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]

Condition: C > (D1 + D2)/2; otherwise belt geometry is not feasible. Add tension allowance to the final length (typically 0.5-1%).

Results

Belt length1115.2 mm

Small pulley wrap angle185.7°

Formula: L = 2C + π/2(D1+D2) + (D2-D1)²/(4C). Small pulley wrap angle: β = π - 2·arcsin((D2-D1)/(2C)). Closed-belt or crossed setups require different formulas.

Standard Documentation

Pulley Belt Length and Wrap Angle

Scope: What does this tool calculate?

Pulley Belt Length and Wrap Angle performs the core engineering calculation for this tool type and presents results in a traceable format.

Assumptions and Units

SI units are the baseline; input unit consistency must be verified by the user.
The calculation path is deterministic (same inputs = same outputs).
If default material/environment values are used, replace them with project-specific values.

Limits / Boundaries

This tool is intended for preliminary sizing and technical checks, not final design approval.
When inputs are outside expected ranges, validate input quality before interpreting outputs.

Reference Standard

ISO / DIN / VDI references and common engineering handbooks

Validation Example

Validation example

Input	Expected Output
Input set: Unit-consistent project values	Expected output: Tool result is in the same order as standard references

Note: In real projects, run at least one manual check or reference-table comparison.

Version and Update

Version: v0.1.0
Last updated: 2026-03-04

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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.

Guides