 3000 RPM develops 50 × 3000 / 5252 = 28.6 HP. In SI: P (W) = T (N·m) × 2π × RPM/60. At constant power, torque and speed are inversely related — this is why electric motors deliver full torque from zero RPM (high torque at low speed), while combustion engines produce peak torque only in a narrow RPM band.
- Fastener torque specs account for friction in threads and under the nut/bolt head. The relationship T = K × F × D (nut factor × clamping force × bolt diameter) shows that for a given bolt size, more torque means more clamping force. Standard torque tables (SAE, ISO) specify torque for a given bolt grade and size assuming clean, dry, unlubricated threads (K ≈ 0.2). Lubricating threads reduces K to ~0.15, meaning the same torque produces ~33% more clamping force — potentially overstressing the bolt. Always match lubrication condition to the spec.
- Torque wrenches (beam, click, digital) measure applied fastener torque directly. Reaction torque sensors (strain gauge based) measure torque in rotating shafts. Dynamometers measure engine or motor torque by applying a controllable braking load and measuring the reaction force at a known arm length. Power analyzers compute torque indirectly from speed and power. For hand-tightened connections where torque wrenches aren't practical, angle-of-turn methods (tighten to snug, then turn an additional specified angle) provide more consistent clamping force than torque alone.