4 Gear Ratio Calculator

Calculate simple and compound four-gear ratios, shaft speeds, torque, power, efficiency, geometry, rotation direction, and practical transmission results quickly and clearly.

Results

Overall Gear Ratio
—
Transmission Type
—
Output RPM
—
Gear 2 RPM
—
Gear 3 RPM
—
Output Torque
—
Output Power
—
Power Loss
—
Output Direction
—
Calculation completed successfully.

Calculator Inputs

RPM
N·m
W
%
mm
teeth/in

Gear Geometry

GearTeethPitch DiameterPitch-Line Speed
Gear 1———
Gear 2———
Gear 3———
Gear 4———

Center distances will appear after calculation.

Formula Used

Simple train: N₄/N₁ = T₁/T₄, so reduction ratio R = T₄/T₁.
Compound train: N₄/N₁ = (T₁/T₂) × (T₃/T₄), so R = (T₂/T₁) × (T₄/T₃).
Torque: τout = τin × R × η. Power: Pout = Pin × η.
Pitch diameter: d = mT in metric, or d = T/DP in imperial units.

How to Use This Calculator

  1. Select simple or compound four-gear operation.
  2. Enter tooth counts for all four gears.
  3. Enter input speed and torque.
  4. Set total efficiency or efficiency per mesh.
  5. Choose module or diametral pitch for geometry.
  6. Press Calculate to update every result.
  7. Export results as CSV or PDF when needed.

4 Gear Ratio Calculator Guide

Understanding Four-Gear Trains

A four-gear train changes rotational speed, torque, and direction between shafts. In a simple train, all four gears mesh in sequence. The middle gears mainly transmit motion and alter rotation direction. The overall speed ratio depends on the first and last gears. In a compound train, gears two and three share one shaft. That arrangement creates two useful ratio stages. Each stage multiplies the other, allowing large reductions inside compact mechanisms.

Speed, Torque, and Efficiency

Gear reduction lowers output speed while increasing ideal output torque. Overdrive does the opposite. Real mechanisms lose energy through tooth friction, bearings, lubrication, and alignment errors. This calculator applies either one total efficiency value or one efficiency value per active mesh. Output power therefore remains below input power whenever efficiency is below one hundred percent. Calculated power loss shows the difference clearly.

Geometry and Practical Checks

Pitch diameter determines how mating gears fit together. Metric gears commonly use module, while imperial gears often use diametral pitch. Meshing gears must share compatible tooth geometry and pressure angle. The calculator estimates pitch diameters, center distances, and pitch-line speeds for quick engineering checks. Very small tooth counts can increase undercut risk, especially with common involute profiles. Always confirm detailed gear strength, material limits, backlash, lubrication, and bearing loads before manufacturing.

Interpreting the Result

A ratio above one indicates reduction when the calculator reports input speed divided by output speed. A ratio below one indicates overdrive. For compound systems, multiply both stage reductions. Direction depends on the number of external meshes. Each external mesh reverses rotation. The exported CSV stores the numerical results for spreadsheets, while the PDF creates a compact engineering record. This tool is useful for education, prototypes, machinery planning, motor drives, robotics, and general transmission analysis. Always verify critical designs before fabrication or operation.

Example Table

GearTeethShaft RPMRole
Gear 1201200Driver
Gear 260400Driven
Gear 315400Compound driver
Gear 445133.33Output

For this compound example, R = (60/20) × (45/15) = 9. The output speed is about 133.33 RPM.

Frequently Asked Questions

What is a four-gear ratio?

It compares input shaft speed with output shaft speed through four meshing gears.

Do intermediate gears change a simple train ratio?

They change direction and spacing, but the first and last tooth counts set the overall simple ratio.

Why does a compound train multiply ratios?

Two gear pairs act as separate stages, so their individual ratios multiply together.

How is output torque estimated?

Input torque is multiplied by the reduction ratio and drivetrain efficiency.

What does efficiency per mesh mean?

It applies the chosen efficiency repeatedly across each active gear mesh.

Can I use module and diametral pitch together?

Use one geometry system consistently for a given gear set.

Does this calculator perform gear strength analysis?

No. Strength, bending stress, contact stress, fatigue, and bearing loads require separate engineering checks.

Can results be exported?

Yes. Use the CSV and PDF buttons above the calculator form.

Use these results as engineering estimates and verify critical designs independently.


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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.