Free tool
Belt Length Calculator
Estimate belt length for a simple open two-pulley path from effective pulley diameters and centre distance, with an optional cut-length allowance.
- Free
- No signup
- Formula shown
- updated 2026-09
Calculate
Enter your values
Results update as you type. Everything is computed in the browser.
Centre to centre, not the free span.
Optional; enter only an allowance from your belt or splice specification.
- Geometric length (mm)
- 8,707.01
- Length incl. allowance (mm)
- 8,707.01
- Length incl. allowance (m)
- 8.707
- Length incl. allowance (ft)
- 28.57
Computed in your browser. Inputs are not sent to a server.
Method
The formula, and every assumption behind it
A number you cannot check is not usable in engineering or finance work. This is the whole calculation.
L = 2√(C² − Δ²) + π(D₁ + D₂)/2 + 2Δ asin(Δ/C); Δ = (D₁ − D₂)/2Exact ideal open-belt tangent geometry. For similar pulleys and long centres it approaches 2C + π(D₁ + D₂)/2 + (D₁ − D₂)²/(4C). Add any specified allowance separately.
Variables
| Symbol | Meaning | Unit |
|---|---|---|
| L | Geometric belt length at effective diameter | mm |
| C | Centre distance between pulley centres | mm |
| D₁ | Drive effective diameter | mm |
| D₂ | Tail effective diameter | mm |
| Δ | Difference between pulley radii | mm |
Assumptions and limits
- Use effective diameters at the belt running line; these depend on belt construction and lagging.
- Pulleys are parallel and the centres are correctly aligned.
- The optional allowance is simply added; take-up and splice geometry are not modelled.
- Only a simple open two-pulley path is modelled. Snub, bend, centre drives and crossed belts are excluded.
How to use it
Five steps
- 01
Measure the centre distance between the two pulley centres, not the gap between the pulley faces.
- 02
Determine both effective running diameters, accounting for lagging and belt construction.
- 03
Check that the path has no additional bend or snub pulleys.
- 04
Enter an additional cut allowance only if your belt or splice specification calls for one.
- 05
Confirm cut length and take-up setting with the belt supplier before ordering.
Worked example
Worked example — 250 mm / 200 mm pulleys at 4000 mm centres
The example shows the inputs and main steps so you can check the result.
Inputs
- Drive effective diameter: 250 mm
- Tail effective diameter: 200 mm
- Centre distance: 4000 mm
- Additional allowance: 300 mm
| Step | Value |
|---|---|
| Term 1 — 2C | 2 × 4000 = 8000 mm |
| Term 2 — π(D₁+D₂)/2 | π × 450 / 2 = 706.9 mm |
| Unequal-diameter adjustment | Exact tangent geometry adds ≈ 0.16 mm |
| Geometric belt length | 8707.01 mm |
| Plus specified allowance | + 300 mm |
| Length incl. allowance | 9007.01 mm (9.007 m / 29.55 ft) |
Units
Useful unit conversions
Shown so you can reconcile the output with the units in your own data.
| Metric | Equivalent |
|---|---|
| 1 m | 3.281 ft |
| 1 mm | 0.03937 in |
| 1000 mm | 3.281 ft |
Questions
Common questions
- Do I measure centre-to-centre or the free span?
- Centre to centre. The free span is not the input this geometry requires.
- How much additional allowance should I add?
- The default is zero. Use the allowance specified for your belt, splice and take-up design; this calculator cannot determine it.
- Why is the unequal-diameter adjustment so small?
- At 50 mm diameter difference and 4 m centres, the exact tangent path adds about 0.16 mm beyond the first two terms. It becomes more important on short centres or strongly unequal pulleys.
- Does this work for a centre drive or multi-pulley path?
- No. Additional pulleys change the belt path and wrap angles. Use the complete conveyor drawing or supplier calculation.
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