What are gearbox ratios?

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I often see ratios for the specs of gearboxes like 4:1, 7:1, 30:1. What does this mean?

In: Engineering

It’s the ratio between the number of teeth on the input gear to the number of teeth on the output gear.

For a ratio of 4:1 (4), the output gear will complete 4 revolutions for each revolution of the input gear.

For ratios where the input gear has more teeth than the output, speed will increase at the cost of torque. If the input gear has less, torque will increase at the expense of speed.