Gearboxes are complex systems primarily composed of gears housed in a box, and their calculations revolve around the gear ratios determined by the number of teeth on each gear. For example, a gear with 100 teeth driving a gear with 50 teeth results in a 2:1 ratio, affecting both speed and torque. When multiple gears are involved, the ratios can be compounded, but efficiency losses due to friction must be considered. Key factors in gearbox design also include heat control, lubrication, and shifting mechanisms. Understanding these principles is essential for effective gearbox calculations and applications, such as with a 12V stepper motor.