What is the Gear Ratio Calculator?
Calculate gear ratio, output RPM, and torque multiplier with this free gear ratio calculator. Enter driver and driven tooth counts for single-stage spur gears, or two stages for compound gear trains. Solve for input RPM, output RPM, or ratio from any two values. Tooth-count finder suggests integer gear pairs for a target ratio. Ideal torque gain and speed reduction with step-by-step math. Runs instantly in your browser.
How to use the Gear Ratio Calculator
- Choose Single Stage, Compound, RPM Solver, or Tooth Count Finder.
- Enter driver and driven tooth counts (two stages for compound mode).
- Optionally enter input RPM to get output speed.
- For RPM solver, enter any two of input RPM, output RPM, and gear ratio.
- Review gear ratio, torque multiplier, speeds, and copy calculation steps.
Common use cases
- Sizing a speed reducer for a motor and load RPM
- Designing a two-stage compound gearbox
- Finding matching tooth counts for a target ratio
- Verifying RPM after changing sprocket or gear sizes
- Mechanical engineering homework on gear trains
Frequently asked questions
- How do you calculate gear ratio?
- Gear ratio GR = teeth on driven gear / teeth on driver gear = N_out / N_in for speed. If the driver has 20 teeth and the driven has 60, GR = 60/20 = 3:1 — the output turns 3× slower.
- How do I find output RPM?
- RPM_out = RPM_in / GR. At 1500 RPM input and 3:1 ratio, output is 500 RPM.
- How does gear ratio affect torque?
- Ideal mechanical advantage: output torque ≈ input torque × GR (ignoring friction). A 3:1 reducer triples torque while dividing speed by 3.
- What is a compound gear train?
- Two meshing stages multiply ratios: overall GR = (N2/N1) × (N4/N3). Stage 1 driven and stage 2 driver are typically on the same shaft.
- How does the tooth finder work?
- It searches integer tooth counts up to your maximum and picks combinations whose ratio N_driven/N_driver is closest to your target — useful for designing real gear pairs.
