By Blake Flournoy
Updated Aug 30, 2022
DragonImages/iStock/GettyImages
Planetary, or epicyclic, gear systems are a cornerstone of modern engineering. Their compact, single‑axis design allows precise speed control and is employed in applications ranging from automotive automatic transmissions and industrial mixers to surgical tables and solar‑panel trackers.
To compute a planetary gear ratio, first determine the tooth counts on the sun and ring gears. Add them together to obtain the combined tooth count of the planetary gears. Then, depending on whether the carrier is the input, output, or remains stationary, divide the appropriate driven tooth count by the driving tooth count. A calculator can simplify the final step.
Begin by noting the number of teeth on the sun gear and the ring gear. The sum of these two numbers equals the total tooth count of each planetary gear that meshes with the carrier. For example, if the sun gear has 20 teeth and the ring gear 60 teeth, each planetary gear will have 80 teeth. From there, the calculation is consistent across all configurations.
When the carrier serves as the input, the ring gear rotates while the sun gear remains fixed. Divide the number of teeth on the ring gear (driven) by the number of teeth on the planetary gears (driving). Using the example above:
60 ÷ 80 = 0.75 → 3:4
If the carrier is the output, it is driven by the rotating sun gear while the ring gear stays stationary. Here, divide the planetary gear teeth (driven) by the sun gear teeth (driving). With the same example:
80 ÷ 20 = 4 → 4:1
When the carrier does not move, the ring gear drives the sun gear. The ratio is calculated by dividing the sun gear teeth (driven) by the ring gear teeth (driving). For our example:
20 ÷ 60 = 0.333… → 1:3
