Belt Length Calculator
Calculate belt length, wrap angle and speed ratio for a two-pulley drive.
Please note: These are idealised textbook models using representative material data. They are for study, sizing and sanity-checking only — never for final design. Real engineering requires code-compliant analysis, verified material certificates and a qualified engineer’s sign-off.
What the Belt Length Calculator does
A two-pulley belt drive wraps part way around each pulley and runs straight between them. Belt length combines those arcs and straight runs, while the wrap angle on the smaller pulley determines how much torque the drive can transmit before slipping.
Formula
L = 2C + π(D₁ + D₂) ÷ 2 + (D₂ − D₁)² ÷ (4C)Speed ratio = D₂ ÷ D₁Wrap angle (small) = 180° − 2 arcsin((D₂ − D₁) ÷ 2C)Belt speed = π D N ÷ 60
Inputs explained
| Input | Unit | Required | Notes |
|---|---|---|---|
| Solve for | one of 2 options | Yes | — |
| Small pulley diameter | number | Yes | — |
| Small pulley diameter unit | one of 9 options | Yes | — |
| Large pulley diameter | number | Yes | — |
| Large pulley diameter unit | one of 9 options | Yes | — |
| Centre distance | number | In some modes | Shown Solve for is Belt length from centre distance. |
| Centre distance unit | one of 9 options | In some modes | Shown Solve for is Belt length from centre distance. |
| Belt length | number | In some modes | Shown Solve for is Centre distance from belt length. |
| Belt length unit | one of 9 options | In some modes | Shown Solve for is Centre distance from belt length. |
| Driver pulley speed | rpm | Optional | Accepts 0 or more. |
| Driver is the | one of 2 options | Yes | — |
How to use it
- Choose Solve for and Small pulley diameter unit.
- Enter Small pulley diameter and Large pulley diameter.
- Fill in the remaining inputs the form shows for your choice.
- Optionally add Driver pulley speed.
- Select Calculate.
Worked example
A 100 mm and a 300 mm pulley on 500 mm centres.
- Small
- 100 mm
- Large
- 300 mm
- Centres
- 500 mm
L = 1,000 + π × 400 ÷ 2 + 200² ÷ 2,000 = 1,648.3 mm. Speed ratio 3:1, with 156.9° of wrap on the small pulley.
Frequently asked questions
Why does wrap angle matter?
Belt drives transmit torque by friction, and friction capacity rises with contact arc. Below about 120° on the small pulley the belt slips long before the motor stalls.
Does centre distance change the speed ratio?
No. Ratio depends only on the pulley diameters. Centre distance sets belt length and wrap angle.
Method and sources
Method. Standard open-belt length approximation, L = 2C + π(D₁ + D₂) ÷ 2 + (D₂ − D₁)² ÷ 4C, with wrap angle and speed ratio reported.
Assumptions
- Two pulleys on parallel shafts with an open (non-crossed) belt, and no idler.
Limitations
- The formula is an approximation that loses accuracy as the pulley diameters diverge relative to the centre distance.
- Belts are supplied in standard lengths, so the exact figure indicates the size to select and the centre distance usually needs adjustment to suit.
- Wrap angle governs how much torque can be transmitted before slipping; a small pulley with a low wrap angle limits the drive regardless of belt length.
Sources
- Standard belt-drive geometry, with the manufacturer's catalogue for available lengths — Established machine design references; catalogue varies by manufacturer. The length relationship. Selecting an actual belt requires the manufacturer's standard sizes and power ratings.