Gear Ratio Calculator
Use one driver-and-driven pair or enter matching driver and driven tooth-count lists for a compound train. Each stage ratio is multiplied into the overall ratio, which is then applied to the input speed.
How to use this calculator
Enter gear-train mode, either one driver and driven tooth count or matching driver and driven tooth-count lists for two to twenty stages, and input speed in rpm.
Review which gear is driver, external versus internal mesh, compatible pitch, stage order, efficiency, load, and maximum rated speed.
Read overall gear ratio, ideal output speed in rpm, and stage count.
Formula
Stage ratio = driven teeth ÷ driver teeth. Overall ratio = product of all stage ratios; ideal output speed = input rpm ÷ overall ratio.
Worked example
Stages of 20→40 teeth and 15→45 teeth have ratios 2 and 3; the compound ratio is 6, so 1,200 rpm input gives 200 rpm ideal output.
Assumptions and limits
- Each entered pair represents one ideal speed-ratio stage. Direction, idlers, shared-shaft topology, torque, pitch compatibility, friction, backlash, strength, and drivetrain losses are not modeled.
- Gear Ratio Calculator treats the entered values as estimates and does not infer missing project, account, or personal details.
- Calculations retain working precision except where the cited method requires an intermediate rounding step; displayed values are then formatted separately. Source rules and dated rates must be rechecked when they change.
Sources
- National Aeronautics and Space Administration: Scalar Comparison — RatiosRatio definitions and proportional comparison used by the gear-ratio model. Reviewed 2026-08-14.
- OpenStax: Prealgebra 2eOfficial formula or method source used by this calculator. Reviewed 2026-08-14.
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Verification
How this calculator is checked
Trust comes from reproducible evidence, not model confidence. You can inspect the formula, assumptions, worked example, and cited sources on this page.
- Versioned calculationFormula logic is kept separate from the interface and covered by automated registry and behavior checks.
- Cited evidenceSources linked for independent checking: 2.
- Transparent AI useAI may assist drafting or adversarial review. Agreement between models is not proof, and no human expert review is claimed unless a named reviewer is shown.
Frequently asked questions
How does the Gear Ratio Calculator work?
Stage ratio = driven teeth ÷ driver teeth. Overall ratio = product of all stage ratios; ideal output speed = input rpm ÷ overall ratio.
What information should I enter in the Gear Ratio Calculator?
Enter gear-train mode, either one driver and driven tooth count or matching driver and driven tooth-count lists for two to twenty stages, and input speed in rpm, then verify which gear is driver, external versus internal mesh, compatible pitch, stage order, efficiency, load, and maximum rated speed.
What should I verify before using this Gear Ratio Calculator result?
Each entered pair represents one ideal speed-ratio stage. Direction, idlers, shared-shaft topology, torque, pitch compatibility, friction, backlash, strength, and drivetrain losses are not modeled.
Last updated 2026-08-25 · single-or-multi-stage-v2 · content-2026-08-14 · Published by YunFanLabs