Gear Ratio, Speed & Torque (2–4 gears) Calculator

Gear Ratio, Speed & Torque (2–4 gears)

CE Style

Inputs

0.90–0.99 typical (per gear mesh)

Gears (Series Train)

GearTeeth (N)
G1 (driver)
G2
G3
G4 (output)
Series trains multiply stage ratios N2/N1 × N3/N2 × …. For a simple idler chain, ratio reduces to Nout/Nin. Each mesh flips rotation.

Key Results

Per-Gear Speeds & Torques

Conventions: Speed ratio i = ωin / ωout. Output speed nout = nin / i. Ideal torque multiplication Tout = Tin · i · ηmeshes. Direction flips with each mesh.

How to Use the Gear Ratio, Speed & Torque Calculator

Quick guide for 2-gear, 3-gear with idler, and 4-gear compound trains. Enter teeth, input speed/torque, mesh efficiencies, then read overall ratio, direction, output speed, torque, and per-stage details.

1) Pick Train Type

  • Simple (2 gears): Z₁ drives Z₂.
  • Idler (3 gears): Z₁ → Z₂ (idler) → Z₃. Ratio is Z₃/Z₁; idler only flips direction and adds loss.
  • Compound (4 gears): two meshes on a shared shaft, overall ratio is (Z₂/Z₁) × (Z₄/Z₃).
Use compound when one stage cannot reach the target ratio or you need packaging flexibility.

2) Enter Teeth

  • Z₁ is the driver (input shaft).
  • For simple, set Z₂ (driven). For idler, Z₂ is the idler and Z₃ is the output. For compound, Z₂ and Z₃ share a shaft, Z₄ is the output.
  • All tooth counts must be positive integers.

3) Input Speed & Torque

  • Enter input speed in rpm and input torque in your preferred units (N·m, lbf·in, lbf·ft).
  • The tool converts units internally and shows power in/out.

4) Efficiencies

  • Set mesh efficiency for each stage (η₁, η₂). Typical values are 0.97–0.99 for well-lubricated spur/helical gears.
  • Total efficiency is the product of stage efficiencies.

5) Read Results

  • Key: number of meshes, overall ratio R = output/input, direction, and total efficiency.
  • Output: output speed (rpm) and torque (unit-matched), plus power in/out.
  • Stage details: each stage ratio and intermediate speeds/torques for idler or compound trains.

6) Direction Notes

  • External meshes flip rotation. An odd number of meshes → output reversed; an even number → same as input.
  • Idler adds one more mesh, so direction becomes the same as input but with additional loss.
This tool assumes external spur/helical meshes. Internal gears or belts are not modeled.

7) Checks & Tips

  • Verify all tooth counts are positive integers and reasonable for your module/DP.
  • Large ratios benefit from compound trains to keep gears within practical sizes.
  • Torque scales with ratio and efficiency: T_out ≈ T_in × R × η_total.
  • Power out should be close to power in × η_total.
FAQ & Troubleshooting

My output torque looks low.
Check efficiencies. Each stage reduces torque by η; total is η₁ × η₂ for two meshes.

Direction seems wrong.
Count meshes. One mesh reverses direction; two meshes restore it.

Units confuse the numbers.
Set torque units correctly (N·m, lbf·in, or lbf·ft). The tool converts automatically.

Can I model multiple idlers?
Additional idlers do not change the ratio, only direction and loss; approximate by reducing efficiency.

Copy-Paste Mini Workflow

1) Choose train type: Simple / Idler / Compound
2) Enter Z₁, Z₂, Z₃, Z₄ as required
3) Set input speed (rpm) and torque (units)
4) Enter mesh efficiencies (η) per stage
5) Read R, direction, rpm_out, torque_out, and stage details