Calculate torque, force, distance, angular acceleration, power from torque, bolt torque specs, and unit conversions for mechanical engineering applications.
Torque — the rotational equivalent of linear force — is everywhere in engineering. From tightening bolts to sizing electric motors, from automotive performance specs to industrial machinery design, torque calculations are fundamental. The Torque Calculator handles everything from basic τ = F × r to power-torque-RPM relationships, angular acceleration, and bolt torque specifications.
Understanding torque is essential for proper fastener installation, engine performance analysis, gear train design, and structural engineering. Under-torqued bolts loosen and fail; over-torqued bolts strip or break. The right torque value depends on bolt size, grade, lubrication, and the materials being joined. This calculator includes common bolt torque specifications for reference.
The calculator also computes the relationship between torque and power — critical for motor selection. A motor's torque output determines its ability to accelerate loads, while power (torque × angular velocity) determines sustained performance. Whether you're selecting a motor, designing a gearbox, or checking bolt specifications, this tool provides comprehensive torque analysis.
Use this calculator when you need to connect force-at-distance problems with motor power, fastener tightening, or rotational mechanics in one place. It is useful for quick engineering checks where the answer might need to move between N·m, ft·lb, and power-at-RPM rather than staying in one unit system, especially when you are comparing bolt specs or drive loads.
Torque: τ = F × r × sin(θ). Power: P = τ × ω = τ × 2π × RPM / 60. Angular Acceleration: α = τ / I (moment of inertia). Unit conversions: 1 N·m = 0.7376 ft·lb = 8.851 in·lb.
Result: Torque = 15.0 N·m (11.06 ft·lb), Power = 4,712 W (6.32 hp)
50 N applied at 0.3 m from the pivot at 90° produces 15 N·m of torque. At 3,000 RPM, this torque delivers 4,712 watts (6.32 horsepower) of mechanical power.
Engine torque curves define vehicle performance character. Diesel engines produce peak torque at 1,500-2,500 RPM, providing strong low-end pulling power — ideal for towing and heavy loads. Gasoline engines typically peak at 3,500-5,500 RPM, requiring higher revs for maximum force. Electric motors produce peak torque from 0 RPM, explaining their instant acceleration feel.
The transmission multiplies engine torque through gear ratios. A 3.5:1 first gear triples the engine torque at the wheels (minus drivetrain losses). This is why vehicles accelerate hardest in first gear despite the engine producing the same torque. Final drive ratio, tire diameter, and vehicle weight complete the acceleration equation.
Bolt torque specifications ensure proper clamping force — typically 75% of the bolt's proof load. The relationship between torque and tension is T = K × D × F, where K is the nut factor (0.20 dry, 0.15 lubricated, varies by plating), D is nominal bolt diameter, and F is desired clamping force. Only 10-15% of applied torque becomes clamping force; the rest overcomes thread and under-head friction.
Critical applications like cylinder heads, structural connections, and pressure vessels use torque-angle methods: tighten to a snug torque, then rotate an additional specified angle. This provides more consistent clamping than torque alone because it's less sensitive to friction variations.
Selecting the right motor requires matching torque requirements at each operating speed. The total torque demand includes: load torque (constant or speed-dependent), acceleration torque (τ = Iα for speed changes), and friction/windage losses. The motor must produce sufficient starting torque (typically 150-250% of running torque) to overcome static friction and accelerate the load within acceptable time.
Torque is the rotational equivalent of force — it's a force applied at a distance from a pivot point, causing rotation. Measured in newton-meters (N·m) or foot-pounds (ft·lb), it equals force × lever arm × sin(angle).
HP = Torque (ft·lb) × RPM / 5,252. Torque and horsepower always cross at 5,252 RPM. Diesel engines produce high torque at low RPM; gasoline engines produce more horsepower at high RPM.
Only the component of force perpendicular to the lever arm produces torque. At 90°, sin(90°) = 1, giving maximum torque. At 0° or 180° (force along the lever), there's no torque. This is why wrench handles are perpendicular to bolts.
Over-torquing can strip threads, stretch or break the bolt, crack the clamped material, or cause hydrogen embrittlement in hardened steel bolts. Always use a calibrated torque wrench and follow manufacturer specifications.
Click-type torque wrenches use a spring-loaded mechanism that releases (clicks) at the set torque value. Beam-type wrenches deflect a calibrated beam. Digital wrenches use strain gauges for precise measurement. All should be calibrated regularly.
Moment of inertia (I) is the rotational equivalent of mass — it measures resistance to angular acceleration. τ = Iα, just as F = ma. A flywheel has high I (resists speed changes); a thin rod has low I.