Synchronous Belt Length
Estimate synchronous belt pitch length from pulley pitch diameters D1/D2 and centre distance C using the open-belt formula.
Inputs
Formula
Fundamentals
Estimate synchronous belt pitch length from pulley pitch diameters D1/D2 and centre distance C using the open-belt formula.
This tool computes Synchronous Belt Length from the formula: L = 2C + π(D1+D2)/2 + (D2−D1)²/(4C)
History
Design theory of gears, threads and bearings matured with machine tools and standardisation (AGMA, ISO) since the Industrial Revolution.
Engineering applications
Used for transmission design, joint strength checks and component selection.
Glossary
| Small pulley D1 | Input parameter |
| Large pulley D2 | Input parameter |
| Centre distance C | Input parameter |
| Belt length L | Output result |
How to use
- Fill in Small pulley D1, Large pulley D2, Centre distance C in the Inputs section (watch the unit on each field).
- Click Calculate; the tool evaluates the formula shown above.
- Read Belt length L in the results area.
Formula · Worked Example · Knowledge
Formula
核心计算关系：L = 2C + π(D1+D2)/2 + (D2−D1)²/(4C)
输入变量：
- Small pulley D1
D1— mm - Large pulley D2
D2— mm - Centre distance C
C— mm
输出结果：
- Belt length L
L— mm
假设/适用：Gearing/thread formulas assume standard, zero-backlash mounting; include error & load factors K_A.
Worked Example
根据公式 L = 2C + π(D1+D2)/2 + (D2−D1)²/(4C)，取 Small pulley D1 = 60 mm；Large pulley D2 = 120 mm；Centre distance C = 300 mm。
代入计算得：Belt length L = 885.7 mm。
Key Points
- Gearing/thread formulas assume standard, zero-backlash mounting; include error & load factors K_A.
- Compare stress with allowable stress and keep a safety factor (≥1.5, ≥2 for critical parts).
- For high speed/load also check lubrication, heat and fatigue life, not just static strength.
Parameters
Inputs
| Parameter | Symbol | Unit | Default |
|---|---|---|---|
| Small pulley D1 (mm) | D1 | mm | 60 |
| Large pulley D2 (mm) | D2 | mm | 120 |
| Centre distance C (mm) | C | mm | 300 |
Outputs
| Result | Symbol | Unit |
|---|---|---|
| Belt length L | L | mm |
Applications
- Common engineering use cases