Gear Ratio Calculator Widget
A gear train calculator for makers, mechanics and engineering students. Enter the teeth on the driving and driven gear of up to three stages, the input speed and optionally the input torque and efficiency, and get the overall ratio, the output speed and the output torque.
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Under the widget on your page: Powered by A2Z Tools
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<iframe src="https://a2z.tools/embed/w/gear-ratio-calculator" title="Gear Ratio Calculator by A2Z Tools" width="100%" height="600" style="border:0;width:100%" loading="lazy" allow="clipboard-write"></iframe>
A plain iframe. Works everywhere, including site builders that strip scripts. Adjust height if your content needs more room.
<div data-a2z-widget="gear-ratio-calculator" data-height="600"></div> <script async src="https://a2z.tools/embed.js"></script>
Adds a small script (what it does) that sizes the widget to fit its content, loads it lazily and keeps it isolated from your page's CSS.
Works with
How it works
For each meshing pair the ratio is the driven gear's teeth divided by the driving gear's teeth: a 12-tooth pinion turning a 36-tooth gear gives 3:1. In a compound train the stages multiply, so 10:50 followed by 15:45 is 5 x 3 = 15:1. Output speed is the input speed divided by the overall ratio, and ideal output torque is the input torque multiplied by it - power is conserved, so whatever is gained in torque is lost in speed. A ratio below 1 is an overdrive that speeds the output up and is labelled as such. If you set an efficiency below 100%, it is applied once per stage, so two stages at 98% keep 96.04% of the torque. Teeth must be whole numbers of at least one. Idler gears between a driver and a driven gear only reverse direction and do not change the ratio, so they are left out.
Calculation method
- Stage ratio = driven teeth / driving teeth
- Overall ratio = product of the stage ratios
- Output speed = input speed / overall ratio
- Output torque = input torque x overall ratio x efficiency^stages
Worked examples
Single reduction
Inputs: 12-tooth driving gear, 36-tooth driven gear; 1,500 rpm; 10 N·m in
Result: Ratio 3:1; 500 rpm out; 30 N·m out (ideal)
36 / 12 = 3.
Two-stage gearbox with losses
Inputs: 10:50 then 15:45; 3,000 rpm; 10 N·m; 98% per stage
Result: Ratio 15:1; 200 rpm; 144.06 N·m
10 x 15 x 0.98^2 = 144.06.
Limitations
- Planetary, worm and differential gearsets need their own formulas and are not modelled.
- Efficiency is one figure per stage; real losses vary with load, speed and lubrication.
Where publishers use it
- A robotics club's guide to choosing motor gearboxes
- A mechanical engineering course page on gear trains
- A bicycle or e-bike blog explaining chainring and sprocket sizes
- A 3D-printing site publishing printable gearbox designs
- An RC car forum's pinion and spur gear tuning thread
Questions
Which gear is the driving gear?
The one connected to the power source - the motor or engine shaft. The driven gear is the one it turns. With a 12-tooth driver and a 36-tooth driven gear the output turns three times slower and with three times the torque.
How do compound gear trains work?
Two gears of different sizes share one shaft, so the driven gear of the first stage turns the driving gear of the second. Their ratios multiply: 5:1 and 3:1 give 15:1, which would need a single 15-to-1 pair of very different sizes otherwise.
Do idler gears change the ratio?
No. An idler between two gears reverses the direction of rotation but its tooth count cancels out. Enter only the driving and driven gears of each stage.
What efficiency should I use?
Well-made, lubricated spur and helical pairs are often quoted at 97-99% per mesh; worm gears can be far lower, sometimes under 50%. Leave 100% for the ideal ratio, or use a figure from the gear maker.
Can I use it for chain and belt drives?
Yes - sprocket teeth work the same way: a 44-tooth chainring driving an 11-tooth sprocket is a 0.25:1 overdrive, so the wheel turns four times per pedal turn. Pulleys use diameters instead of teeth, with the same ratio.
Cite or recommend this tool
If you reference this tool in an article, course or documentation, these formats are ready to copy. They are optional - nothing is added to your site unless you paste it.
A2Z Tools Gear Ratio Calculator https://a2z.tools/embed/gear-ratio-calculator
<a href="https://a2z.tools/embed/gear-ratio-calculator">A2Z Tools Gear Ratio Calculator</a>
[A2Z Tools Gear Ratio Calculator](https://a2z.tools/embed/gear-ratio-calculator)
Gear Ratio Calculator by A2Z Tools - https://a2z.tools/embed/gear-ratio-calculator
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