Chain Drive Length
Estimate chain link count Lp and actual length L from pitch p, sprocket teeth Z1/Z2 and centre distance C (in pitches) using the Ham correction formula.
Inputs
Formula
Fundamentals
Estimate chain link count Lp and actual length L from pitch p, sprocket teeth Z1/Z2 and centre distance C (in pitches) using the Ham correction formula.
This tool computes Chain Drive Length from the formula: Lp = 2C + (Z1+Z2)/2 + (Z2−Z1)²/(4π²·C); L = Lp·p
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
| Pitch p | Input parameter |
| Small sprocket Z1 | Input parameter |
| Large sprocket Z2 | Input parameter |
| Link count Lp | Output result |
| Chain length L | Output result |
How to use
- Fill in Pitch p, Small sprocket Z1, Large sprocket Z2, Centre dist C (pitches) in the Inputs section (watch the unit on each field).
- Click Calculate; the tool evaluates the formula shown above.
- Read Link count Lp, Chain length L in the results area.
Formula · Worked Example · Knowledge
Formula
核心计算关系：Lp = 2C + (Z1+Z2)/2 + (Z2−Z1)²/(4π²·C); L = Lp·p
输入变量：
- Pitch p
p— mm - Small sprocket Z1
Z1 - Large sprocket Z2
Z2 - Centre dist C (pitches)
C
输出结果：
- Link count Lp
Lp - Chain 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 Lp = 2C + (Z1+Z2)/2 + (Z2−Z1)²/(4π²·C); L = Lp·p，取 Pitch p = 12.7 mm；Small sprocket Z1 = 17；Large sprocket Z2 = 34；Centre dist C (pitches) = 30。
代入计算得：Link count Lp = 85.74；Chain length L = 1,089 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 |
|---|---|---|---|
| Pitch p (mm) | p | mm | 12.7 |
| Small sprocket Z1 | Z1 | 17 | |
| Large sprocket Z2 | Z2 | 34 | |
| Centre dist C (pitches) | C | 30 |
Outputs
| Result | Symbol | Unit |
|---|---|---|
| Link count Lp | Lp | |
| Chain length L | L | mm |
Applications
- Common engineering use cases