# Chain Sprocket Ratio Calculator Calculate the ratio, driven speed and chain linear speed of a chain drive. i = z₂/z₁ = n₁/n₂, chain speed v = z₁·p·n₁/60000. Enter the pitch to compute chain speed. > Canonical page: https://elysiatools.com/en/tools/chain-sprocket-ratio - **Category:** Math & Numbers - **Keywords:** chain drive, sprocket, chain speed, transmission ratio, roller chain, pitch, mechanical engineering ## Overview The Chain Sprocket Ratio Calculator helps mechanical engineers and designers quickly determine the transmission ratio, driven sprocket speed, and linear chain speed of a chain drive system. By entering the tooth counts of the driver and driven sprockets, along with optional driver speed and chain pitch, you can instantly calculate mechanical outputs to optimize roller chain drive configurations. ## Inputs - **Driver Sprocket Teeth (z₁)** (number): e.g. 17 - **Driven Sprocket Teeth (z₂)** (number): e.g. 51 - **Driver Speed n₁ (rpm)** (number): Optional. If provided, the driven speed is computed. - **Chain Pitch (mm)** (number): Optional. Combined with n₁ it yields the chain linear speed (m/s). - **Decimal Places** (number) ## When to use - When designing or analyzing a roller chain drive system to determine the exact speed reduction or increase ratio. - When calculating the output RPM of a driven sprocket based on a known motor or input shaft speed. - When evaluating the linear velocity of a chain to ensure it operates within safe, recommended speed limits for a given pitch. ## How it works - Enter the number of teeth on the driver sprocket (z₁) and the driven sprocket (z₂). - Optionally input the driver speed in RPM (n₁) and the chain pitch in millimeters (pitch). - Set the desired decimal precision for the calculation results. - Click calculate to generate the transmission ratio, driven speed, and linear chain speed in meters per second. ## Use cases - Designing industrial conveyor systems to match motor speeds with target conveyor line velocities. - Calculating gear ratios for motorcycles, bicycles, or go-karts when changing sprocket sizes to tune acceleration or top speed. - Verifying mechanical design specifications for agricultural machinery chain drives to prevent chain over-speeding. ## Frequently asked questions ### How is the chain transmission ratio calculated? It is calculated by dividing the number of teeth on the driven sprocket (z₂) by the number of teeth on the driver sprocket (z₁). ### What formula is used to calculate the linear chain speed? The linear speed (v) is calculated using the formula v = (z₁ * pitch * n₁) / 60,000, which outputs the speed in meters per second. ### Do I need to provide the chain pitch to get the transmission ratio? No, the transmission ratio only requires the tooth counts of the driver and driven sprockets. ### Can this calculator determine if my chain drive is a speed reducer or speed multiplier? Yes, the calculator identifies whether the setup acts as a speed reducer (ratio > 1) or a speed multiplier (ratio < 1). ### What units should I use for the chain pitch? The chain pitch must be entered in millimeters (mm) to correctly calculate the linear speed in meters per second (m/s). ## Related tools - [Absolute Value Calculator](https://elysiatools.com/en/tools/absolute-value-calculator): Calculate the absolute value of positive, negative, or decimal numbers and explain the sign relationship - [Air Changes per Hour (ACH, n = Q/V)](https://elysiatools.com/en/tools/air-changes-per-hour): Compute the air change rate (ACH / n) of a room from the outdoor supply airflow Q and the room volume V: n = Q/V (1/h). Three modes: solve ACH (given Q and V), solve airflow (given n and V), or solve volume (given n and Q). Flow in m³/s/m³/h/CFM, volume in m³/ft³/L. Also reports the well-mixed single-zone purge time to reach a target residual fraction ε (default 1%): t = −ln(ε)/n hours. - [Bearing Life L10 Calculator](https://elysiatools.com/en/tools/bearing-life-l10): Calculate the basic rating life of a rolling bearing: L10 = (C/P)^p, with p = 3 for ball bearings and p = 10/3 for roller bearings. When a speed is provided, converts to L10h in operating hours. - [Bolt Torque Clamp Force Calculator](https://elysiatools.com/en/tools/bolt-torque-clamp-force): Convert between bolt tightening torque and axial clamp force. T = K·F·d, where K is the nut factor (~0.20 for dry steel). Solve torque from force, or force from torque. - [Cable Ampacity Calculator (IEC 60364-5-52)](https://elysiatools.com/en/tools/cable-ampacity-calculator): Estimate copper cable current-carrying capacity per the simplified IEC 60364-5-52 reference method. Combines cross-section, insulation (PVC 70°C / XLPE 90°C), installation method, and ambient temperature to derive the corrected allowable ampacity (A). - [Capacitor Reactive Power Calculator (Q_c = 2πfCU²)](https://elysiatools.com/en/tools/capacitor-reactive-power): Compute the reactive power produced by a known capacitor: Q_c = 2π·f·C·U². Supports single-phase, three-phase star (Y) and delta (Δ) connections. Returns Q_c in var/kvar, capacitive reactance Xc, and capacitor current Ic. Complementary to the power-factor-correction tool (which sizes a capacitor for a target cosφ). - [Condensing / Evaporating Temperature Calculator](https://elysiatools.com/en/tools/condensing-temperature-calculator): Estimate the saturated condensing temperature (T_cond) and evaporating temperature (T_evap) of a refrigeration circuit. Three modes: (1) from coil approach — T_cond = T_ambient + condenser ΔT approach, T_evap = T_medium − evaporator ΔT approach; (2) from measured saturated pressures — given P_cond and P_evap for a known refrigerant (R-22 / R-134a / R-410A), invert the Antoine fit; (3) from subcooling & superheat — T_cond = T_liquid − SC, T_evap = T_suction − SH. Temperature in °C/K/°F; pressure in bar/MPa/kPa/PSI absolute or gauge (atmospheric default 1.01325 bar). Results reported in °C. - [Conditional Probability Calculator](https://elysiatools.com/en/tools/conditional-probability-calculator): Calculate P(A given B) from joint probability P(A and B) and condition probability P(B) ## Samples - [Web Image Processing Python Samples](https://elysiatools.com/en/samples/web-image-processing-python): Web Python image processing examples using PIL/Pillow including reading, saving, resizing, and format conversion - [Android Image Processing Java Samples](https://elysiatools.com/en/samples/android-image-processing-java): Android Java image processing examples including reading/saving images, scaling, and format conversion - [Android Image Processing Kotlin Samples](https://elysiatools.com/en/samples/android-image-processing-kotlin): Android Kotlin image processing examples including reading/saving images, scaling, and format conversion - [Web Image Processing Rust Samples](https://elysiatools.com/en/samples/web-image-processing-rust): Web Rust image processing examples including image read/save, scaling, and format conversion ## Related content - [Mechanical Transmission and Machine-Element Sizing](https://elysiatools.com/en/hubs/mechanical-transmission-and-machine-element-sizing): Screen a gear, belt/pulley, chain/sprocket, torque, or spring-rate calculation by matching the transmission type to the known quantities. Treat every result as preliminary, not a certified design.