Free · Mechanics and material properties

Gear Teeth Ratio & Output RPM

Calculate a gear ratio from tooth counts and convert between input and output rotation rates.

Formula & worked example
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How to use this calculator

Enter the known values in the units shown. Results update as you type.
Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
Use the worked example to check the method. Reset restores the starting fields.

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Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

A 20-tooth input driving a 60-tooth output has ratio 3. At 1,800 rpm input, the output speed magnitude is 600 rpm.

Ratio = output teeth ÷ input teeth; output rotation rate = input rotation rate ÷ ratio

Worked example

Enter these known values and leave the other values blank.

Input gear teeth: 20
Output gear teeth: 60
Input speed magnitude: 1800 rpm

Output-to-input tooth ratio: 3 :1
Output speed magnitude: 600 rpm

Assumptions and limitations

Tooth counts are whole numbers of at least three, matching this model’s lower limit. The gears are assumed compatible and engaged without slip.
The reported rates are nonnegative speed magnitudes. Rotation direction and efficiency are not modeled.
The ratio describes one pair or an already-combined equivalent ratio, not automatic enumeration of a full gear train.

Common questions

Does a larger output gear rotate faster?

For a compatible pair, more output teeth increase the reduction ratio and reduce output speed magnitude.

Does this calculate torque capacity?

No. Tooth ratio alone does not determine material strength, allowable torque or transmission losses.

References

Bookify requires whole gear-tooth counts and nonnegative speed magnitudes, retaining the captured minimum of three teeth. Bookify uses the exact relationship one revolution = 2π radians instead of the captured rounded angular-speed factor.

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