Gear Ratio Calculator
Determine the output speed and mechanical advantage of a gear pair by entering tooth counts, input RPM, and system efficiency. Ideal for engineers and hobbyists designing gearboxes, drivetrains, or robotics.
About this calculator
A gear ratio describes how rotational speed and torque are transformed between a driving gear and a driven gear. The fundamental relationship is: Output Speed = (inputSpeed × drivingTeeth / drivenTeeth) × (efficiency / 100). When the driven gear has more teeth than the driving gear, output speed decreases and torque increases — this is a speed reduction. Conversely, fewer driven teeth yield a speed increase with lower torque. Efficiency accounts for real-world losses from friction and gear mesh imperfections, typically ranging from 95–99% for well-lubricated spur gears. The mechanical advantage equals the ratio drivenTeeth / drivingTeeth; a ratio greater than 1 means the system multiplies torque at the cost of speed.
How to use
Suppose a motor spins at 1,800 RPM and drives a 20-tooth gear meshed with a 60-tooth driven gear, with 97% system efficiency. Step 1 — Enter drivingTeeth = 20, drivenTeeth = 60. Step 2 — Enter inputSpeed = 1,800 RPM. Step 3 — Enter efficiency = 97. Calculation: Output Speed = (1,800 × 20 / 60) × (97 / 100) = 600 × 0.97 = 582 RPM. The gear ratio is 3:1, so torque at the output shaft is approximately tripled before efficiency losses.
Frequently asked questions
What does a higher gear ratio mean for torque and speed?
A higher gear ratio (e.g., 4:1) means the driven gear turns more slowly than the driving gear, but the output torque is multiplied by that same factor (minus efficiency losses). This is why low gears in a vehicle provide more pulling power at lower speeds. Conversely, a ratio below 1:1 increases output speed while reducing torque. Choosing the right ratio is a trade-off between speed and force for your application.
How does system efficiency affect gear output speed?
System efficiency represents power losses due to friction, gear mesh imperfections, and lubrication drag. A 97% efficiency means 3% of the input power is lost as heat. In the output speed formula, efficiency directly scales the result: a lower efficiency reduces both effective output speed and torque. For critical designs, always account for efficiency rather than assuming a perfect 100% transmission.
When should I use a gear ratio calculator instead of just counting teeth?
Simply dividing tooth counts gives the ideal speed ratio, but a calculator adds efficiency to give real-world output speed. It also helps when chaining multiple gear stages, where you multiply individual ratios together. A calculator prevents arithmetic errors and lets you quickly iterate through different tooth-count combinations to hit a target output speed. This is especially valuable in robotics, CNC machine design, and automotive drivetrain work.