# Gear Ratio Calculator 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. > Canonical page: https://elysiatools.com/en/tools/gear-ratio-calculator - **Category:** Math & Numbers - **Keywords:** gear ratio, transmission ratio, speed ratio, pinion, gear, rpm, gearbox, mechanical engineering ## Overview 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. ## Inputs - **Driver Teeth (z₁)** (number): e.g. 20 - **Driven Teeth (z₂)** (number): e.g. 60 - **Driver Speed n₁ (rpm)** (number): Optional. If provided, the driven speed n₂ is computed. - **Decimal Places** (number) ## When to use - Designing a gearbox or transmission system and needing to verify the speed reduction or multiplication ratio. - Calculating the output RPM of a driven gear based on a known motor input speed. - Selecting appropriate gear tooth counts to achieve a target mechanical advantage or speed ratio. ## How it works - Enter the number of teeth on the driver gear (z₁) and the driven gear (z₂). - Optionally input the rotational speed of the driver gear (n₁) in RPM. - Set the desired decimal precision for the calculations. - The calculator computes the gear ratio (i = z₂/z₁) and determines the driven gear speed (n₂ = n₁ / i). ## Use cases - Determining the output speed of a robotics drive system powered by a DC motor. - Sizing gears for custom automotive or bicycle transmission modifications. - Verifying mechanical design specifications in industrial machinery gearboxes. ## Frequently asked questions ### What is the formula used to calculate the gear 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. ### How is the output speed calculated? The output speed (n₂) is calculated by dividing the driver speed (n₁) by the gear ratio (i), resulting in n₂ = n₁ / i. ### What does a gear ratio greater than 1 mean? A ratio greater than 1 indicates a speed reducer, where the output speed is lower than the input speed, increasing torque. ### Can I calculate the ratio without entering the driver speed? Yes, the driver speed (RPM) is optional; you can calculate just the gear ratio using only the tooth counts. ### What units are used for the driver and driven speeds? 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Treat every result as preliminary, not a certified design.