Gear ratio calculator

Why tooth count determines speed

Put a paint mark on one tooth of a small gear and turn it once. Every tooth on that gear passes the contact point. If it has 15 teeth, it advances the larger gear by exactly 15 teeth. A 45-tooth wheel therefore turns one third of a revolution. Looking at both gears from the same side, their shafts rotate in opposite directions.

Here gear ratio means driven teeth divided by driver teeth. A 3:1 reduction takes three turns of the input for one turn of the output. Output speed equals input speed divided by this ratio. You can check which way round your fraction goes by asking which wheel should turn more slowly.

Design a model winch

A motor runs at 600 revolutions per minute. The drum should turn at 200 rpm. Divide 600 by 200 to find the required reduction of 3:1. A 15-tooth driver and 45-tooth driven gear are one possible pair. A 20-tooth driver with a 60-tooth driven gear gives the same shaft speeds but needs more space if the teeth are the same size.

In an ideal gear pair the slower output delivers proportionally more torque. At 3:1, a motor supplying 0.2 N·m would deliver 0.6 N·m at the drum before losses. Bearing friction and contact losses reduce the torque available in a real mechanism. The actual motor speed also depends on its load.

Add or remove an idler

Between two external gears, an extra freely rotating gear reverses the direction once more. The first wheel still advances one tooth at each contact for every tooth it moves. Its final speed ratio therefore depends only on the first and last tooth counts. A compound train is different. On a shared shaft two wheels with different tooth counts can turn together, allowing reductions to multiply.

Try a prediction. Swap the 15 and 45 tooth wheels. At 600 rpm input, the smaller output should now make 1,800 rpm. Would that be a sensible change for a winch that already struggles to lift its load? Relate your answer to the turning effect in the mechanics lesson.