Gear Ratio Calculator
A gear ratio determines how speed and torque are transmitted between meshing gears. By dividing the number of driven gear teeth by driving gear teeth, you get the gear ratio. A ratio greater than 1 reduces speed but multiplies torque (useful for hill climbing), while a ratio less than 1 increases speed at the cost of torque. This calculator gives you all the key relationships.
The gear ratio = driven teeth / driving teeth. When a 20-tooth gear drives a 40-tooth gear, the ratio is 2:1. The output shaft turns at half the input speed but delivers twice the torque. This is the fundamental trade-off in all gear systems: you cannot increase both speed and torque simultaneously (conservation of energy).
In automotive transmissions, first gear has a high ratio (e.g., 3.5:1) for maximum torque to accelerate from a stop. Higher gears have progressively lower ratios (e.g., 0.7:1 in overdrive) to allow high-speed cruising at lower engine RPM. Bicycles work the same way: a small front chainring with a large rear sprocket gives a low gear for climbing.
Gear systems are everywhere: clocks, industrial machinery, robotics, wind turbines, and power tools. Multi-stage gear trains multiply ratios: two stages of 3:1 give an overall ratio of 9:1. The mechanical advantage equals the gear ratio for an ideal (frictionless) system; real systems lose 1–3% per gear mesh to friction and heat.