Science
Angular momentum
Multiply moment of inertia about a fixed axis by angular velocity to find signed angular momentum; reversing rotation reverses its sign.
Calculators / Science / Two-stage gear ratio
Two-stage gear ratio calculator
Calculate the speed reduction across two gear meshes with a shared intermediate shaft.
On this page
Overall reduction ratio9
Output speed200rpm
Calculator controls
How to calculate
Calculate the speed reduction across two gear meshes with a shared intermediate shaft.
Overall reduction ratio =
b/a*d/cOutput speed =
rpm*a/b*c/d rpmWorked example
- First driver teeth: 20
- First driven teeth: 60
- Second driver teeth: 15
- Second driven teeth: 45
- Input speed (rpm): 1800
- Overall reduction ratio: 9
- Output speed: 200 rpm
Assumptions and limits
The first driven gear and second driver must share a shaft. This ideal tooth-count model excludes slip, losses, torque capacity and mechanical safety checks.
Results are rounded for display; calculations use unrounded values. Read our calculation methodology.
Understanding the result
Calculate the speed reduction across two gear meshes with a shared intermediate shaft. Multiply driven-to-driver tooth ratios. Two external meshes restore the input rotation direction; other arrangements can differ.
When this tool is useful
Multiply driven-to-driver tooth ratios. Two external meshes restore the input rotation direction; other arrangements can differ.
Understanding your inputs
| Input | Example |
|---|---|
First driver teeth a | 20 |
First driven teeth b | 60 |
Second driver teeth c | 15 |
Second driven teeth d | 45 |
Input speed (rpm) rpm | 1800 |
Frequently asked questions
What does this model leave out?
The first driven gear and second driver must share a shaft. This ideal tooth-count model excludes slip, losses, torque capacity and mechanical safety checks.
How do I reproduce the example?
Enter the displayed example values in their labelled units. Apply the formula before rounding; change one input at a time to compare scenarios.