Gear Ratio Calculator
Gear ratios multiply rather than add, which is why a compact gearbox can turn a fast motor into something that moves very slowly and very hard. Two three-to-one stages give nine to one, not six. This builds random gear trains, works out the overall ratio and the resulting output speed, and checks the answer by multiplying it back to see if the input speed reappears.
What this generator does
Generates gear stages with realistic tooth counts, computes each stage's ratio as driven over driver, multiplies them into an overall ratio, and derives the output speed and the torque multiplication that comes with it. The check multiplies the output speed by the ratio and requires the input speed back.
How to use this tool
- Choose how many stages and the input speed in rpm.
- Read each stage's tooth counts and its individual ratio.
- Check the overall figure is the product of the stages, not the sum.
- Note that whatever happens to speed happens inversely to torque.
Understanding the controls
- How many stages
- Between 1 and 4 gear pairs in series. Each stage multiplies the ratio so far, which is how large reductions are built compactly.
- Input speed
- The speed driving the first gear, in rpm. The output scales inversely with the overall ratio.
- Seed
- Any word reproduces exactly the same tooth counts and the same ratio.
Common use cases
- Working out the output speed of a multi-stage gearbox
- Teaching why gear ratios compound
- Generating practice problems with tooth counts and known answers
- Sizing a reduction for a motor and a target speed
- Setting the same gear train twice from a seed
How this generator works
A single stage's ratio is the driven gear's tooth count divided by the driver's, and stages in series multiply. Speed divides by the overall ratio while torque multiplies by it, because power is speed times torque and gears do not create power. The check does not recompute the ratio the same way — it takes the reported output speed, multiplies by the reported ratio, and requires the input speed to reappear.
Randomness and fairness
The tooth counts are chosen randomly to give a varied train; the ratios and speeds are then deterministic. A seed reproduces the same train exactly and is therefore explicitly not cryptographically secure. Without a seed the browser's cryptographically secure generator is used.
For how randomness is produced across the whole site, see how Generate Random works.
Limitations and good to know
- Ideal gears: no friction, backlash or efficiency loss, so real torque will be lower than the figure shown.
- Idler gears reverse direction without changing the ratio, and are not modelled.
- Tooth counts are random rather than chosen for a target ratio.
- No check that the tooth counts are physically compatible in module or pitch.
- Trains are not stored between visits; seed one you want again.
Privacy and your data
The gear train and its ratios are computed in your browser. Nothing about the train or your seed is transmitted or kept.
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