The ratio: trading speed for torque

A 1750 RPM motor and a conveyor that needs 580. Between them sits the oldest machine element there is — two wheels and a ratio — and one rule that never breaks.

The ratio is pure geometry

Divide the driven size by the driver size — diameters for pulleys, tooth counts for gears:

• 4" pulley driving a 12" pulley → 3:1.
• 15-tooth gear driving a 45-tooth gear → 3:1.

The belt travels at one speed, so the small wheel must turn three times for every turn of the big one. That's the whole mechanism.

The trade

The drive can't create power — power in equals power out (minus a little friction), and power is speed × torque. So the ratio divides one and multiplies the other:

Slow and strong, or fast and weak — pick one. Gearboxes, sheave swaps, and bicycle gears are all this same trade at different sizes.

Reading it in the field

Two habits worth having:

• Ratio over 1 = speed reducer (most industrial drives — motors spin faster than loads want). Under 1 = overdrive.
• Swapping a sheave changes both numbers at once. Bigger driven pulley: slower, stronger. Bigger driver: faster, weaker.

Run your own drive in the pulley & gear ratio tool — it also estimates the belt length for the sheave pair and center distance.

Why this matters

Half the mechanical questions on a floor — why is this shaft slow, what sheave do I order, can this drive turn that load — are this one ratio asked different ways. Next: choosing what connects the two wheels.