Gear Train Ratio Calculator

What Is a Gear Train? A gear train is a set of meshing gears that transmit torque and rotational speed from one shaft to another. By choosing different numbers of teeth on each gear, engineers can reduce speed and multiply torque (for machinery) or increase speed and reduce torque (for high-speed applications).

Single Gear Pair Ratio For a single pair of meshing gears, the gear ratio is simply:

Ratio = N_driven / N_driver

Where N is the number of teeth. If the driver (input) gear has 20 teeth and the driven (output) gear has 80 teeth, the ratio is 80/20 = 4. This means the output shaft rotates 4 times slower than the input, but produces 4 times the torque.

Output Speed and Torque Output Speed = Input Speed / Ratio Output Torque = Input Torque × Ratio (at 100% efficiency)

In real gears, each meshing pair has approximately 95-98% efficiency due to friction. The actual output torque is: Output Torque = Input Torque × Ratio × Efficiency

Compound Gear Train A compound gear train uses multiple gear pairs in series. The overall ratio is the product of all individual ratios:

Overall Ratio = R1 × R2 × R3 = (N_driven1/N_driver1) × (N_driven2/N_driver2) × …

This allows very large ratios to be achieved in a compact package. For example, three stages of 4:1 each give an overall ratio of 64:1.

Gear Train Types

• Simple gear train: One gear per shaft. Speed ratio equals tooth ratio.
• Compound gear train: Two or more gears on intermediate shafts. Each intermediate shaft carries both a driven and a driver gear.
• Planetary gear train: gears orbit a central sun gear, which allows very high ratios in minimal space (used in automatic transmissions and hub gears).

Speed Reduction vs. Speed Increase If the driven gear has more teeth than the driver, speed decreases and torque increases. That is a speed reducer, and it is what most industrial drives are. If the driven gear has fewer teeth than the driver, speed increases and torque decreases. That is a speed increaser, used in wind turbines and some pumps.

Practical Notes This calculator takes up to three gear pairs. Fill in stage 1 and leave stages 2 and 3 blank if you do not have them, and the calculator ignores them entirely rather than pretending they are 1:1. Efficiency is charged at roughly 97% per meshing pair for spur gears, so a three-stage box starts from about 91% before you have specified anything else about it.

Worth knowing: a stage that genuinely is 1:1, an idler pair used to reverse direction or bridge a distance, still costs you that 3%. Ratio and loss are separate things. If you enter a real 1:1 stage here it is counted as a stage, because it is one.

Applications Gear trains are found everywhere: vehicle transmissions, industrial gearboxes, robotics, watches, bicycles, wind turbines, and electric motors.