Gear Ratio Calculator
Find the gear ratio between two meshing gears by entering their tooth counts. Use it when designing drivetrains, selecting motor gears, or analysing speed-versus-torque trade-offs.
About this calculator
The gear ratio describes how many times the driving gear must rotate to turn the driven gear once. It is calculated as: Gear Ratio = Driven Teeth / Driving Teeth. A ratio greater than 1 means the driven gear rotates more slowly than the driving gear, multiplying torque (a reduction gear set). A ratio less than 1 means the driven gear rotates faster, sacrificing torque for speed (an overdrive). For example, a 60-tooth driven gear meshing with a 20-tooth driving gear gives a ratio of 3:1 — the driving gear turns three times for every single rotation of the driven gear. This relationship is fundamental in bicycles, automotive transmissions, industrial machinery, and robotics, where matching speed and torque to a load is critical.
How to use
Imagine a driving gear with 18 teeth connected to a driven gear with 54 teeth. Using the formula: Gear Ratio = Driven Teeth / Driving Teeth = 54 / 18 = 3.0. This 3:1 ratio means the driven shaft rotates once for every three rotations of the driving shaft. If the driving gear spins at 900 RPM, the driven gear turns at 900 / 3 = 300 RPM. Conversely, the output torque is multiplied by a factor of 3 (ignoring friction losses), so a 10 N·m input produces roughly 30 N·m at the output.
Frequently asked questions
How does gear ratio affect speed and torque in a transmission?
Gear ratio determines the trade-off between rotational speed and torque transmitted through a gear pair. A high gear ratio (e.g., 4:1) reduces output speed but multiplies torque, useful for starting heavy loads or climbing hills. A low ratio (e.g., 0.8:1) increases output speed at the cost of torque, useful for high-speed cruising. In multi-speed transmissions, different gear ratios allow an engine to operate in its efficient power band across a wide range of vehicle speeds.
What is the difference between gear ratio and mechanical advantage in a gear system?
Gear ratio and mechanical advantage are closely related but not always identical. The gear ratio (driven/driving teeth) describes the speed relationship between two gears, while mechanical advantage in a gear context equals the same ratio when considering torque amplification. However, real-world mechanical advantage is always slightly less than the theoretical ratio due to friction and gear mesh losses, typically 95–99% efficiency for well-lubricated spur gears. Gear ratio is a kinematic property; mechanical advantage is a dynamic (force-related) property.
Why do bicycles have multiple gears and how do I calculate which ratio to use?
Bicycles use multiple gear ratios to allow the rider to maintain a comfortable and efficient cadence (pedalling rate) across varied terrain and speeds. On steep climbs, a high gear ratio (large chainring to small sprocket) would require excessive force, so cyclists shift to a low ratio (small chainring to large sprocket) to reduce pedal effort. To calculate the ratio, divide the number of teeth on the front chainring by the rear sprocket teeth. For example, a 44-tooth chainring with a 22-tooth sprocket gives a 2:1 ratio — the rear wheel turns twice per pedal revolution. Choosing the right ratio prevents muscle fatigue and improves efficiency.