Gear Train Ratio Calculator
Calculate the overall gear ratio, output speed, and output torque for a compound gear train with up to 3 gear pairs.
Input RPM, torque, and tooth counts for each stage.
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 — 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, torque increases (speed reducer — most common in industrial drives). If the driven gear has fewer teeth than the driver: speed increases, torque decreases (speed increaser — used in wind turbines, some pumps).
Practical Notes This calculator uses three gear pairs. Enter tooth counts for only the pairs you are using — set unused pair tooth counts equal (e.g., both = 1) to produce a ratio of 1:1 for that stage. The efficiency note assumes approximately 97% per stage for spur gears.
Applications Gear trains are found everywhere: vehicle transmissions, industrial gearboxes, robotics, watches, bicycles, wind turbines, and electric motors.