How to use this calculator

Choose a single gear pair or a two-stage train, enter the tooth counts, then the input speed, torque and the efficiency of each stage. The driver is the gear on the input shaft.

Formulas

Gear ratioi = N_drivenN_driver (multiply stages)

Speed and torquen_out = n_ini T_out = T_in i η

PowerP = Tω P_out = ηP_in

Worked example

20-tooth pinion driving a 60-tooth gear at 1,750 rpm and 20 N·m (the default)

i = 60 / 20 = 3.
n_out = 1,750 / 3 = 583.3 rpm.
T_out = 20 × 3 × 0.98 = 58.8 N·m.
P_in = 20 N·m × 183.3 rad/s = 3.67 kW; 2% of it (73 W) becomes heat.

Frequently asked questions

Does an idler gear change the ratio?

No. An idler between two gears only reverses the direction of rotation. The ratio depends on the first driver and last driven gear.

Can I use pulley diameters instead of teeth?

Yes. For belts and chains the ratio is the driven diameter (or sprocket teeth) over the driver diameter, ignoring slip.

Why does torque go up when speed goes down?

Power is torque times speed. With almost no power lost, cutting speed by a factor i multiplies torque by about i.