# Belt Pulley Speed Ratio Calculator Calculate the ratio, driven speed and belt linear speed of a belt drive. i = d₂/d₁ = n₁/n₂, belt speed v = π·d·n/60. Supports mm/cm/m/inch diameter units. > Canonical page: https://elysiatools.com/en/tools/belt-pulley-speed-ratio - **Category:** Math & Numbers - **Keywords:** belt drive, pulley, belt speed, transmission ratio, v-belt, timing belt, linear speed, mechanical engineering ## Overview The Belt Pulley Speed Ratio Calculator helps mechanical engineers, technicians, and hobbyists quickly determine the transmission ratio, driven pulley speed, and linear belt speed of a belt drive system. By entering the driver and driven pulley diameters along with the driver speed, you can instantly calculate mechanical outputs using metric or imperial units. ## Inputs - **Driver Pulley Diameter (d₁)** (number): e.g. 100 - **Driven Pulley Diameter (d₂)** (number): e.g. 300 - **Driver Speed n₁ (rpm)** (number): Optional. If provided, the driven speed and belt linear speed are computed. - **Diameter Unit** (select) - **Belt Speed Unit** (select) - **Decimal Places** (number) ## When to use - When designing or analyzing belt drive systems to determine speed reduction or multiplication ratios. - When calculating the linear speed of a belt to ensure it operates within safe manufacturer limits. - When sizing replacement pulleys for motors, fans, or spindles to achieve a target output RPM. ## How it works - Enter the diameters of the driver pulley (d₁) and driven pulley (d₂), then select your preferred unit (mm, cm, m, or inches). - Optionally input the driver pulley rotational speed (n₁) in RPM to calculate the output speed and belt linear velocity. - Select the desired belt speed unit (m/s or m/min) and set the decimal precision for the output. - Click calculate to generate the transmission ratio (i), driven speed (n₂), and linear belt speed (v). ## Use cases - Sizing replacement pulleys for HVAC blower fans to adjust airflow rates. - Verifying that a custom machinery belt drive does not exceed the maximum safe linear speed of a V-belt. - Configuring industrial electric motor setups to match specific gearbox or spindle speed requirements. ## Frequently asked questions ### How is the belt transmission ratio calculated? The transmission ratio (i) is calculated by dividing the driven pulley diameter (d₂) by the driver pulley diameter (d₁). ### Can I calculate the belt linear speed without the driver RPM? No, calculating the linear belt speed requires both the driver pulley diameter and its rotational speed (RPM). ### What units of measurement does this calculator support? It supports millimeters, centimeters, meters, and inches for diameters, and meters per second (m/s) or meters per minute (m/min) for belt speed. ### What does a transmission ratio greater than 1 indicate? A ratio greater than 1 indicates a speed reducer, meaning the driven pulley rotates slower than the driver pulley but outputs higher torque. ### Does this calculator account for belt slippage? 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Treat every result as preliminary, not a certified design.