Planetary Gear Ratio
Compute the ratio, output speed and output torque of a single-stage planetary set with ring fixed, sun input and carrier output (assembly condition Zr = Zs + 2Zp).
Inputs
Formula
Fundamentals
Compute the ratio, output speed and output torque of a single-stage planetary set with ring fixed, sun input and carrier output (assembly condition Zr = Zs + 2Zp).
This tool computes Planetary Gear Ratio from the formula: i = 1 + Zr/Zs; n2 = n1 / i; T2 = T1 · i
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
| Sun teeth Zs | Input parameter |
| Ring teeth Zr | Input parameter |
| Input speed n₁ | Input parameter |
| Ratio i | Output result |
| Output speed | Output result |
How to use
- Fill in Sun teeth Zs, Ring teeth Zr, Input speed n₁, Input torque T₁ in the Inputs section (watch the unit on each field).
- Click Calculate; the tool evaluates the formula shown above.
- Read Ratio i, Output speed, Output torque in the results area.
Formula · Worked Example · Knowledge
Formula
核心计算关系：i = 1 + Zr/Zs; n2 = n1 / i; T2 = T1 · i
输入变量：
- Sun teeth Zs
Zs - Ring teeth Zr
Zr - Input speed n₁
n1— rpm - Input torque T₁
T1— N·m
输出结果：
- Ratio i
i - Output speed
n2— rpm - Output torque
T2— N·m
假设/适用：Gearing/thread formulas assume standard, zero-backlash mounting; include error & load factors K_A.
Worked Example
根据公式 i = 1 + Zr/Zs; n2 = n1 / i; T2 = T1 · i，取 Sun teeth Zs = 18；Ring teeth Zr = 54；Input speed n₁ = 1,500 rpm；Input torque T₁ = 20 N·m。
代入计算得：Ratio i = 4；Output speed = 375 rpm；Output torque = 80 N·m。
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 |
|---|---|---|---|
| Sun teeth Zs | Zs | 18 | |
| Ring teeth Zr | Zr | 54 | |
| Input speed n₁ (rpm) | n1 | rpm | 1500 |
| Input torque T₁ (N·m) | T1 | N·m | 20 |
Outputs
| Result | Symbol | Unit |
|---|---|---|
| Ratio i | i | |
| Output speed | n2 | rpm |
| Output torque | T2 | N·m |
Applications
- Common engineering use cases