Calculate gear ratios for gear trains and planetary systems. Visualize meshing gears with animated rotation at correct speed ratios.
Enter tooth counts and an input RPM; the tool returns the gear ratio, the output speed, and the torque the train would deliver, then animates the meshing gears turning at exactly proportional rates so the result is visible. Simple two-gear trains, multi-stage compounds, and a planetary mode with sun, ring, and carrier are covered. The surprise for most users is direction: the tool writes the ratio as driven teeth over driver teeth, so 2:1 is a reduction that halves speed and doubles torque, while 1:2 is a speed increase.
A concrete input and expected output from the current implementation.
Input
Driver: 20 teeth at 300 RPM. Driven: 40 teeth.
Expected output
Gear ratio 2:1 (reduction). Output speed 150 RPM. Torque multiplied by 2 (ideal, no losses).
The ratio is driven teeth over driver teeth, 40/20 = 2. Speed divides by the ratio, 300/2 = 150 RPM, and because power is conserved in an ideal train, torque multiplies by it, so 5 Nm in becomes 10 Nm out.
For a meshing pair the speed ratio is the inverse of the tooth-count ratio: output RPM equals input RPM times driver teeth divided by driven teeth. The tool reports the ratio as driven over driver, so values above 1 are reductions. In a compound train the overall ratio is the product of the stage ratios, and an idler gear between driver and driven changes only the rotation direction, never the ratio.
Planetary mode applies the Willis relation, (sun speed minus carrier speed) over (ring speed minus carrier speed) equals minus ring teeth over sun teeth. You hold one member fixed and supply the speed of another; the tool solves for the third, for each fixed-member choice. The sign of an answer is the rotation direction: with the carrier locked the sun and ring turn opposite ways, so a negative speed is correct, not an error.
Slower at the output, with more torque. In the driven-over-driver convention used here, 4:1 means four input turns for each output turn: speed divides by four and torque multiplies by four. Some catalogs write input-over-output instead, where 4:1 would be a speed increase, so confirm the convention before trusting any ratio number.
The sign is the rotation direction. With the carrier locked, the sun and ring turn in opposite directions by geometry, so one of the two speeds is genuinely negative. With the ring locked, all three members rotate the same way and nothing is negative. A minus sign is expected behavior; a surprising sign usually means the wrong member is fixed.
The example and behavioral notes were checked against the browser implementation. Standards and primary references below define the relevant format, formula, or platform behavior.
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