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Belt & Pulley Speed Ratio and Length Calculator

Belt and pulley drives transfer torque and rotary motion between shafts separated by considerable center distances via friction or positive synchronous engagement.

Pitch diameter of driving pulley mounted to motor shaft in mm.

Pitch diameter of driven equipment pulley in mm.

Operating speed of motor shaft in RPM.

Direct center distance between both pulley shafts in millimeters.

Calculated Result
875 RPM

Driven Pulley Speed

Driven Sheave Speed

875 RPM

Pulley Ratio (D₂ / D₁)

2:1

Pitch Belt Length (L)

1473.5 mm (58.01 inches)

Belt Linear Speed

11 m/s

Small Sheave Wrap Angle

164.7° (Adequate Traction)

Calculation Breakdown

  1. 1. Pulley Ratio and Output RPMSpeed Ratio = 240 mm / 120 mm = 2:1. Driven RPM = 1750 / 2 = 875 RPM
  2. 2. Pitch Belt Length CalculationL ≈ 2·C + (π/2)·(D₁ + D₂) + (D₂ - D₁)² / (4·C) = 2·450 + 565.5 + 8.0 = 1473.5 mm (58.01 in)
  3. 3. Belt Velocity & Wrap AngleLinear speed V = (π · 120 mm · 1750) / 60,000 = 11 m/s. Wrap on driver = 164.7°

Drive Kinematics Overview

Interactive visualization based on your current inputs

Value
0.04488131175Driver RPM / 10Driven RPM / 10Belt Speed (m/s)Driver Wrap (° / 10)ParameterValue

What Is the Belt & Pulley Speed Ratio and Length Calculator?

Belt and pulley drives are flexible mechanical power transmissions connecting two rotating parallel shafts.

How Does the Belt & Pulley Speed Ratio and Length Calculator Work?

Continuous belts stretch taut across pulley perimeters, transmitting power via static friction against V-grooves or tooth shear in timing belts.

Belt & Pulley Speed Ratio and Length Calculator Formula & Variables

The core mathematical equation utilized by this calculator is expressed as:

N_2 = N_1 \left(\frac{D_1}{D_2}\right), \quad L \approx 2C + \frac{\pi}{2}(D_1 + D_2) + \frac{(D_2 - D_1)^2}{4C}, \quad V = \frac{\pi \cdot D_1 \cdot N_1}{60000}

Driven speed equals driver speed times diameter ratio. Belt length sums straight spans, curved semicircular wrap, and geometric angle correction.

How to Use the Belt & Pulley Speed Ratio and Length Calculator

  1. Enter driver and driven pitch diameters in millimeters.
  2. Input motor driver RPM.
  3. Enter the shaft center-to-center distance in mm.

Step-by-Step Example Calculation

2:1 Reduction Drive (120mm to 240mm at 450mm Center Distance)

Input Values:

driverDiameterMm:120
drivenDiameterMm:240
driverSpeedRpm:1750
centerDistanceMm:450
Worked Steps: Driven pulley rotates at 875.0 RPM. Pitch belt length is 1,473.5 mm (58.01 inches) with 10.99 m/s belt velocity and 164.7° driver wrap angle.

Understanding Your Result

Driven Speed (RPM): Output machinery rotational velocity.

Pitch Belt Length (mm/in): Theoretical continuous loop belt length.

Linear Belt Velocity (m/s): Peripheral belt travel speed.

Wrap Angles: Arc of contact in degrees across both sheaves.

Factors That Affect the Result

  • Center distance governs total belt length; diameter difference determines wrap angle reduction on the smaller pulley.

When Should You Use This Calculator?

  • Air compressor drives, automotive alternator belts, agricultural combine machinery, and conveyor belt rollers.

Assumptions & Limitations

  • Assumes open belt drive configuration (non-crossed) with negligible elastic belt stretch and creep.

Frequently Asked Questions

Calculation Accuracy & Reference Note

Standard RMA / ISO industrial belt drive geometric formulation.

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