Identified content errors were corrected on 2026-10-25. Sources and scope for this page: Gates PowerGrip drive design manual (accessed 2026-10-25), covering pitch-line geometry and the distinction between approximate and more precise open-drive formulas, page 177. The worked numbers are calculated from the displayed equations; no power rating is calculated. What the 2026-10-25 correction changed is stated with the source above; nothing beyond that scope was re-checked. Full sources, values and limits on this page.
Page last changed 2026-10-25 · based on Public reference accessed 2026-10-25; scope stated on page
Quick Answer
Belt Length
The Formulas Used
Open belt: L ≈ 2C + π(D₁ + D₂)/2 + (D₂ − D₁)² ÷ (4C)
Crossed belt: L ≈ 2C + π(D₁ + D₂)/2 + (D₂ + D₁)² ÷ (4C)
Wrap angle on the small pulley: θ = 180° − 2·asin(|D₂ − D₁| ÷ 2C)
Recalculate the wrap-angle example
For pitch diameters 4 and 8 in and a centre distance of 16 in (twice the larger diameter), the small-pulley wrap is 180° − 2 asin(4/32) = 165.64°. The approximate open-belt length is 51.100 in. Increasing centre distance moves this wrap angle toward 180°.
Wrap alone does not establish power capacity. Belt type, teeth in mesh or friction, speed, tension and manufacturer ratings also matter. Select a catalogue length, then check installation travel and tension using that belt manufacturer’s instructions.
Basis and scope
Gates PowerGrip drive design manual: Pitch-line geometry and the distinction between approximate and more precise open-drive formulas, page 177. The worked numbers are calculated from the displayed equations; no power rating is calculated.
Frequently Asked Questions
- Which pulley diameter should I enter?
- Use the pitch or datum diameter required by the selected belt system and keep the length convention consistent. Do not substitute outside diameter without the manufacturer’s conversion.
- Is the displayed length exact?
- No. The displayed open and crossed lengths use approximation formulas. Crossed routing also requires a belt designed for that arrangement.
- Is there a universal minimum centre distance or take-up percentage?
- No value is established by this calculator. Check the chosen belt, pulley combination, installation allowance and tensioning method in the manufacturer design manual.
Related
Value Sources
References and calculation methods used for this page are listed below. Numbered markers connect table columns where present. A reference listing does not itself establish that every value has been independently checked.
| # | Source | Type | Revision / method |
|---|---|---|---|
| [1] | Gates PowerGrip drive design manual | reference | Public reference accessed 2026-10-25 — source |
Data Sources
| Standard | Revision | What it covers on this page |
|---|---|---|
| Gates PowerGrip drive design manual | Public reference accessed 2026-10-25; scope stated on page | Pitch-line geometry and the distinction between approximate and more precise open-drive formulas, page 177. The worked numbers are calculated from the displayed equations; no power rating is calculated. |
Verification scope
- 2026-10-25 — Content corrected 2026-10-25. Pitch-line geometry and the distinction between approximate and more precise open-drive formulas, page 177. The worked numbers are calculated from the displayed equations; no power rating is calculated. Evidence
Content corrected 2026-10-25. Pitch-line geometry and the distinction between approximate and more precise open-drive formulas, page 177. The worked numbers are calculated from the displayed equations; no power rating is calculated.
Cite This Page
Read the source notes, calculation methods and verification scope above before reusing a value. To cite this page: