EngineerBenchCalculating gear ratio and output torque
Gear ratio relates the speed of a driving gear to the speed of the gear it turns. A 20-tooth driver turning a 60-tooth driven gear gives a 3:1 reduction: output speed is one third of input speed. Torque increases with the reduction, less the transmission losses you enter.
Which gear is the driver?
The driver receives power from the motor or previous stage. Enter its tooth count first, even if it is the larger gear. For a second reduction, use the additional ratio. Stage ratios multiply; they do not add.
Choosing teeth for a target speed
The driven-tooth mode rounds to a whole tooth and reports the speed that tooth count actually produces. Treat that as a speed match, not a finished gear design. Tooth strength, matching pitch, center distance, and lubrication still need separate checks.
Checking a proposed gear train
For a reduction ratio of three and an input speed of 900 RPM, the output is 300 RPM. With 10 N·m at the input and 90 percent transmission efficiency, the corresponding output torque is 27 N·m. The speed ratio comes from the geometry; efficiency reduces transmitted power rather than changing the tooth-count ratio. This distinction matters when comparing a geared motor with a direct drive.
Work backward from the driven machine's required speed, then compare the calculated tooth count with practical gear pairs. Rounding a tooth count changes the achievable ratio, so use the reported achieved speed rather than the original target. A simple idler between two gears changes the arrangement and direction but does not create another independent reduction. A compound stage, with two gears fixed to one shaft, does. Keep track of which shafts carry each gear before multiplying stage ratios or interpreting an additional-stage input.
Formula
Ratio = driven / driver. Output RPM = input RPM / ratio. Output torque = input torque × ratio × efficiency.