# Gear Reducing Formulas

## Output torque, speed and horsepower when using gears

### 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)*

*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 *

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