How this calculator works
The reduction convention is input speed divided by output speed. For a meshing pair it is driven teeth divided by driving teeth. Ideal output torque rises by this factor while power is conserved. Vehicle mode measures the overall engine-to-wheel reduction, including the transmission and differential, and assumes no clutch slip or tyre slip. All outputs are magnitudes; external gears turn in opposite directions.
Formula
R = Nout/Nin = RPMin/RPMout = Tout/Tin. For a vehicle, wheel RPM = 60v/(pi D) and R = engine RPM/wheel RPM.
Worked example
A 20-tooth driver and 60-tooth driven gear give 3:1 reduction. At 1200 input rpm and 10 N m, ideal output is 400 rpm and 30 N m. A 1 m tyre at 31.4159 m/s turns 600 rpm; an engine at 3000 rpm has overall ratio 5.
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Frequently asked questions
What does a ratio above one mean?
It is a speed reduction under the input/output convention used here.
Do idler gears change the ratio?
A simple idler changes direction and spacing but cancels out of the overall tooth-count ratio.
Why is real output torque lower?
Bearing, tooth and lubricant losses reduce transmitted power. This tool reports the ideal relation.