How to use the gear ratio calculator
Use this calculator to understand how a simple external gear pair or a compound train changes rotational speed. It is useful for checking classroom examples and comparing ideal tooth-count combinations before detailed mechanical design. The driver receives rotation; the driven gear receives motion from that driver. The ratio here is input speed divided by output speed, so a value above one means a reduction in speed.
- Choose one, two or three stages. Enter the input shaft speed in revolutions per minute (RPM), then the driver and driven tooth counts for each active stage. Hidden stages are excluded. For a compound train, the driven gear of one stage is fixed to the same shaft as the next stage’s driver. This is different from a row of simple idler gears.
- Optionally enter a wheel diameter in millimeters if a wheel is fixed directly to the final output shaft. Leave it blank to calculate gears only. Press Calculate, or press Enter in an input field. Read the total ratio, final RPM, direction and connected stage diagram. Editing an input immediately updates the preview when valid and invalidates the confirmed result; calculate again to confirm it. Clear empties all numeric fields and disables copying.
How the ratio and output speed are calculated
For one pair, i = Zdriven / Zdriver and nout = nin / i. For multiple compound stages, multiply the individual ratios: itotal = i₁ × i₂ × i₃, including only selected stages. The diagram shows each pair’s tooth counts and input and output RPM, so you can follow how the intermediate shaft speed becomes the next stage’s input.
An external gear mesh reverses rotation. One or three stages turn opposite to the input; two turn in the same direction. The animation assumes clockwise input and slows all shafts by the same factor so their speed ratios remain visible. At zero input RPM there is no motion. Pitch-circle sizes are proportional to tooth counts within each pair except where extreme proportions need compression for visibility. The tooth outlines are schematic, not manufacturing geometry.
For a directly attached wheel, v = nout × π × d × 60 / 1,000,000 gives km/h when d is in mm. This is a rolling-speed estimate with no slip. It does not account for tire deflection, gearing after the output shaft, traction, load or any actual vehicle operating limit.
Two worked examples
Reduction: a 20-tooth driver and 60-tooth driven gear at 1,200 RPM give 3 : 1 and 400 RPM, opposite to the input. With a 500 mm output wheel, the theoretical speed is 37.70 km/h (displayed as 37.7). Adding a second stage of 20 teeth driving 40 gives 6 : 1 overall and 200 RPM in the same direction as the input.
Speed increase: a 60-tooth driver and 20-tooth driven gear at 900 RPM give about 0.33 : 1 and 2,700 RPM. The internal ratio remains exactly the floating-point value of one third; the rounded display is never fed back into subsequent calculations. Leaving the wheel blank suppresses only wheel speed, not the gear results.
Input limits, precision and copying
Tooth counts must be integers from 1 through 10,000. Input RPM may be zero through 1,000,000,000. Optional wheel diameter must be positive and at most 1,000,000 mm. These are calculator bounds, not recommendations for realizable hardware. Use a decimal point or comma without thousands separators; do not append units. Scientific notation is accepted for numeric values, provided tooth counts still resolve to whole numbers.
Ordinary results use up to two decimal places and omit trailing zeros. Very small nonzero results and very large results use scientific notation so a nonzero speed or ratio is not falsely shown as zero. Copy result copies the displayed values and stage details as plain text. No file is saved automatically. Language switching reloads the page; record your result before changing language.
Frequently asked questions
Does this calculate torque or efficiency?
No. It calculates ideal speed relationships only. Losses, torque capacity, tooth contact, material strength and safe operating speed require additional information and are outside this tool.
Can I use it for planetary gears or chains?
The connected drawing and direction logic describe external gear pairs on parallel shafts. Planetary sets, internal gears, worm drives and chain paths do not follow this exact model. Do not interpret their directions from this drawing.
Why does a larger driven gear rotate more slowly?
Each revolution of the larger gear needs more teeth to pass the contact point. At the same tooth-passing rate, its shaft makes fewer revolutions. Reversing the driver and driven counts reverses the speed relationship.
Why is an extra idler not another reduction stage?
A simple idler passes motion onward and its tooth count cancels from the overall speed ratio. Here every added stage is a compound pair with two gears fixed on the intermediate shaft. Model that arrangement only.