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Count the teeth

The smaller gear of a pair is the pinion. Which shaft it sits on decides whether you gain turning force or gain speed.

The smaller of a gear pair is called the pinion. Britannica Scholars: gear If the pinion is on the driving shaft, the pair acts to reduce speed and to amplify torque. Britannica Scholars: gear If the pinion is on the driven shaft, the pair acts as a speed increaser and a torque reducer. Britannica Scholars: gear

If the driven gear has twice as many teeth as the pinion, the torque of the driven gear is twice the pinion torque, and the pinion speed is twice the speed of the driven gear. Britannica Scholars: gear

Try a pair. The example from Britannica uses a driven gear with twice as many teeth as the pinion.

This is an ideal pair, with no friction or other losses. Real gears waste a little energy as heat and noise.

Teeth and radii

Britannica counts teeth to explain how a pair trades speed for turning force. OpenStax gives the mechanical advantage of wheels and gears as the ratio of the radii, written ri/r0. For ordinary circular gears the two pictures agree, because the number of teeth is proportional to the radius; they are two ways of writing the same trade-off.

OpenStax writes the same trade-off as a ratio of radii. See mechanical advantage.