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# Gear Reducing Formulas

## Output torque, speed and horsepower with gears.

### Gear Output Torque

Mo = Mi r μ                               (1)

where

Mo = output torque (Nm, lbf ft)

Mi = input torque (Nm, lbf 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

Mo = (500 Nm) (3.8) (0.9)

= 1710 Nm

### Gear Output Speed

So = Si  / r                             (2)

where

So = output speed (rad/s, rpm)

Si = 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

So = (2000 rpm) / (3.8)

= 526 rpm

Gear Output Horsepower

Po = Pi  μ                              (3)

where

Po = output horsepower (W, hp)

Pi = 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

Po = (300 kW) (0.9)

= 270 kW

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## Citation

• The Engineering ToolBox (2010). Gear Reducing Formulas. [online] Available at: https://www.engineeringtoolbox.com/gear-output-torque-speed-horsepower-d_1691.html [Accessed Day Month Year].

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12.8.9