The Transmission Gear Ratio & Vehicle Speed Calculator determines cruising velocity from engine rotational speed, transmission gear reduction, differential final drive, and tire height.

### Drivetrain Velocity Equations & Mechanical Derivation Vehicle ground velocity directly correlates with crankshaft rotation through drivetrain reduction ratios: - **Total Drivetrain Gear Reduction**: $$\text{Overall Ratio} = \text{Transmission Ratio} \times \text{Differential Final Drive}$$ - **Vehicle Ground Speed (MPH)**: Accounting for tire circumference ($D \times \pi$) and unit conversions ($60\text{ min/hr} / 63{,}360\text{ in/mi} \approx 1 / 336$): $$\text{Speed (MPH)} = \frac{\text{Engine RPM} \times \text{Tire Diameter (inches)}}{\text{Overall Ratio} \times 336}$$ - **Metric Velocity (km/h)**: $$\text{Speed (km/h)} = \text{Speed (MPH)} \times 1.60934$$

### Worked Mechanical Example Evaluating highway cruising speed in an overdrive 6th gear: - **Engine Operating Speed**: 2,500 RPM - **Transmission Ratio (6th Overdrive)**: 0.68 - **Differential Axle Ratio**: 3.73 - **Tire Height**: 28.0 inches - **Total Ratio**: $0.68 \times 3.73 = 2.5364\text{:1}$ - **Calculated Speed**: $$\text{Speed} = \frac{2{,}500 \times 28.0}{2.5364 \times 336} = \frac{70{,}000}{852.23} \approx \mathbf{82.1\text{ MPH}} \quad (132.2\text{ km/h})$$

### In-Browser Processing & Privacy Note All powertrain calculations evaluate locally in client-side JavaScript. No vehicle builds, gear ratios, or performance numbers are stored or transmitted across external networks.