Gear Ratio
Ratio of driven to driving gear teeth.
Formula
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Example
40 driven, 10 drive: GR = 4:1
How it works
A gear ratio compares how many teeth the driven gear has to how many teeth the driving gear has. Because the teeth must mesh one-for-one, a gear with more teeth turns more slowly but can deliver more torque, while a gear with fewer teeth turns faster. This ratio tells you how the rotation speed and force are changed from one gear to the next.
When to use it
Use this when analysing gear pairs in engines, transmissions, bikes, or any machine with meshing gears. It helps predict output speed, torque change, and whether a setup is geared for power or speed.
Worked example, step by step
Given: Driven gear teeth, N_out = 30 Drive gear teeth, N_in = 12 Use the formula: GR = N_out / N_in Substitute the values: GR = 30 / 12 Calculate: GR = 2.5 So the gear ratio is 2.5:1, meaning the driven gear turns once for every 2.5 turns of the driving gear.
Common mistakes to avoid
- Reversing the ratio and dividing drive teeth by driven teeth
- Using gear diameter instead of tooth count unless the gears are the same pitch
- Forgetting that the ratio is often written as a comparison like 2.5:1, not just 2.5
Did You Know?
A low first gear (high ratio) multiplies torque for acceleration; overdrive gears below 1:1 save fuel at cruise.
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