Pulley & gear ratio
Belt or gears: enter driver and driven sizes and get the ratio, output speed, torque multiplication and belt length.
Result
What you give up in speed you gain in torque: the ratio divides one and multiplies the other. Free lunch not included — that's the whole deal of power transmission.
How is this calculated?
Using the tool
The drive-train trade in one calculator: pick belt or gears, enter the driver and driven sizes, and read the ratio, output speed, torque multiplication, and belt length — with the schematic showing which way everything turns.
The mechanics
A drive transmits power, and power is speed × torque — so whatever the ratio does to one, it must undo on the other. The ratio itself is pure geometry: driven ÷ driver (diameters for pulleys, tooth counts for gears). A 4" pulley driving a 12" pulley is 3:1 — the motor's 1750 RPM becomes 583 RPM, and every ft·lb of motor torque becomes three at the shaft (minus a few percent of belt losses in real life). Belts keep both shafts turning the same way; a meshed gear pair reverses, which is why idler gears exist. The belt-length formula is the standard shop approximation — order the nearest stock size.
New to the math? Learn the concept: Industrial mechanic fundamentals