Planetary Gear Sizing: Calculating Ratios in Automatic Transmissions

Planetary (epicyclic) gear sets are the core components of automatic transmissions. Unlike manual gearboxes that slide gears along shafts, planetary systems keep all gears in constant mesh, using clutches and bands to hold different components stationary.

The Three Elements of a Planetary Set

A planetary gear set consists of a central sun gear, multiple planet gears mounted on a carrier, and an outer ring gear. By holding one component stationary and driving another, you can achieve different gear ratios and directions.

Formulas for Ratios

When the ring gear is held stationary and the sun gear is the driver, the carrier rotates in the same direction with a reduction ratio calculated by:

$$\text{Ratio} = 1 + \frac{\text{Teeth on Ring Gear}}{\text{Teeth on Sun Gear}}$$

Determine transmission gear dynamics using our interactive automotive gear ratio calculator. For motorcycle chains and sprockets, refer to our sprocket and chain ratio guide.