Drawing No. EH–ME–006 // Mechanical Engineering
Gear Ratio & Gear Train Calculator
Reviewed August 2026
Analyze one- to three-stage external gear reductions, output speed, torque, efficiency and basic pitch geometry.
Calculation workflow
Inputs are converted internally to SI, the engineering model is solved, and results are converted back to the selected unit system.
Gear train inputs
Results
Active gear-train geometry (schematic)
| Stage | Ratio | Driver pitch dia. | Driven pitch dia. | Center distance |
|---|
Worked example
Two stages: 20→60 teeth followed by 24→48 teeth. The overall reduction is 3 × 2 = 6:1.
1450 rpm / 6 = 241.7 rpm output.
At 97% per mesh, total efficiency is 0.97² = 94.1%.
Output torque is ideal torque multiplication × total mesh efficiency.
Background
Gear trains trade rotational speed for torque while preserving power only in the ideal lossless case.
i = zdriven / zdriver; itotal = ∏ istage
For the compound trains modeled here, each stage consists of one external gear mesh. Gears on the same intermediate shaft rotate at the same speed.
T = P / ω; nout = nin/itotal
Output power is input power multiplied by the product of entered mesh efficiencies.
Frequently asked questions
Practical questions about assumptions, limits and interpretation.
For a compound external gear train, the overall reduction ratio is the product of each stage ratio: driven teeth divided by driver teeth.
A simple idler between a driver and driven gear changes rotation direction and spacing but not the numerical speed ratio, unless it is part of a compound shaft arrangement.
Real meshes lose power through tooth friction, bearings, seals and lubricant churning. The calculator applies an entered efficiency to each active mesh.
No. It calculates kinematics and basic geometry only. Tooth bending, pitting/contact stress, dynamic factors, backlash, profile shift and lubrication require a gear-design standard and detailed geometry.