Gear Output Speed CalculatorFree online other calculator — instant results, no sign-up
Calculate driven gear speed from tooth counts and input speed.
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About the Gear Output Speed Calculator
The Gear Output Speed Calculator finds the rotational speed of a driven gear from the driver tooth count, driven tooth count, and input speed in rpm. It uses the inverse relationship between gear tooth count and rotational speed: a larger driven gear turns more slowly than its driver. With 20 driver teeth, 60 driven teeth, and an input speed of 1200 rpm, the driven gear turns at 400 rpm.
- Driver teeth
- The number of teeth on the gear supplying motion, entered as a positive whole-number count with no units; the default is 20.
- Driven teeth
- The number of teeth on the gear receiving motion, entered as a positive whole-number count with no units; the default is 60.
- Input speed (rpm)
- The rotational speed of the driver gear in revolutions per minute (rpm); the default is 1200 rpm.
Formula and method
n_out = n_in × (T_driver / T_driven); with the defaults, n_out = 1200 × (20 / 60) = 400 rpm.
- n_outDriven gear output speed, in rpm.
- n_inDriver gear input speed, in rpm.
- T_driverNumber of teeth on the driver gear, a dimensionless positive integer.
- T_drivenNumber of teeth on the driven gear, a dimensionless positive integer.
Divide the driver tooth count by the driven tooth count to obtain the speed multiplier, then multiply the input speed by that multiplier. For the default inputs, 20 / 60 equals one-third, so 1200 rpm × one-third gives an output speed of 400 rpm.
Worked example
These are the calculator's starting values and the results it actually produces for them.
Inputs
- Driver teeth20
- Driven teeth60
- Input speed1200 rpm
Results
- Result400 rpm
How to use the Gear Output Speed Calculator
- 1Identify which gear supplies motion and which gear receives it.
- 2Enter the driver tooth count in Driver teeth; use 20 for the worked example.
- 3Enter the driven tooth count in Driven teeth; use 60 for the worked example.
- 4Enter the driver speed in Input speed (rpm); use 1200 for the worked example.
- 5Read the calculated result: the default inputs produce a driven gear speed of 400 rpm.
Reading your result
The Result row reports the driven gear's rotational speed in rpm. A result of 400 rpm means the driven gear completes 400 revolutions per minute. Because the default driven gear has three times as many teeth as the driver, it turns at one-third of the 1200 rpm input speed. The result is a speed magnitude, not a rotation-direction indicator.
Limitations
This calculation assumes a compatible, directly meshing gear pair with positive whole-number tooth counts and continuous engagement. The driven tooth count cannot be zero. It does not verify tooth geometry, gear strength, allowable speed, or mechanical compatibility, and it does not calculate torque, efficiency, or power. Losses affect the power required to maintain the input speed, but do not change the tooth-count speed ratio while the gears remain engaged. Compound gear trains require the ratios of all stages, and planetary gear arrangements require additional information.
Common questions
Why do the default inputs produce 400 rpm rather than a higher output speed?+
The 60-tooth driven gear needs three times as many teeth to pass the mesh for one revolution as the 20-tooth driver does. Its speed is therefore 1200 × (20 / 60) = 400 rpm.
What happens if the driven gear has fewer teeth than the driver?+
The fraction T_driver / T_driven becomes greater than one, so the driven gear turns faster than the input gear. A driven gear with more teeth produces a speed reduction instead.
Does the 400 rpm result tell me which direction the driven gear rotates?+
No. Two directly meshing external gears rotate in opposite directions, while an external gear meshing with an internal gear rotates in the same direction. Tooth counts and input speed alone do not specify the mesh type.
Can I use only the first and last tooth counts for a multi-gear train?+
For a simple train with intermediate idler gears, the idler tooth counts cancel from the overall speed magnitude ratio. For a compound train with gears sharing shafts, calculate each meshing stage and multiply the stage ratios; the first and last tooth counts alone are generally insufficient.
Does the calculator save my information?+
Calculations run in your browser. While signed in, inputs and results are automatically recorded in account history; saving a result creates a separate saved record.
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Results are estimates for informational purposes and are not financial, medical or legal advice.