Gear Ratio & Output Speed Calculator
Enter the driver and driven tooth counts with the input speed to find the gear ratio, the output rpm, and — if you add an input torque — the torque delivered at the output shaft.
Drive output
How the calculation works
The ratio is simply driven teeth divided by driver teeth. Output speed is the input speed scaled by the inverse of that ratio — driver over driven — so a larger driven gear always turns more slowly. Output torque is the input torque multiplied by the ratio, capturing the speed-for-torque trade that gearing exists to provide.
The same ratio is reported as the mechanical advantage, since it tells you how much the pair multiplies turning force. Values are rounded for readability, and the output-torque field stays blank until you supply an input torque.
Frequently Asked Questions
How is the gear ratio calculated?
For a single meshing pair the gear ratio is the number of teeth on the driven (output) gear divided by the number on the driver (input) gear. A 12-tooth driver turning a 36-tooth driven gear gives a ratio of 3, usually written 3:1. Because tooth spacing is identical on meshing gears, comparing tooth counts is exactly the same as comparing pitch diameters.
Why does a reduction slow the output but increase torque?
Energy is conserved, so power in roughly equals power out. Power is speed times torque, which means if a gear pair divides the speed by three, it multiplies the torque by three (minus small losses). That is why the gear ratio is also called the mechanical advantage — a reduction is the standard way to turn a fast, low-torque motor into a slow, high-torque drive.
What is the difference between a reduction and an overdrive?
When the driven gear has more teeth than the driver, the ratio is greater than one: output speed drops and torque rises — a reduction. When the driven gear is smaller, the ratio is less than one: the output spins faster than the input but with less torque — an overdrive. This tool handles both; just enter the tooth counts as they actually are.
Does this account for friction and efficiency losses?
No. The output torque shown assumes an ideal, lossless pair, so real-world torque will be a few percent lower depending on gear type, lubrication, and bearing drag. For a quick design estimate that is usually fine; for a precise figure, multiply the output torque by the drive's efficiency.
Educational tool only. Results are idealised estimates rounded for display and ignore drive losses; verify any figure that matters for design or safety against a full efficiency-corrected calculation.