Gear Ratio Calculator
Calculate the gear ratio between two meshing gears using their tooth counts. Useful for designing drivetrains, bicycles, RC vehicles, and any mechanical power-transmission system.
About this calculator
Gear ratio describes how much the output gear rotates relative to the input gear for every full rotation of the driving gear. The formula is: Gear Ratio = output_teeth / input_teeth. A ratio greater than 1 means the output gear turns more slowly than the input (torque multiplication), while a ratio less than 1 means the output spins faster (speed multiplication). For example, a ratio of 3:1 means the output shaft makes one revolution for every three of the input shaft, tripling the torque while reducing speed by the same factor. This principle is fundamental to transmissions, differentials, clock mechanisms, and industrial machinery. Understanding gear ratios helps engineers and hobbyists select the right combination of gears to achieve desired speed or torque output.
How to use
Suppose a driving gear (input) has 20 teeth and the driven gear (output) has 60 teeth. Step 1: Identify input teeth = 20 and output teeth = 60. Step 2: Apply the formula: Gear Ratio = 60 / 20 = 3.0. This means the output gear rotates once for every three rotations of the input gear — a 3:1 ratio. The output shaft delivers three times the torque of the input, at one-third the speed. If the input gear spins at 900 RPM, the output will spin at 300 RPM.
Frequently asked questions
What does a gear ratio greater than 1 mean for torque and speed?
A gear ratio greater than 1 means the output gear has more teeth than the input gear, so it rotates more slowly but with greater torque. This is called a reduction gear arrangement and is used in applications like car axles and electric motors where high torque at low speed is needed. The trade-off is always speed: you gain torque by sacrificing rotational speed by the same factor as the ratio.
How do I calculate gear ratio for a multi-stage gear train?
For a gear train with multiple stages, you multiply the individual gear ratios of each stage together to get the overall ratio. For example, if stage one has a ratio of 3:1 and stage two has a ratio of 4:1, the total ratio is 3 × 4 = 12:1. This compounding effect is why multi-stage gearboxes can achieve very high ratios in a compact package, as seen in industrial reducers and automotive transmissions.
Why does the number of teeth determine gear ratio rather than physical gear diameter?
The number of teeth is directly proportional to the circumference of a gear for any given tooth pitch, so tooth count is an accurate and precise proxy for diameter. Using teeth count rather than diameter avoids measurement errors and is the standard engineering approach because teeth are discrete, countable, and manufacture-controlled. In practice, if two gears have the same tooth pitch, their diameters are proportional to their tooth counts, so the ratio calculated from teeth is identical to the ratio calculated from diameters.