Internal Gear Dimensions
Compute pitch, addendum and root diameters of an internal gear (addendum points inward, so da=m(Z−2), df=m(Z+2.5), the reverse of external gears).
Inputs
Formula
Fundamentals
Compute pitch, addendum and root diameters of an internal gear (addendum points inward, so da=m(Z−2), df=m(Z+2.5), the reverse of external gears).
This tool computes Internal Gear Dimensions from the formula: d = mZ; da = m(Z−2); df = m(Z+2.5)
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
| Module m | Input parameter |
| Teeth Z | Input parameter |
| Pitch dia. d | Output result |
| Tip dia. da | Output result |
How to use
- Fill in Module m, Teeth Z in the Inputs section (watch the unit on each field).
- Click Calculate; the tool evaluates the formula shown above.
- Read Pitch dia. d, Tip dia. da, Root dia. df in the results area.
Formula · Worked Example · Knowledge
Formula
核心计算关系：d = mZ; da = m(Z−2); df = m(Z+2.5)
输入变量：
- Module m
m— mm - Teeth Z
Z
输出结果：
- Pitch dia. d
d— mm - Tip dia. da
da— mm - Root dia. df
df— 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 d = mZ; da = m(Z−2); df = m(Z+2.5)，取 Module m = 3 mm；Teeth Z = 50。
代入计算得：Pitch dia. d = 150 mm；Tip dia. da = 144 mm；Root dia. df = 157.5 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 |
|---|---|---|---|
| Module m (mm) | m | mm | 3 |
| Teeth Z | Z | 50 |
Outputs
| Result | Symbol | Unit |
|---|---|---|
| Pitch dia. d | d | mm |
| Tip dia. da | da | mm |
| Root dia. df | df | mm |
Applications
- Common engineering use cases