BIZOMAT MAKEOS · Gears
Gear Train Ratio, Speed and Torque
What is the overall ratio, output speed and output torque of this gear train?
Overall ratio, output speed, direction, output torque and efficiency of a simple or compound gear train with up to four meshes.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Input speed | rpm | Speed of the first driver. |
| Input torque | N·m | Torque at the first driver. |
| Efficiency per mesh | % | Efficiency of each external spur or helical mesh (typically 97–99% including bearings). |
| Mesh 1 | ||
| Driver teeth | teeth | Teeth on the driver of mesh 1. |
| Driven teeth | teeth | Teeth on the driven gear of mesh 1. |
| Mesh 2 | ||
| Driver teeth | teeth | Teeth on the driver of mesh 2 (on the same shaft as driven gear 1); 0 if not used. |
| Driven teeth | teeth | Teeth on the driven gear of mesh 2. |
| Mesh 3 | ||
| Driver teeth | teeth | Mesh 3 driver, or 0. |
| Driven teeth | teeth | Mesh 3 driven gear, or 0. |
| Mesh 4 | ||
| Driver teeth | teeth | Mesh 4 driver, or 0. |
| Driven teeth | teeth | Mesh 4 driven gear, or 0. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Input speed
- What it is
- The rotational speed of the first driving gear, at the input shaft of the train.
- Units and format
- Enter a number in rpm: revolutions per minute. The form accepts 0.000001 rpm to 1000000 rpm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1450 rpm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Output speed changes in proportion.
- Get it right
- Use the speed of the first driver, not of the motor if there is a belt or coupling ratio in between.
What this means: Input torque
- What it is
- The torque delivered to the first driving gear at the input shaft.
- Units and format
- Enter a number in N·m: newton-metres. The form accepts 0 N·m or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20 N·m as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Output torque changes in proportion.
- Get it right
- Use the torque at the gear shaft, after any belt or coupling ratio upstream.
What this means: Efficiency per mesh
- What it is
- The efficiency of each single gear mesh in the train; the tool applies it once for every mesh in use.
- Units and format
- Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 1% to 100%. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 98% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Overall efficiency is this value raised to the number of meshes, so it lowers output torque.
- Get it right
- Enter the efficiency per mesh, not the overall train efficiency. Type the percentage, not a fraction.
Mesh 1
What this means: Driver teeth
- What it is
- The number of teeth on the driving gear of the first mesh, on the input shaft.
- Units and format
- Enter a number in teeth: a whole number of teeth. The form accepts 0 teeth to 5000 teeth. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20 teeth as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- More driver teeth lower the ratio and raise output speed.
- Get it right
- A mesh is used only when both its driver and driven teeth are above 0.
What this means: Driven teeth
- What it is
- The number of teeth on the driven gear of the first mesh.
- Units and format
- Enter a number in teeth: a whole number of teeth. The form accepts 0 teeth to 5000 teeth. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 60 teeth as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- More driven teeth raise the ratio and output torque and lower output speed.
- Get it right
- The mesh ratio is driven teeth divided by driver teeth.
Mesh 2
What this means: Driver teeth
- What it is
- The number of teeth on the driving gear of the second mesh, on the same shaft as the first driven gear.
- Units and format
- Enter a number in teeth: a whole number of teeth. The form accepts 0 teeth to 5000 teeth. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 18 teeth as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- More driver teeth lower the ratio and raise output speed.
- Get it right
- 0 leaves this mesh out of the train.
What this means: Driven teeth
- What it is
- The number of teeth on the driven gear of the second mesh.
- Units and format
- Enter a number in teeth: a whole number of teeth. The form accepts 0 teeth to 5000 teeth. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 54 teeth as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- More driven teeth raise the ratio and output torque and lower output speed.
- Get it right
- 0 leaves this mesh out of the train.
Mesh 3
What this means: Driver teeth
- What it is
- The number of teeth on the driving gear of the third mesh, on the same shaft as the second driven gear.
- Units and format
- Enter a number in teeth: a whole number of teeth. The form accepts 0 teeth to 5000 teeth. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 teeth as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- More driver teeth lower the ratio and raise output speed.
- Get it right
- 0 leaves this mesh out of the train.
What this means: Driven teeth
- What it is
- The number of teeth on the driven gear of the third mesh.
- Units and format
- Enter a number in teeth: a whole number of teeth. The form accepts 0 teeth to 5000 teeth. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 teeth as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- More driven teeth raise the ratio and output torque and lower output speed.
- Get it right
- 0 leaves this mesh out of the train.
Mesh 4
What this means: Driver teeth
- What it is
- The number of teeth on the driving gear of the fourth mesh, on the same shaft as the third driven gear.
- Units and format
- Enter a number in teeth: a whole number of teeth. The form accepts 0 teeth to 5000 teeth. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 teeth as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- More driver teeth lower the ratio and raise output speed.
- Get it right
- 0 leaves this mesh out of the train.
What this means: Driven teeth
- What it is
- The number of teeth on the driven gear of the fourth mesh.
- Units and format
- Enter a number in teeth: a whole number of teeth. The form accepts 0 teeth to 5000 teeth. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 teeth as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- More driven teeth raise the ratio and output torque and lower output speed.
- Get it right
- 0 leaves this mesh out of the train.
Method and formulas
- Ratio of each mesh = driven ÷ driver; overall ratio = product of mesh ratios.
- Output speed = input ÷ overall ratio; each external mesh reverses direction.
- Output torque = input torque × ratio × efficiency^(number of meshes).
- Example: 20:60 then 18:54 gives 9:1, 161.11 rpm and 172.87 N·m.
Limitations
- External meshes only; idler gears change direction but not the ratio (enter them as a mesh with equal teeth if needed).
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Design a reduction from available gears
- Check output speed of an existing train
- Estimate torque at the output shaft
Who it is for
- Gear designers
- Machinists
- Maintenance engineers
What you get
- Overall ratio
- Output speed and direction
- Output torque
- Overall efficiency
Interpreting the result
- Check each mesh for strength with its own torque, not only the output.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2122–2160. Topic reference; no source tables or recommended settings are reproduced.
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