Gear Ratio & Torque 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 Local Efficiency Placeholders

   Select a gear type for each stage. The calculator uses local placeholder efficiencies for arithmetic only. Replace them with manufacturer curves, measured data, or current engineering sources for decision use.

4. Review Output and Warnings

   See output RPM, output torque, transmitted horsepower, heat loss, and source/use boundary warnings. Direction, tooth stress, service factor, lubrication, and thermal capacity are outside this calculator.

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 Placeholders

Applies local placeholder values by gear type and exposes worm efficiency as an editable input. Manufacturer or measured efficiency controls final decisions.

HP = T x RPM / 5252

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

Source Boundary Warnings

Flags that AGMA rating, tooth stress, service factor, lubrication, thermal rating, guarding, and qualified review remain outside the app.

Multiple Gear Type Inputs

Supports spur, helical, bevel, worm, planetary, and chain/sprocket labels for screening while warning that each needs configuration-specific validation.

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 x pi 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 are local placeholders and not AGMA, ISO, or manufacturer rating data
• Direction, idlers, internal gears, planetary paths, chain wrap, belt paths, and right-angle layouts are not validated
• Gear teeth are not checked for bending stress, contact stress, profile shift, pressure angle, backlash, quality, material, or wear

Limitations

• Does not reproduce AGMA, ISO, or manufacturer rating methods or tables
• Does not calculate gear tooth bending stress, contact stress, service factor, dynamic factor, reliability, or life
• Worm efficiency is highly dependent on lead angle, sliding velocity, lubricant, temperature, and manufacturer geometry
• Does not model backlash, contact ratio, profile shift, pressure angle, mesh quality, or noise/vibration
• Does not account for thermal power limits, lubricant temperature, housing cooling, duty cycle, or ambient conditions
• Does not validate planetary arrangements, chain pitch/tension/wrap, shafting, bearings, couplings, guards, lockout, or machine-safety controls

References

• NIST SP 811 - SI and unit-conversion source pointer
• MPMA/AGMA Standards and Technology - gear standards source pointer
• MPMA/AGMA Gear Technical Committees - application, rating, wormgearing, lubrication, and related source-gap context
• Manufacturer gearbox catalogs and rating curves for final ratio, efficiency, thermal, lubrication, and service-factor review

Frequently Asked Questions