Gear Ratio
Ratio of teeth (or speeds) between gears.
Formula
Variables
Example
40/10 = 4:1
How it works
Gear ratio compares how many teeth the driven gear has relative to the driving gear. Because gears mesh tooth-for-tooth, the gear with more teeth must turn more slowly, so the tooth count ratio matches the speed ratio between the output and input. This makes it a simple way to predict whether a gearbox will increase speed, increase torque, or do the opposite.
When to use it
Use this when analyzing simple gear trains in machines like bicycles, clocks, engines, and robotics. It helps you estimate output speed or choose gear sizes to get the motion or force you want.
Worked example, step by step
Input gear teeth, N_in = 15 Output gear teeth, N_out = 45 GR = N_out / N_in GR = 45 / 15 GR = 3 So the gear ratio is 3:1 This means the output gear turns 3 times slower than the input gear, but with more torque.
Common mistakes to avoid
- Swapping the input and output gear counts and getting the ratio backwards
- Using wheel diameter instead of tooth count for meshing gears
- Forgetting that a larger gear ratio usually means lower speed at the output
Did You Know?
A bicycle's gears are just ratios, trading pedalling ease for speed exactly as the numbers dictate.
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