Mechanical & Civil Engineering
Planetary Epicyclic Gearbox Speed Ratio Calculator
Determine the output speed ratio and torque multiplication of a simple planetary gearbox with a fixed ring.
Your inputs
Change any value to update the result instantly.
Gear ratio
4 :1
Output speed
437.5 rpm
Output torque
200 lb·ft
Planet gear teeth (approx.)
20
What this calculator does
Planetary Epicyclic Gearbox Speed Ratio Calculator: Applies the standard machine-element relationship used in design textbooks so the capacity, rating or geometry can be worked out step by step.
What your result means
The headline figure is the capacity, rating or geometric result for the element you described. Compare it with the manufacturer's rating and your required service factor.
Formula and working
GR = 1 + Nr/Ns (ring fixed, sun input, carrier output)
- 1
Collect the inputs
Sun gear teeth = 20; Ring gear teeth = 60; Sun input speed = 1,750 rpm; Sun input torque = 50 lb·ft
- 2
Apply the formula
GR = 1 + Nr/Ns (ring fixed, sun input, carrier output)
- 3
Result
Gear ratio = 4 :1
Frequently asked questions
Symbols and assumptions
- Ns
- Sun gear teeth
- Nr
- Ring gear teeth
- inputSpeed
- Sun input speed (rpm)
- inputTorque
- Sun input torque (lb·ft)
- • Standard textbook geometry and steady operating conditions are assumed; shock, misalignment and wear factors are not applied automatically.
- • Material and surface-finish allowances must be chosen by the user for their actual component.
Sources and review
Reviewed 2026-09-22 · Next review 2027-09-22
- • This is an educational estimate for learning and checking, not a design deliverable.
- • Real design must follow the governing code or standard for your jurisdiction and be reviewed and signed off by a qualified engineer.
- • Safety factors, load combinations and material certification are the responsibility of the designer, not of this page.
Important limitation
This is an educational estimate based only on the values and formula shown. Verify current rates, rules, units, and professional standards before relying on the result. It is not personalized financial or investment advice.
Report a mistake or request an improvement
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