Planetary Gear Speed Calculator
Solve carrier speed in a simple sun–ring planetary set from tooth counts and signed sun/ring speeds.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Use the Willis relative-speed relation about the carrier, with the same positive rotation convention for every member.
Carrier rpm=(sun teeth×sun rpm+ring teeth×ring rpm)/(sun teeth+ring teeth)
Worked example
Sun 20 teeth at 3000 rpm and ring 60 teeth fixed give carrier 750 rpm; the corresponding planet has 20 teeth.
Assumptions and input details
Requires ring−sun to be a positive even integer for a same-module unshifted simple set. This checks kinematics, not tooth interference, planet spacing, assembly fit, strength, efficiency or torque ratings.
References: Jönköping University: planetary gear kinematics
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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