Automotive & Engines

What makes cars go: horsepower, torque, compression, gearing, fuel economy and braking

From horsepower and torque to compression, gearing, fuel economy, and braking, this category brings together the core formulas that explain how cars move and perform. It’s useful for students, exam prep, mechanics, engineers, and anyone working with vehicle data, because these equations help you estimate speed, power, efficiency, stopping distance, and overall performance in real-world automotive situations.

Power from Torque & RPM

NEWIntermediate

P = \frac{\tau \times N}{9549}

Engine power in kW from torque and rotational speed.

Horsepower from Torque (Imperial)

HP = \frac{\tau \times N}{5252}

Horsepower from torque (lb-ft) and engine rpm.

Compression Ratio

NEWIntermediate

CR = \frac{V_d + V_c}{V_c}

Ratio of cylinder volume at bottom vs top of the stroke.

Engine Displacement

V = \frac{\pi}{4} b^2 s\, n

Total swept volume of all cylinders.

Gear Ratio

GR = \frac{N_{out}}{N_{in}}

Ratio of driven to driving gear teeth.

Vehicle Speed from RPM

NEWIntermediate

v = \frac{\pi d N}{GR \cdot G_f}

Road speed from engine rpm, gearing and tyre diameter.

Fuel Economy (L/100km)

E = \frac{100\, F}{d}

Litres of fuel used per 100 km travelled.

Miles Per Gallon

MPG = \frac{d}{F}

Distance in miles per gallon of fuel.

Braking Distance

NEWIntermediate

d = \frac{v^2}{2 \mu g}

Distance to stop from speed v with friction μ.

Power-to-Weight Ratio

NEWIntermediate

PWR = \frac{P}{m}

Engine power divided by vehicle mass — the key to acceleration.

Aerodynamic Drag

F_d = \tfrac{1}{2}\rho v^2 C_d A

Air resistance a car must overcome, rising with speed squared.

Kinetic Energy of Vehicle

KE = \tfrac{1}{2} m v^2

Energy that brakes must dissipate to stop a moving car.

Torque from Force

\tau = F \times r

Turning effect of a force applied at radius r.

EV Range

NEWIntermediate

R = \frac{E}{c}

Electric-vehicle range from battery capacity and consumption.

EV Charging Time

t = \frac{E}{P}

Hours to charge a battery at a given power.

Tyre Rolling Circumference

C = \pi d

Distance covered in one wheel revolution.