CNC / machinist calculator
Gear Ratio Calculator
Work out a gear ratio from the tooth counts and see exactly what it does to speed and torque. Enter the driving and driven gear teeth and the calculator returns the reduction ratio, then applies it to an input speed and torque so you can see the trade in real numbers. For a gearbox or a lathe change gear set you can chain several stages together and read the overall ratio of the whole train at once.
- Output speed
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- Output torque
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How it works
A gear ratio compares the driven gear to the driving gear by tooth count. A small gear driving a large one is a reduction: the output turns slower and pushes harder. The ratio is simply the driven tooth count divided by the driving tooth count, so a ten-tooth gear driving a forty-tooth gear is a four to one reduction.
Speed and torque move in opposite directions through the ratio, ignoring friction. The output speed is the input speed divided by the ratio, and the output torque is the input torque multiplied by the ratio. A four to one reduction therefore quarters the speed and quadruples the torque, which is why reductions are used to turn a fast, weak motor into a slow, strong output.
A gear train made of several meshes multiplies its stage ratios. Two stages of two to one and three to one combine to six to one overall. Idler gears between stages change direction but not the ratio, so they drop out of the multiplication.
Worked example
A 10-tooth gear driving a 40-tooth gear is a 4 : 1 reduction: a 1000 RPM input turns the output at 250 RPM, with four times the torque.
Frequently asked questions
How do I calculate a gear ratio?
Divide the driven gear tooth count by the driving gear tooth count. A ten-tooth gear driving a forty-tooth gear gives a ratio of four, written four to one, which is a speed reduction and a torque increase.
Does a gear reduction increase torque?
Yes. A reduction trades speed for torque. The output torque is the input torque multiplied by the ratio, so a four to one reduction roughly quadruples torque while quartering the output speed, minus small friction losses.
What does an idler gear do to the ratio?
An idler gear sits between the driver and the driven gear and reverses the direction of rotation, but it does not change the overall ratio. Its tooth count cancels out, so only the first and last gears set the ratio.
How do I find the ratio of a multi-stage gear train?
Multiply the ratios of each stage together. A first stage of two to one followed by a second stage of three to one produces an overall ratio of six to one between the input and the final output shaft.
Is gear ratio the same as the speed ratio?
They are inverses. A four to one gear reduction is a one to four speed ratio, because the output turns a quarter as fast. People usually quote the gear ratio as the larger number for a reduction to emphasise the torque gain.
Related calculators
Sources
Every formula on this page is shown and sourced. See how we verify.
These calculators are for planning and as a starting point. Recommended speeds and feeds are published starting values that vary with your specific tool, coating, machine rigidity, workholding and coolant. Always start conservative, listen to the cut, and follow your tool maker data sheet.