Calculate Planetary Gear Ratio

Enter gear teeth and member speeds for evaluation. Select fixed parts and output targets quickly. See ratios, torque, planets, exports, and design checks clearly.

Planetary Gear Ratio Calculator

Use known speed fields for general equation modes. Use input speed for fixed member modes.

Formula Used

The core planetary gear equation is the Willis relationship.

(ωs - ωc) / (ωr - ωc) = -Nr / Ns

Here, ωs is sun speed, ωr is ring speed, and ωc is carrier speed.

Ns means sun teeth. Nr means ring teeth.

For ring fixed with sun input and carrier output:

Ratio = 1 + Nr / Ns

For sun fixed with ring input and carrier output:

Ratio = 1 + Ns / Nr

For carrier fixed between sun and ring:

ωs / ωr = -Nr / Ns

Planet tooth estimate for a simple set:

Np = (Nr - Ns) / 2

Estimated output torque:

Output torque = Input torque × speed ratio × efficiency

How to Use This Calculator

  1. Select the planetary arrangement from the mode list.
  2. Enter the sun gear teeth and ring gear teeth.
  3. Enter planet count for load sharing and phasing checks.
  4. Enter input speed, input torque, and efficiency.
  5. For general modes, enter the two known member speeds.
  6. Press Calculate to show results below the header.
  7. Use CSV for spreadsheet work.
  8. Use PDF for a simple saved report.

Example Data Table

Case Sun Teeth Ring Teeth Fixed Member Input Output Basic Ratio
Reduction drive 30 90 Ring Sun Carrier 4:1
Carrier output 36 84 Sun Ring Carrier 1.4286:1
Reversing train 24 72 Carrier Sun Ring 3:1
Overdrive drive 30 90 Ring Carrier Sun 0.25:1

Engineering Notes About Planetary Gear Ratio

Compact Power Transfer

A planetary gear set is compact and strong. It uses a sun gear, planet gears, a carrier, and an internal ring gear. Several power paths are possible. One member can drive, one can react, and one can deliver output.

Speed Relationship

The calculator applies the Willis relationship. This relation compares sun, ring, and carrier speeds. It also checks the tooth geometry used by simple planetary sets. When the ring and sun tooth counts are known, each planet tooth count should equal half the difference. The value must be practical for manufacturing.

Design Applications

Use this tool when selecting a reduction stage. It is useful for gearboxes, robotics, winches, vehicle transmissions, indexing drives, and compact actuators. The result shows speed ratio, output speed, torque change, pitch consistency, and direction notes. It also estimates planet load sharing when you enter planet count and efficiency.

Member Selection

Planetary ratio can be confusing because the answer changes with the held member. For example, fixing the ring and driving the sun gives carrier reduction. Fixing the sun and driving the ring gives another carrier speed. Holding the carrier creates a reversing train between sun and ring. The general speed equation keeps each case consistent.

Tooth Checks

Good designs need more than a ratio. Tooth count choices should avoid tiny planets, poor clearances, and impossible mesh geometry. The ring count should exceed the sun count. The ring and sun difference should be divisible by two when identical planets are used. Many designs also prefer phasing checks, bearing checks, and strength calculations.

Efficiency And Torque

Efficiency matters. Real gear meshes lose power through sliding, rolling, bearings, seals, and lubricant churning. The calculator includes an efficiency field, so output torque is not overstated. It also displays ideal torque for comparison. Use conservative efficiency when the stage is small, loaded, or poorly lubricated.

Exporting Results

The example table gives common cases. You can change every value and export the result. The CSV file helps with spreadsheets. The PDF file gives a simple record for reports. Always confirm final gears with standards, material data, stress ratings, backlash targets, lubrication plans, and supplier limits before production. For early sizing, the calculator gives a clear starting point. It cannot replace detailed tooth stress analysis, thermal review, shaft deflection checks, or prototype testing under real loads.

FAQs

What is a planetary gear ratio?

It is the speed relationship between selected input and output members in a planetary gear set. The value changes when the fixed member changes.

Why does the fixed member matter?

The fixed member creates the reaction path. Holding the ring, sun, or carrier gives different speed ratios, torque changes, and direction behavior.

What tooth counts are required?

You need sun gear teeth and ring gear teeth. For simple equal planet gears, the planet tooth estimate is half the ring and sun difference.

What does a negative speed mean?

A negative speed means the calculated member rotates opposite the positive reference direction. This often appears when the carrier is fixed.

How is torque estimated?

Torque is estimated from input torque, speed ratio, and efficiency. It is an early sizing value, not a final gear strength rating.

Why include efficiency?

Efficiency accounts for losses from gear mesh friction, bearings, seals, and lubricant drag. It prevents output torque from being overstated.

What is the phasing check?

The phasing check reviews whether planet spacing is practical for the entered tooth counts and planet count. Failed checks need design review.

Can this replace full gearbox design?

No. Use it for ratio planning and quick review. Final design also needs stress, wear, bearing, lubrication, tolerance, and thermal checks.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.