Gear Ratio Calculator
Work out a gear ratio from tooth counts or pulley sizes, then the output speed and torque for a motor RPM, across one stage or a whole gear train. Works from tooth counts, pulley diameters or known ratios, with an optional efficiency per stage.
Your numbers
The driver is the gear on the input side (the motor or the shaft before it), the driven gear is the one it turns.
Optional: the motor or engine speed, for the output speed.
Optional. Blank means no losses. One spur, helical or bevel gear mesh is about 98 to 99% (RoyMech); use the gearbox maker's figure where you have it.
Optional: the torque going in, for the output torque.
Overall ratio
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- Output speed
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- Output torque
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- Output turns
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Idler gears between a driver and a driven gear do not change the ratio, only the direction: count the first and last gear as one stage.
Output torque is what the gears deliver; check it against the gearbox, shaft and coupling ratings.
The calculation runs in your browser and ParrotNotes does not store your numbers. They sit in the page address so you can bookmark or share the result.
How a gear ratio is worked out
Two meshing gears move the same number of teeth past each other, so the gear with more teeth turns fewer times. The ratio is the driven gear's teeth over the driver's: 42 teeth driven by 13 is 3.23 : 1. The same holds for the pitch radii, which is why a belt drive's ratio comes from the pulley pitch diameters, with belt slip left out.
A ratio above 1 is a reduction: the output turns slower and, with the same power going through, harder. Below 1 is an overdrive. The calculator shows which, and how each stage contributes.
Output speed and torque
Output speed is the input speed divided by the ratio. Output torque is the input torque times the ratio: with no losses, the torque ratio of a gear train equals its speed ratio, which is also its mechanical advantage.
Real gears lose a little to friction at every mesh. Enter an efficiency per stage and the calculator multiplies it once per stage before it scales the torque; the speed does not change. Leave the field blank for the ideal figure.
Gear trains, idlers and direction
In a compound train, two gears share a shaft and each pair is one stage: the total reduction is the product of the stage ratios. Three stages of 3 : 1 are 27 : 1. Pick up to four stages; for known ratios, such as a transmission gear and an axle, choose "Known ratios" and enter each one.
An idler gear between a driver and a driven gear leaves the ratio unchanged; it only reverses the direction. Each external gear pair reverses the rotation, so one or three stages turn the output the opposite way and two or four the same way. An open belt keeps the direction.
Efficiency per stage
RoyMech's efficiency table gives one mesh of spur, helical, double helical or bevel gears 98 to 99% from tooth friction, crossed helical gears 70 to 98% and worm gears 20 to 98%, depending mostly on the lead angle. For a drive train, the efficiencies of each mesh are multiplied together: two pairs at 90% give 81%.
Those are tooth-friction figures. Bearings, seals and oil churning add losses, so a whole gearbox does a little worse. When the gearbox is bought, its catalogue efficiency is the number to use.
For power transmission sales and sales engineers
A gearbox or drive is sized from the application: motor speed and power, the output speed and torque the machine needs, the duty, the mounting. Most of that comes in on a call or a plant visit, and a wrong number there means the wrong reducer on the quote.
Sources, each read on 2026-10-29. Results are estimates for sizing and quoting; the gearbox or drive maker's ratings decide the final selection:
More for manufacturers' reps and sales engineers: Sales engineer, Manufacturers' rep, Industrial distributor sales, Selling to engineers.
The application comes in on the call
Motor speed, the output speed and torque the machine needs, the duty and the mounting are all said on the call before a spec sheet arrives. Record it in ParrotNotes and get a transcript, a summary and the action items, so the drive you quote matches the application.
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