Shaft Torque Calculator

Shaft Torque Calculator: engineering calculator for shaft torque. Formula derivation, tolerances, and design tips.

A shaft torque calculator computes the torque (T) produced by a force applied at a given radius from a shaft centreline (T = F × r), then calculates the mechanical power transmitted by that torque at a given rotational speed (P = 2π × N × T ÷ 60). Torque and power are the two fundamental quantities in rotating machinery — torque measures the twisting moment on the shaft, while power measures the rate of energy transmission. Beam Load Calculator covers related mechanical engineering calculations.

The distinction between torque and power is important: a shaft can produce high torque at low speed or low torque at high speed, with similar power in both cases. Electric motors are typically specified by rated power and rated torque at rated speed; gearboxes trade speed for torque (or vice versa) while approximately conserving power. Knowing the torque at a given speed allows shaft, coupling, key, and gearbox sizing.

Enter the force applied to the shaft (in N). For a torque wrench or tightening application, convert the torque directly — the force and radius fields compute torque from first principles.
Enter the lever arm (radius from shaft centreline to force application point, in metres).
Enter the rotational speed in RPM — the calculator uses this to compute transmitted shaft power in kW and hp.
Select the output unit (N·m for metric engineering, lb·ft for US/imperial specifications).
Read torque, power in kW and hp — use these to size shafts, couplings, gearboxes, and motors.

Shaft torque and power formulas

Torque: T = F × r (N·m, where F is force in N and r is radius in m)

Shaft power: P = 2π × N × T ÷ 60 (W, where N is speed in RPM)

Unit conversions: 1 N·m = 0.7376 lb·ft; 1 kW = 1.341 hp; 1 hp = 745.7 W.

Worked example: 500 N force at 0.2 m radius → T = 500 × 0.2 = 100 N·m = 73.8 lb·ft. At 1,500 RPM: P = 2π × 1,500 × 100 ÷ 60 = 15,708 W = 15.7 kW = 21.1 hp.

Reading your shaft torque result

Typical torque and power reference values

Typical shaft torques by application: Hand torque wrench — 10–200 N·m; Small electric motor (1–5 kW) — 7–50 N·m at 1,500 RPM; Car petrol engine — 150–400 N·m at 3,000–5,000 RPM; Diesel truck engine — 500–2,500 N·m at 1,000–2,000 RPM; Large industrial gearbox output — 10,000–100,000 N·m. Power reference: 1 kW ≈ 1.34 hp; a 100 kW motor at 1,500 RPM produces approximately 637 N·m. Torque × speed = power — if torque doubles through a gearbox, speed halves to maintain the same power (minus gearbox losses).

Engineering tips and best practices

For shaft sizing, maximum shear stress τ = T × r ÷ J, where J = π × d⁴ ÷ 32 (polar second moment of area for a solid circular shaft) — minimum shaft diameter is typically set by this criterion plus a safety factor.
When specifying a motor, add 10–20% to the calculated power requirement to account for friction losses, startup torque demands, and future load increases — motors should not operate at 100% rated capacity continuously.
Gearboxes multiply torque by the gear ratio but divide speed: T_out = T_in × ratio × efficiency; P_out = P_in × efficiency (typically 95–98% for a well-maintained gearbox stage).
High-torque low-speed applications (e.g. conveyor drives, crushers) often use worm or planetary gearboxes; high-speed applications use helical or spur gears with higher efficiency.
Torque measurement in practice uses strain gauge torque transducers or reaction torque sensors — the lever-arm calculation here is for design estimation, not measurement.

An electric motor rated at 75 kW running at 1,500 RPM produces approximately 477 N·m — calculated as P × 60 ÷ (2π × N).
1 N·m = 0.738 lb·ft — the US automotive convention still specifies torque in lb·ft, making this conversion essential when working from UK/EU to US specifications.
A standard M12 bolt tightened to 80 N·m preloads at approximately 28 kN clamping force — torque wrench tightening is the most common application of T = F × r in mechanical maintenance.
Power loss = torque × angular velocity × (1 − efficiency); for a 95%-efficient gearbox transmitting 100 kW, the heat dissipation is approximately 5 kW — significant for enclosed housing thermal design.

Common mistakes to avoid

Confusing torque (N·m) with energy (J) — both have the same SI unit, but torque is a vector (moment of force) while energy is a scalar; they are dimensionally identical but physically different quantities.
Ignoring gearbox efficiency — a gearbox that doubles output torque does not deliver double the power; mechanical losses (typically 2–5% per stage) reduce the power transmitted.
Not accounting for dynamic torque — starting torque for an induction motor or loaded conveyor can be 2–3× the running torque; size the shaft for peak torque, not rated running torque.
Mixing N·m and lb·ft in the same calculation — these are common in combined UK/US projects; always convert to a single consistent unit system before sizing shafts or selecting couplings.

Shaft and coupling design calculations, including torque capacity, fatigue life, and key sizing, must comply with applicable mechanical engineering standards (BS EN, ISO, ASME, and equivalent national standards). Motor and gearbox selection must account for starting conditions, duty cycle, and environmental factors per manufacturer specifications. This calculator provides educational estimates only and does not constitute professional engineering advice. Safety-critical rotating machinery calculations must be reviewed by a chartered or licensed mechanical engineer.