Set teeth counts for a simple (1-stage) or compound (2-3 stage) external gear train and watch the gears spin at the correct relative speed and direction, with live output RPM, gear ratio, and output torque.
This simulator animates a simple or compound external gear train — up to three meshing stages — rotating at the correct relative speed and direction, and computes output RPM, overall gear ratio, output torque, and rotation direction from the teeth counts you choose at each stage.
For any two meshing gears, the ratio of angular velocities is inversely proportional to their teeth counts: ω_driven/ω_driver = N_driver/N_driven. A small driver gear meshing with a large driven gear reduces speed and increases torque; a large driver meshing with a small driven gear increases speed and reduces torque. In a compound gear train, the driven gear of one stage shares a rigid shaft with the driver gear of the next stage (same speed, same direction), so overall speed reduction is the product of each stage's individual ratio: total ratio = Π(N_driven,i / N_driver,i).
Ignoring losses, power is conserved through a gear train: P = T·ω stays constant across a mesh, so as speed drops by the gear ratio, torque rises by that same ratio — output torque = input torque × overall ratio. Real gear meshes lose a small percentage of power to friction (typically 1-2% per mesh for well-lubricated spur or helical gears), so overall efficiency compounds multiplicatively across stages: a 3-stage train at 98% per mesh only retains 0.98³ ≈ 94.1% of input power, meaning output torque is slightly less than the ideal ratio would suggest.
When two external gears mesh (their teeth on the outside of each gear, the common configuration), their pitch circles roll against each other like two wheels touching side by side — this forces them to spin in opposite directions, exactly like adjacent bicycle chain sprockets. Each additional external mesh flips the direction again, so an odd number of stages reverses the output direction relative to the input, while an even number of stages restores the original direction. (Internal gear meshes — a small gear inside a ring gear — behave differently and do not reverse direction, but are not modeled by this simulator.)
A simple gear train has each gear on its own separate shaft, meshing in a single-file chain — adding "idler" gears in between changes direction at each mesh but does not change the overall speed ratio (only the first and last gear teeth counts matter for the ratio). A compound gear train has two or more gears rigidly fixed to the same shaft, so that shaft's driven gear from one stage becomes the driver for the next stage at the same speed — this is what actually multiplies the ratio across stages, enabling large speed reductions (or increases) in a compact space, as modeled by this simulator.
This follows directly from conservation of power (ignoring friction losses): power P = torque × angular velocity must stay constant across an ideal gear mesh. If a gear train reduces angular velocity by a factor of 3, torque must increase by that same factor of 3 to keep power constant — this is the entire reason gear reducers exist on motors: to trade rotational speed for higher usable torque.
Each individual gear mesh typically loses 1-2% of transmitted power to friction between meshing teeth, bearing drag, and lubricant churning, for a per-mesh efficiency around 98-99% in a well-designed spur or helical gear set. Because these losses compound multiplicatively, a train with several stages accumulates more loss: at 98% per mesh, a single-stage train retains 98% of input power, while a three-stage train retains only 0.98³ ≈ 94%, and a five-stage train around 0.98⁵ ≈ 90%.
Yes — for any pair of external spur or helical gears meshing directly with each other, the output shaft always rotates opposite to the input shaft, because their pitch circles roll against each other like two coins pressed edge to edge. This is different from a belt-and-pulley drive (same direction, unless the belt is crossed) or an internal ring-gear mesh (same direction as the internal pinion), so direction tracking always has to account for how many external meshes the power actually passes through.
Try our Mechanical Studio
More calculators, simulators, and guides for this discipline.