Almost all electric motors are used in conjunction with gearboxes. The reason for this is the electric motors produce relatively low torque. They not particularly strong. However, they are capable of rotating very very quickly. So we can use a gearbox to trade off speed for torque. Of course, there is no such thing as a free lunch and a gearbox introduces some inefficiency, there is some lost of power. That power lost is in terms of heat and acoustic noise.
If you use a bicycle you are probably quite familiar with the concept of gearing. Electric motors are capable of spinning very very quickly but they don't produce very much torque they are kind of weak.
Now it's a bit like the problem of riding your bicycle uphill. You want to trade off a large number of rotations of the pedals in order to reduce the load that you have to exert on those pedals. You are trading off a lot of speed for a large amount of torque.
For an electric motor it's the same thing and as with the bicycle you have a small sprocket at the front on the pedals, and you have a larger sprocket on the back wheel. So for every rotation of the electric motor, we only have half a rotation of the output shaft of the motor's gearbox. So the motor is spinning quite quickly, the output shaft is rotating rather slowly but the torque of the motor is amplified by the gear ratio.
Here we have a motor with a single stage reduction gearbox. We call it a reduction gearbox because for every rotation of the motor, the output shaft rotates less than once. When we refer to the two sides of the gearbox we refer to as the motor side which indicated by the subscript M and the load side indicated the subscript L. The ratio of the gearbox is capital G and that's the ratio of the number teeth on the big wheel to the number teeth on the little wheel. And for a reduction gearbox G is greater than one.
The output speed omega L is equal to 1 on G times omega N. So the output shaft speed is lower than the motor speed. The output torque tau L is equal to G times the motor torque tau M so the output torque is greater than the motor torque. These are the fundamental equations that describe the characteristics of a gearbox. It reduces the speed and it increases the torque.
Electric motors are typically quite weak, they produce a low torque, so it’s very common to add a reduction gearbox.
High school mathematics
This content assumes an understanding of high school-level mathematics, e.g. trigonometry, algebra, calculus, physics (optics) and some knowledge/experience of programming (any language).