Physics
Gear ratio from tooth counts
The definition. Above one is a reduction, below one is an overdrive, and exactly one passes the rotation through unchanged.
The Formula
ratio = N_driven / N_driving
The definition. Above one is a reduction, below one is an overdrive, and exactly one passes the rotation through unchanged.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| N_driven | Driven gear teeth | teeth | The output gear, counting every tooth. |
| N_driving | Driving gear teeth | teeth | The input gear that does the pushing. |
| i | Gear ratio | dimensionless | A dimensionless number. |
What Each Symbol Means
N_driventeeth
Driven gear teeth
The output gear, counting every tooth.
N_drivingteeth
Driving gear teeth
The input gear that does the pushing.
idimensionless
Gear ratio
A dimensionless number.
See It Worked With Real Numbers
A formula on its own does not tell you which number goes where. The how to calculate gear ratio page applies this equation to a concrete case, shows every intermediate step, and names the mistakes that produce a wrong answer even when the algebra is right.
Where This Formula Appears
This equation is the working core of How To Calculate Gear Ratio, filed under Science. Every number the guide produces comes from substituting into this one line.