Load power
-Load torque
-Motor power needed
-Motor speed
-load speed x ratioAll results
| Load power | - |
| Load torque | - |
| Load speed | - |
| Load angular speed | - |
| Motor speed | - |
| Motor torque (at the motor shaft) | - |
| Motor power before service factor | - |
| Motor power with service factor | - |
| Power lost in the gearbox | - |
Method and formulas
Steady-state rigid power transmission, so every figure can be checked by hand. Power is torque times angular speed, and a gear reducer exchanges speed for torque at constant power, less its losses.
| Quantity | Formula |
|---|---|
| Angular speed | ω = 2 π n / 60 (rad/s, n in rpm) |
| Power | P = T ω |
| Metric shortcut | P (kW) = T (N·m) × n (rpm) / 9 549.3 |
| US shortcut | P (hp) = T (lbf·ft) × n (rpm) / 5 252.1 (1 hp = 33 000 ft·lbf/min) |
| Motor speed | nm = n × i |
| Motor torque | Tm = T / (i η) |
| Motor power | Pm = P × SF / η |
Mechanical horsepower of 745.70 W is used. Efficiency is taken as constant; in practice it depends on load, speed, temperature and the gear type (worm drives in particular can be well below 90 %).
Worked example: 50 N·m at 120 rpm through a 12.5:1 reducer
Load power P = 50 × 120 / 9 549.3 = 0.628 kW. With i = 12.5, η = 0.92 and SF = 1.25: motor speed = 120 × 12.5 = 1500 rpm, motor torque = 50 / (12.5 × 0.92) = 4.348 N·m, motor power = 0.628 × 1.25 / 0.92 = 0.854 kW. Pick the next standard motor size above this.
Questions
What is the formula for power from torque and speed?
Power equals torque times angular speed: P = T x omega, with omega = 2 pi n / 60 for n in rpm. In metric units P (kW) = T (N·m) x n (rpm) / 9 549.3. In US units P (hp) = T (lbf·ft) x n (rpm) / 5 252, because 33 000 ft·lbf/min per horsepower divided by 2 pi is 5 252.1. Example: 50 N·m at 120 rpm is 0.628 kW.
How do I size a motor for a gear reducer?
Work from the load back to the motor. The motor speed is the load speed times the reduction ratio. The motor torque is the load torque divided by the ratio and the gearbox efficiency. The motor power is the load power divided by the efficiency, times a service factor for shock, duty cycle or margin. Example: 50 N·m at 120 rpm through a 12.5:1 reducer at 92 % efficiency needs a motor speed of 1500 rpm, 4.35 N·m and at least 0.85 kW with a 1.25 service factor.
What service factor should I use?
A service factor is a margin that covers load peaks, starting torque and duty cycle. Typical values run from about 1.0 for smooth, continuous loads to 1.5 or more for heavy shock, but the right number comes from your gearbox or motor manufacturer's selection tables and the standard they follow. The calculator simply multiplies the power by the factor you enter. It is not a substitute for the manufacturer's selection procedure.
Why does torque go up when speed goes down through a gearbox?
A gear reducer trades speed for torque while the power stays constant, less the losses. A ratio of i divides speed by i and multiplies torque by i, then the efficiency takes a percentage off. That is why a small, fast motor can drive a slow, high-torque load.
Is horsepower the same in the US and elsewhere?
This calculator uses the mechanical horsepower common in US motor ratings, 1 hp = 745.70 W. The metric horsepower (PS or CV) is 735.5 W, and the electrical horsepower used for some motor ratings is 746 W. The differences are small but matter in a precise comparison.
What does this calculator not cover?
It covers steady-state, rigid-shaft power transmission with a constant efficiency. It does not cover acceleration torque and inertia matching, thermal rating of motors, belt or chain slip, variable efficiency at part load, or motor torque-speed curves. It is an engineering aid; verify critical designs.
Engineering aid for guidance. It covers steady-state power transmission with constant efficiency and does not cover inertia and acceleration torque, thermal motor rating, part-load efficiency or motor curves. Verify critical designs.