Gear Reducing Formulas

Gear Output Torque

M_o = M_i r μ                               (1)

where 

M_o = output torque (Nm, lb_f ft)

M_i = input torque (Nm, lb_f ft)

r = gear transmission ratio

μ = gear efficiency (%)

Example - Geear Output Torque

The output torque from a transmission with input torque 500 Nm, gear transmission ratio 3.8 and gear efficiency 0.9 - can be calculated as

M_o = (500 Nm) (3.8) (0.9)

    = 1710 Nm   

Gear Output Speed

S_o = S_i  / r                             (2)

where 

S_o = output speed (rad/s, rpm)

S_i = input speed (rad/s, rpm)

Example - Gear Output Speed

The output speed of a transmission with input speed 2000 rpm and transmission ratio 3.8 can be calculated as

S_o = (2000 rpm) / (3.8)

    = 526 rpm 

Gear Output Horsepower

P_o = P_i  μ                              (3)

where 

P_o = output horsepower (W, hp)

P_i = input horsepower (W, hp)

Example - Gear Output Power

The output power from a transmission with input power 300 kW and efficiency 0.9 can be calculated as

P_o = (300 kW) (0.9)

    = 270 kW