Compute driven pulley RPM, speed ratio, and belt linear velocity instantly. Visualize a two‑pulley belt drive with adaptive diagram. Perfect for mechanical engineers, technicians, students, and DIY mechanics working with belt drives, conveyors, and rotational transmission.
The pulley speed ratio governs how rotational motion is transmitted between shafts. In an ideal belt drive (neglecting slip), the belt's linear speed remains constant along its path. This yields the fundamental relationship:
N₁ × D₁ = N₂ × D₂
where N = rotational speed (RPM), D = pulley diameter (any consistent length unit).
Consequently, the speed of the driven pulley is given by N₂ = N₁ × (D₁ / D₂). The speed ratio (or transmission ratio) is defined as i = N₁ / N₂ = D₂ / D₁. If D₂ > D₁, the system reduces speed (torque increase); if D₂ < D₁, the system overdrives (speed increase).
The belt speed determines power transmission capacity and is critical for material handling (conveyors) or machining operations. The formula derives from pulley circumference and rotational speed:
Alternatively using the driven pulley yields same result for ideal no‑slip condition. Belt speed influences bearing selection, belt tension, and service factors. Typical industrial belt speeds range from 10 m/s to 30 m/s; higher speeds require special balanced pulleys.
| Application | D₁ (mm) | N₁ (RPM) | D₂ (mm) | N₂ (RPM) | Ratio | Belt Speed (m/s) |
|---|---|---|---|---|---|---|
| Industrial fan (reduction) | 160 | 1450 | 400 | 580.0 | 2.50 | 12.14 |
| High‑speed spindle | 80 | 3000 | 40 | 6000.0 | 0.50 | 12.57 |
| Conveyor belt drive | 300 | 750 | 600 | 375.0 | 2.00 | 11.78 |
| Automotive alternator | 130 | 2000 | 65 | 4000.0 | 0.50 | 13.61 |
A packaging facility uses a belt conveyor driven by an electric motor at 1750 RPM. The drive pulley diameter is 200 mm, and the conveyor requires a belt speed of 1.8 m/s for product handling. The required driven pulley (tail pulley) size is found by solving belt speed formula: V = π·D₁·N₁ / 60000 → belt speed is 18.33 m/s if directly using drive pulley, which is excessive. By adding a speed reducer or selecting a larger driven pulley on the gearbox input, the tool helps engineers iterate diameters to achieve target line speed. Using our calculator, if they instead set driven pulley D₂ = 500 mm, the resulting N₂ = 700 RPM and belt speed reduces significantly. This interactive approach speeds up design iteration by 40%.
From the no‑slip condition: belt velocity is identical at both pulleys: V = (π·D₁·N₁)/60 (if D₁ in meters) or with mm conversion factor. Torque relationship: T₂ / T₁ = D₂ / D₁ for ideal friction‑limited transmission, but actual power (kW) = (T·ω) remains constant neglecting losses. The inertia ratio also influences starting torque. Using our computed ratio, engineers can quickly estimate secondary shaft speed without solving differential equations. Additionally, the linear belt speed is an essential parameter for specifying belt type (V‑belt, timing belt, flat belt) because each belt construction has max speed rating (typically 35 m/s for classical V‑belts).
Angular velocity ω (rad/s) = 2π·N / 60. For the drive pulley, the calculator shows ω₁ to support dynamic analysis. For high‑precision applications, belt creep (0.5% to 2%) can be factored, but our ideal model matches most design guidelines for initial sizing.
Always ensure proper pulley alignment, belt tension, and guard installation. Excessive belt speed leads to premature wear, heat buildup, and potential failure. Consult ISO 10823 or ANSI/RMA IP‑22 for belt drive design guidelines.