# Gear Ratio

Gear ratios are super useful to either increase torque or the rotation speed.

The Torque is caused by the size of the gear. Bigger gears have greater diameters, which results in a greater torque (from the formula $rfsin(θ)$). However, the bigger gear has to rotate more on the outside to complete the same rotation compared to a smaller gear (because of larger circumference), which results in a lower speed.

- Question: How many tooth do we really need considering all we care about is the gear ratio? Answer

Note

A gear ratio > 1 between two gears means the torque transferred will increase. A small gear ratio means the RPM will increase.

### Formula

$Gear ratio=Teeth of input gearTeeth of output gear $

$RPM output=Gear ratioRPM input $

$Torque output=ratio∗Torque input$

We can see from these formula that the RPM output is inversely proportional to the Torque output.

Example: Gear 1 - 8 teeth - 50 RPM and 25 Nm torque Gear 2 - 16 teeth - 25 RPM and 50 Nm torque

## OLD NOTES: Gear Ratio Calculator

Gears Explained - mechanical engineering - YouTube by Engineering Mindset

- Low gear = gear that turns super slow, → low speed, high torque
- High gear = gear that turns super fast →high speed, low torque

The torque is caused by the size of the gear. Bigger gears have greater diameters, which results in a greater torque (from the formula F_L_sintheta). However, the bigger gear has to rotate more on the outside to complete the same rotation compared to a smaller gear (because of larger circumference)

$Gear ratio=Driver sizeDriven size $

$Gear ratio=RPM drivenRPM driver $

A positive gear ratio results into an increase in torque.

Gear ratio is input: output, or output/input