Gear Ratio

Also known as speed ratio · gear reduction

GR = \frac{N_{out}}{N_{in}}

Worked example: 20 teeth driving 60 teeth → 3:1 — press Try an example to run it live, then adjust anything.

Enter your known values, leave one input blank, and solves for the missing one. Tap a variable’s symbol to see what it means, with a typical value. Try different units for next level excitement!

Learning zone

Gear Ratio explained

Meshing teeth must pass the same point at the same rate, so a 20-tooth driver turning a 60-tooth gear gives GR = 3: the output turns a third as fast and, ideally, with three times the torque. Any ratio above 1 is a reduction (more torque, less speed); below 1 is an overdrive. The Antikythera mechanism, built around 100 BC and recovered from a Greek shipwreck in 1901, already used more than 30 bronze gears — including a 223-tooth wheel — to predict eclipses, an achievement not matched in Europe for another 1,400 years.

Because power is torque times angular speed and gears conserve power apart from a percent or two of tooth friction, whatever you gain in torque you lose in speed. Chain a second pair in series and the ratios multiply, which is how a three-stage industrial reducer reaches 100:1 in a compact housing. Watch the convention: automotive and bicycle literature sometimes quotes the reciprocal, so always state which count is the driver.

Gear Ratio formula

GR = \frac{N_{out}}{N_{in}}

Where

$GR$ = Gear ratio
$N_{in}$ = Teeth on driver gear
$N_{out}$ = Teeth on driven gear

Missing one of these? Work it out first, then come back

Teeth on driver gear — Pulley System Effort Force, Compound Gear Train Value
Teeth on driven gear — Compound Gear Train Value, Pulley System Effort Force