Use this engineering calculation for a transparent preliminary estimate or independent arithmetic check when geometry, materials, loads, operating conditions, and units are defined consistently.

Center Distance Millimeters (mm)

Required number input.

Large Diameter Millimeters (mm)

Required number input.

Small Diameter Millimeters (mm)

Required number input.

Approximate open-belt pitch length 2C+π(D+d)/2+(D−d)²/(4C) for center distance C. The tool evaluates the supplied inputs together and returns the named outputs below; it does not infer omitted operating conditions or change the units shown.^[1]

Belt Length Millimeters (mm)

The resulting belt length millimeters returned as a number.

• A compact formula cannot establish code compliance, safety, durability, manufacturability, or fitness for service. Boundary conditions, material variability, tolerances, dynamic and fatigue effects, environmental exposure, uncertainty, and failure modes may require a fuller model and governing standard.
• Use finite inputs in the displayed units and preserve more precision than the final presentation requires. Independently verify safety-critical, financial, compliance, or production decisions.

Check assumptions against drawings, measurements, current material data, and the applicable design code. Apply required load combinations and safety factors, then obtain qualified review and testing for consequential designs.

• Belt Drive Speed Ratio

  Ideal no-slip driven-to-driver pulley speed ratio from pitch diameters.

• Orbital Velocity

  Circular-orbit speed √(μ/r) around a central body from its gravitational parameter and distance from its center.

• Battery Internal Resistance

  Apparent battery DC internal resistance from open-circuit and loaded terminal voltages at a measured discharge current.