Gear Ratio Calculator: Compound Train Speed and Torque

How It Works

1. Enter Gear Stages

   For each stage (up to 4), input the driving gear tooth count and driven gear tooth count. Stage ratio = driven teeth / driving teeth. The overall ratio is the product of all stage ratios.

2. Enter Input Conditions

   Input driving speed in RPM and input torque in ft-lbs. If you know motor HP instead, enter it and the calculator converts using T = HP x 5252 / RPM.

3. Apply Efficiency Per Stage

   Select gear type for each stage. Spur gears run 95-98% efficient per mesh. Worm gears range from 50-90%. The calculator multiplies per-stage efficiencies to find actual output torque.

4. Review Output

   See output RPM (input RPM / overall ratio), output torque, transmitted horsepower, and rotation direction. Odd numbers of external meshes reverse rotation.

Built For

• Millwrights replacing a gearbox and verifying the new unit matches the required ratio and output torque
• Machine designers selecting gear stages to hit a target output speed from a standard motor RPM
• Maintenance techs checking whether a conveyor drive has enough torque after a motor swap
• Plant engineers evaluating gearbox efficiency losses to size replacement motors correctly
• Automation techs calculating stepper motor gear reductions for positioning applications
• Shop instructors teaching compound gear train math with real tooth count examples

Features & Capabilities

Up to 4 Compound Stages

Enter tooth counts for 1 to 4 gear stages. Overall ratio is the product of all individual stage ratios.

Per-Stage Efficiency

Apply different efficiency values per stage based on gear type. Accounts for cumulative power loss through the entire train.

HP = T x RPM / 5252

Converts between torque and horsepower at any point in the train. Shows power consumed by friction at each stage.

Rotation Direction Tracking

Tracks direction changes through external meshes. Odd mesh count reverses output. Internal gears maintain direction.

Multiple Gear Type Support

Covers spur, helical, bevel, worm, and planetary types with appropriate efficiency ranges for each.

PDF Export

Export gear train analysis as a branded PDF for maintenance records or machine design files.

Assumptions

• Overall gear ratio equals the product of individual stage ratios: GR_total = GR_1 x GR_2 x ... x GR_n
• Power conversion uses HP = T x RPM / 5252 where T is in ft-lbs (derived from HP = T x 2\u03c0 x RPM / 33,000)
• Per-stage efficiency applied as a multiplier on output torque — cumulative efficiency is the product of all stage efficiencies
• Default efficiency values: spur/helical 95-98%, bevel 95-97%, worm 50-90%, planetary 95-97% per mesh
• All external gear meshes assumed to reverse rotation direction — internal (ring) gears maintain direction
• Gear teeth assumed to be properly designed with standard involute profiles — no correction for non-standard pressure angles or profile shifts

Limitations

• Does not calculate gear tooth bending stress or contact stress per AGMA 2001/2101 — gear strength analysis requires detailed geometry
• Worm gear efficiency is highly dependent on lead angle, sliding velocity, and lubricant — single efficiency value is an approximation
• Does not model backlash, which affects positioning accuracy in servo and CNC applications
• Does not account for thermal power limits — high-speed, high-load gearboxes may be limited by oil temperature rather than mechanical stress
• Planetary gearset analysis simplified to a single ratio and efficiency — does not model compound planetary or differential arrangements
• Does not evaluate gear noise, vibration, or dynamic load factors that affect gear life at high speeds

References

• AGMA 2001-D04 — Fundamental Rating Factors and Calculation Methods for Involute Spur and Helical Gear Teeth
• AGMA 6034-B92 — Practice for Enclosed Cylindrical Wormgear Speed Reducers and Gearmotors
• Dudley's Gear Handbook, 2nd Edition — Gear Design, Manufacturing, and Application
• Shigley's Mechanical Engineering Design — Chapter 13: Gears (gear train analysis and efficiency)
• ANSI/AGMA 6010-F97 — Standard for Spur, Helical, Herringbone, and Bevel Enclosed Drives
• Machinery's Handbook — Gear Ratio, Tooth Count, and Power Transmission Calculations

Frequently Asked Questions