Pulley Belt Length and Wrap Angle

For an open-belt configuration, calculates belt length and small pulley wrap angle from two pulley diameters and center distance. Formula is a straight-line estimate; tensioning, poly-V profile, and manufacturer tolerances should also be considered.

Inputs

Pulley 1 diameter D1 [mm]Pulley 2 diameter D2 [mm]Center distance C [mm]

Conditions: diameters and C must be positive; pulley pitch circles must not overlap and (Dbig-Dsmall)/(2C) must be below 1. Evaluate tension allowance and manufacturer tolerances separately.

Results

Belt length1115.2 mm

Small pulley wrap angle174.3°

Large pulley wrap angle185.7°

Pulley treated as small80.0 mm (D2)

Pulley treated as large120.0 mm (D1)

Formulas: L = 2C + π/2(Dbig+Dsmall) + (Dbig-Dsmall)²/(4C); βsmall = π - 2·asin(r), βbig = π + 2·asin(r), r=(Dbig-Dsmall)/(2C). Crossed belts require different formulas.

Calculation explanation

Use this calculator to estimate open pulley belt length and the small pulley wrap angle from two pulley diameters and the center distance. It is intended for early mechanical layout checks before selecting the final catalog belt size.

Open belt length and wrap angle

L = 2C + (π/2)(D1 + D2) + (D2 − D1)^2 / (4C)
β = π − 2·arcsin((D2 − D1)/(2C))

Assumptions

Open belt geometry, not a crossed belt.
Belt thickness, stretch, and manufacturer tension allowance are not included.
Final selection should be checked against catalog belt lengths and pulley profile data.

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