Free · Mechanics and material properties

Gear Speed Reduction & Reciprocal Multiplier

Find the tooth ratio, output speed and reciprocal speed multiplier for a compatible gear pair.

  • Formula & worked example
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Calculator inputs

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How to use this calculator

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

Private by default

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 gives tooth ratio 3 and output/input speed multiplier 1/3. An input of 1,800 rpm gives 600 rpm output.

Tooth ratio = output teeth ÷ input teeth; speed multiplier = 1 ÷ tooth 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. Gears are compatible and engaged without slip.
  • The speed multiplier is the reciprocal of the tooth ratio. A multiplier below one means reduced speed, not a speed increase.
  • Results describe magnitudes; rotation direction, efficiency, wear and torque capacity are separate.

Common questions

Why are two ratios described?

Output/input tooth count and output/input rotation rate are reciprocals for this model. The labels identify which ratio is being used.

Can I enter an output speed?

Yes. Enter the ratio or tooth counts and output speed to recover the input speed.

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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