How to Calculate the Gearbox Torque

• 1
  Key takeaways
• 2
  What torque actually means inside a gearbox
• 3
  Gather the load data before you touch a formula
• 4
  Core formulas for calculate the gearbox torque
• 5
  Why the housing and shafts decide the real limit
• 6
  Step by step: size a gearbox from scratch
• 7
  Service factor by load type
• 8
  Gearbox type versus typical efficiency

Torque is a turning force, measured as force times lever arm. A 10 N force on a 0.1 m arm gives 1 N·m. Inside a reducer, the input shaft turns fast with low torque, and the output shaft turns slow with high torque. The gear ratio multiplies torque and divides speed. Energy is conserved, minus friction losses, so you can never get more power out than you put in.

For a first estimate, output torque equals input torque multiplied by the gear ratio and by the efficiency of the gear train. A single-stage helical pair runs at 0.96 to 0.98. A worm gearbox drops to 0.50 to 0.85 depending on the lead angle, because sliding friction is high. Planetary stages sit around 0.94 to 0.97 each. If you stack three planetary stages, multiply the three stage efficiencies together.

Engineers often ask about torque in N·m when the motor data sheet gives kW. The bridge is rotational power. Power in watts equals torque in N·m times angular speed in rad/s. In practical units, T (N·m) = 9550 × P (kW) / n (rpm). So a 2.2 kW motor at 1,450 rpm carries about 14.5 N·m at the shaft. That number is your input torque before anything else.

Most bad gearbox sizing starts with missing load data, not bad math. You need the driven mass, the radius or lead at which the force acts, the friction coefficient, and the acceleration time. For a conveyor, the pull force at the drum is the belt tension difference. For a ball screw, thrust force times lead divided by 2π gives the torque at the screw. For a rotating table, torque is inertia times angular acceleration.

Inertia matters more than people expect. The torque needed to accelerate a load is J × α, where J is the reflected inertia in kg·m² and α is angular acceleration in rad/s². Reflected inertia rises with the square of the ratio, so a high ratio can make a small load feel enormous at the motor. Keep the load-to-motor inertia ratio under 10:1 for servo systems, and under 5:1 when you need tight positioning.

Friction torque is easier to miss because it hides in bearings, seals and guideways. A rough rule for a ball screw axis is that preload and seal drag add 10 to 30 percent to the running torque. On a worm gearbox, self-locking means the load cannot drive the input backward, but it also means you pay for that safety in efficiency.

Write everything in one unit system before you start. We use N·m, kg, m and rad/s internally. Converting at the end, after you have already mixed kg and lb, is where errors survive into the purchase order. If a customer sends a drawing with a torque callout in lb·in, convert first: 1 lb·in = 0.113 N·m.

Three formulas cover most sizing work. First, torque from power and speed: T (N·m) = 9550 × P (kW) / n (rpm). This gives the torque at any shaft where you know power and rotational speed. Second, torque through a ratio: T_out = T_in × i × η, where i is the numerical ratio (input speed divided by output speed) and η is the overall efficiency. Third, acceleration torque: T_acc = J × α, added to the steady-state torque to get the peak demand.

When you calculate the gearbox torque for a catalog selection, work backwards from the load. Find the torque required at the machine shaft, divide by the gearbox ratio and efficiency, and that is the required motor torque with margin. Then compare that required motor torque against the motor's rated and peak torque. If the number is larger than peak, the axis will stall and the drive will fault on overload.

Always separate continuous torque from peak torque. Continuous torque sets the thermal rating and the gearbox life. Peak torque sets the gear tooth bending stress and can cause a one-time failure. A gearbox can survive a peak for a few seconds per cycle, but not for minutes. Check the catalog for both values, and check the number of starts per hour the manufacturer allows.

A gearbox rating on paper assumes the housing holds the bearing centers in line. In a machined aluminum or cast iron housing, bore position tolerance and bore roundness set how the gears mesh. If the center distance drifts, the contact pattern moves to the tooth tip and bending stress rises quickly. That is why we hold bearing bores to ±0.005 mm on our 5-axis and mill-turn centers, then verify with a CMM report.

Output shafts carry both torque and side load. A 344 N·m output through a Ø25 mm shaft is comfortable, but a 100 mm overhung sprocket adds a bending moment that the bearing, not the shaft, must absorb. Check the catalog's permitted radial load at the actual distance from the shoulder. If the load point is farther out than the catalog point, derate the permitted value.

Material choice matters less than people assume for the housing, but a lot for the gears. Through-hardened 4140 or 4340 gears handle moderate loads. Case-hardened 20MnCr5 or 17-4PH gets a hard skin with a tough core, which resists pitting and bending together. For prototypes and low-volume reducers, machined gears in 7075 or 4140 are practical, because you avoid the tooling cost of a forging.

Surface finish on the bearing seats is not cosmetic. A seat turned at Ra 1.6–3.2 μm can let the outer race creep under vibration. We usually specify Ra 0.8–1.6 μm for bearing seats and Ra 0.2–0.8 μm where a seal runs. That finish is achievable on a lathe with a wiper insert, and it is cheap compared to a field failure.