Gear Ratio Calculator

A gear ratio compares the rotational relationship between a driving gear and a driven gear. For a simple pair of external gears, divide the driven gear tooth count by the driver gear tooth count. A 12-tooth driver turning a 48-tooth driven gear produces a ratio of 4 to 1. The driven shaft completes one revolution while the driver completes four. This calculator also divides input speed by that ratio to estimate theoretical output speed. A ratio greater than one is a speed reduction. The driven shaft turns more slowly but can deliver proportionally greater torque before losses. A ratio below one is a speed increase: the driven gear rotates faster, while available output torque falls. Meshing external gears also reverse rotational direction. An idler gear may change direction or spacing, but it does not change the overall numerical ratio unless it is part of a compound gear arrangement. Tooth counts provide the most convenient ratio calculation because meshing gears share the same tooth pitch. Pitch diameters can be used instead when both gears have compatible geometry. In a compound train, calculate each driving-to-driven stage ratio and multiply the stage ratios. Planetary gearsets require a different relationship involving the sun, ring, carrier, and which member is fixed, so a simple two-gear result should not be applied directly. The calculated speed is ideal. Real transmissions experience friction, tooth deformation, bearing drag, lubricant losses, backlash, and load-dependent slip elsewhere in the drivetrain. Those losses affect efficiency and delivered torque, although a properly engaged gear pair maintains nearly the same speed ratio. Confirm that selected gears share module or diametral pitch and a compatible pressure angle. Designers should also check tooth strength, contact stress, lubrication, alignment, center distance, shaft loading, and safe operating speed. Use this result as a clear kinematic starting point, then apply appropriate mechanical design and safety factors.