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Calculate the gear ratio and output speed of a meshing gear pair. i = z₂/z₁ = n₁/n₂. Enter the tooth counts to get the ratio; add the driver speed to get the driven speed.
Execution
Fill in the form, run the tool, and review the result in one place.
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Tool usage guide
The Gear Ratio Calculator helps mechanical engineers, designers, and hobbyists quickly determine the transmission ratio and output speed of a meshing gear pair. By entering the tooth counts of the driver and driven gears, along with the optional driver speed in RPM, the tool computes the exact speed ratio and driven gear RPM.
Background
Designing a small mobile robot using a motor that runs at 3000 RPM. The motor shaft has a 12-tooth pinion driving a 48-tooth gear on the wheel axle.
Problem
Need to find the final wheel speed (RPM) and the reduction ratio.
How to use
Enter 12 for Driver Teeth (z₁), 48 for Driven Teeth (z₂), and 3000 for Driver Speed (n₁).
Outcome
The tool calculates a gear ratio of 4.0000 (speed reducer) and an output speed of 750.0000 RPM.
Background
Verifying the specifications of a replacement gear pair in a conveyor belt drive system. The driver gear has 24 teeth and the driven gear has 72 teeth.
Problem
Determine the exact transmission ratio to ensure it matches the original design specifications.
How to use
Enter 24 for Driver Teeth (z₁) and 72 for Driven Teeth (z₂), leaving the driver speed blank.
Outcome
The tool outputs a gear ratio of 3.0000, confirming a 3:1 speed reduction ratio.
The gear ratio (i) is calculated as z₂ / z₁, where z₂ is the number of teeth on the driven gear and z₁ is the number of teeth on the driver gear.
The output speed (n₂) is calculated by dividing the driver speed (n₁) by the gear ratio (i), resulting in n₂ = n₁ / i.
A ratio greater than 1 indicates a speed reducer, where the output speed is lower than the input speed, increasing torque.
Yes, the driver speed (RPM) is optional; you can calculate just the gear ratio using only the tooth counts.
The speeds are measured in revolutions per minute (RPM).