MCPCalc

Gear Ratio Calculator

Calculate single-stage ratios, multi-stage compound gear trains, and vehicle final drive speed from one consistent engineering layout.

Single-Stage Gear Ratio

τ = F·r · GR. Speed ratio = 1/GR.

Gear Ratio (GR)3.0000 : 1
Speed Ratio (output/input)0.3333 : 1
Ideal Torque Multiplier3.0000 ×
Rotation DirectionOpposite
TypeSpeed Reduction

Multi-Stage Compound Gear Train

Up to 4 stages. Overall ratio = product of all stage ratios.

Stage 1
Stage ratio
3.000:1
600.0 RPM
Stage 2
Stage ratio
3.000:1
200.0 RPM
Compound Overall Ratio9.0000 : 1
Overall Torque Multiplier (ideal)9.0000 ×
Output Shaft RPM200.00 RPM
TypeSpeed Reduction

Vehicle Final Drive & Wheel Speed

Engine → transmission → differential → wheel → speed.

635 mm = 25.0 in

Vehicle Speed27.5 km/h = 17.1 mph
Wheel RPM229.80 RPM
Total drive ratio (trans × final)13.0550 : 1

What This Calculator Does

The gear ratio calculator covers three common scenarios: single-stage gear pair (by tooth count or diameter), multi-stage compound gear trains (up to 4 stages with intermediate shaft speeds), and vehicle final drive — computing wheel RPM and speed in mph and km/h from engine RPM, transmission ratio, differential ratio, and tyre diameter.

It combines Driver Gear Teeth, Driven Gear Teeth to estimate Gear Ratio, Speed Ratio, Ideal Torque Multiplier.

Formula & Method

Single stage: GR=Ndriven/NdriverGR = N_{driven} / N_{driver}, speed ratio =1/GR= 1/GR, torque multiplier =GR= GR (ideal). Compound train: GRtotal=GR1×GR2×⋯×GRnGR_{total} = GR_1 \times GR_2 \times \cdots \times GR_n. Vehicle speed: v=nengineGRtrans×GRfinal×πdtyre60v = \frac{n_{engine}}{GR_{trans} \times GR_{final}} \times \frac{\pi d_{tyre}}{60}

Notation used in the formulas: RR = Gear Ratio; x1x_{1} = Driver Gear Teeth; x2x_{2} = Driven Gear Teeth.

Method summary: inputs are normalized to consistent units, core equations are evaluated, then secondary values are derived and rounded for display.

Use this calculator for quick scenario analysis. Start with baseline values, change one driver at a time, and compare how sensitive the results are to each input shown above.

Worked Examples

Single stage — 16-tooth driver, 48-tooth driven

GR = 48/16 = 3.0 : 1 (speed reduction) Speed ratio = 1/3 = 0.333 : 1 Torque multiplier = 3× (ideal, no friction) Rotation direction = opposite

Vehicle speed — 3000 RPM, 3.5 trans ratio, 3.73 final, 635mm tyre

Wheel RPM = 3000 / (3.5 × 3.73) = 3000 / 13.055 = 229.8 RPM Circumference = π × 0.635 = 1.994 m Speed = 229.8 × 1.994 / 60 = 7.64 m/s = 27.5 km/h = 17.1 mph

Inputs Used

  • Driver Gear Teeth: Used directly in the calculation.
  • Driven Gear Teeth: Used directly in the calculation.

See Also

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