Gear Ratio Calculator

Enter the tooth counts of the driving (input) and driven (output) gears, plus the input speed and torque, and this calculator gives the gear ratio, output RPM, output torque and mechanical advantage. It is used for sizing gearboxes and reduction drives, choosing sprockets, checking an axle's final drive ratio, and working out belt-and-pulley speeds.

The same calculation works for pulleys and V-belt sheaves: enter the pulley diameters instead of tooth counts, in any unit as long as both match. A ratio above 1 is a reduction (slower, more torque); below 1 is an overdrive (faster, less torque); exactly 1 changes nothing but direction.

Results are ideal values. Real gear trains lose a little power at each mesh to friction, so actual output torque is slightly lower than shown, while speed is set exactly by the tooth counts. Belts can also slip slightly under load. For turning torque and RPM into power, use the horsepower from torque calculator.

This follows from conservation of power (power = torque × angular speed) as covered in standard machine-design texts such as Shigley's Mechanical Engineering Design. For multi-stage trains, multiply the stage ratios: a 3:1 stage followed by a 4:1 stage is 12:1. Idler gears between driver and driven do not change the ratio, only the direction. For an axle final drive, the driving gear is the pinion and the driven gear is the ring gear; the overall ratio in any gear is the transmission ratio × the final drive ratio.

To pick a pulley, rearrange the formula: driven diameter = driving diameter × motor rpm ÷ target rpm. The table assumes a 4 in driving pulley on a 1,750 rpm motor (a common 4-pole speed on 60 Hz supplies). Use pitch diameters for V-belt sheaves — the diameter where the belt rides, which is smaller than the outside diameter — and expect the actual speed to be slightly lower because of belt slip.

• Gears: two meshing external gears turn in opposite directions. Add an idler to keep the direction, or use an internal (ring) gear.
• Chains and sprockets: count sprocket teeth just like gears; both sprockets turn the same way. A motorcycle with a 15-tooth front and 45-tooth rear sprocket has a 3:1 secondary ratio.
• Pulleys and sheaves: use diameters. The ratio is identical in metric or inches as long as both pulleys use the same unit.
• Bicycles: the chainring drives and the rear cog is driven, so a 50-tooth chainring on a 25-tooth cog gives 0.5 in this calculator — one pedal turn spins the wheel twice. Cyclists usually quote it the other way up (chainring ÷ cog = 2.0).
• Worm gears: the ratio is worm-wheel teeth ÷ number of worm starts, and efficiency is much lower than for spur gears, so the torque output here will be optimistic.

A numerically higher final drive (for example 4.10 instead of 3.55) multiplies torque more, which helps towing and acceleration, but the engine turns faster at a given road speed, which usually costs fuel economy and adds noise. A lower ratio does the opposite. Changing tire size has a similar effect — larger tires behave like a lower ratio — which is why regearing often follows a tire upgrade. Check the effect on your speedometer with the tire size calculator, and work out wheel torque from engine output with the torque calculator.