Physics
Output speed
Speed falls in proportion to the ratio. A ratio of 3 cuts the output speed to one third of the input.
The Formula
rpm_out = rpm_in / i
Speed falls in proportion to the ratio. A ratio of 3 cuts the output speed to one third of the input.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| rpm_in | Input speed | revolutions per minute | The speed of the driving shaft. |
| i | Gear ratio | dimensionless | Driven teeth divided by driving teeth. |
| rpm_out | Output speed | revolutions per minute | The speed of the driven shaft. |
What Each Symbol Means
rpm_inrevolutions per minute
Input speed
The speed of the driving shaft.
idimensionless
Gear ratio
Driven teeth divided by driving teeth.
rpm_outrevolutions per minute
Output speed
The speed of the driven shaft.
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.