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Gear Teeth, Speed, Torque and Vehicle Ratio

Calculate gear teeth, speed, torque and vehicle ratio with local equations, selectable units and supported inverse relationships.

  • Formula & worked example
  • Private in your browser
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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

gearRatio = 3; outputSpeed = 100; outputTorque = 30. Values use the worked example unit selections.

ratio = Tout/Tin = teethout/teethin = rpmin/rpmout; vehicle speed = wheel rpm × circumference

Worked example

Enter these known values and leave the other values blank.

I want to find gear ratio from:
number of gear teeth.
Input gear teeth number
20
Output gear teeth number
60
Input rotational speed
300 rpm
Input torque
10 N·m
Gear Ratio
3 :1
Output rotational speed
100 rpm
Output torque
30 N·m

Assumptions and limitations

  • Ideal gears conserve power and omit mechanical losses. Tooth counts are positive integers. Vehicle mode assumes no tire slip and uses effective rolling diameter with a combined drivetrain ratio.
  • Unit selectors convert known physical quantities. Leave a supported unknown blank; derived inverse branches are limited by the stated model and available captured equations.

Common questions

What does this calculation assume?

Ideal gears conserve power and omit mechanical losses. Tooth counts are positive integers. Vehicle mode assumes no tire slip and uses effective rolling diameter with a combined drivetrain ratio.

Can I solve for an input?

Where the captured model supplies an inverse, leave that quantity blank and enter the remaining known quantities. A positive square-root or principal trigonometric inverse may represent only one of multiple mathematical branches.

Which unit should I use for the worked example?

The example uses the initial metric unit selection beside each field. Change a unit using its selector to convert the same known quantity; switching a unit does not change the underlying physical value.

References

Original accessible explanations preserve the captured diagram geometry, quantities and conditional variants without external image loading. Restrict the physical model to non-singular dimensions and stated principal inverse branches; discrete gear/fringe counts are exact integers. Bookify uses the exact relationship one revolution = 2π radians instead of the captured rounded angular-speed factor. Kilogram-force centimeters use standard gravity and exactly one centimeter. Pound-force feet use the exact international pound and foot with standard gravity. Pound-force inches use the exact international pound and inch with standard gravity.

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