This calculator helps you determine the approximate speed of a vehicle based on its engine's revolutions per minute (RPM), the overall gear ratio, and the diameter of its wheels. Understanding these relationships is crucial in automotive engineering, performance tuning, and even for everyday drivers interested in their vehicle's mechanics.
Key Components:
Engine RPM (Revolutions Per Minute): This measures how fast the engine's crankshaft is rotating. Higher RPM generally means more power output, but also higher fuel consumption and wear.
Gear Ratio: This is a numerical value representing the reduction or increase in rotational speed between two meshing gears. In a vehicle, it's the combined ratio of all the gears in the transmission (for the selected gear) and the final drive (differential). A higher gear ratio (e.g., 4.10:1) means the engine turns more times for each rotation of the drive wheels, resulting in more torque but lower top speed. A lower gear ratio (e.g., 3.08:1) means less engine torque but higher top speed.
Wheel Diameter: The overall diameter of the tire and wheel assembly. This is critical because the circumference of the tire determines how much distance the vehicle travels for each wheel rotation.
The Calculation:
The formula used in this calculator to estimate vehicle speed (in Miles Per Hour – MPH) is derived from the fundamental relationship between rotational speed, circumference, and linear speed:
The speed of the vehicle is directly proportional to the rotational speed of the wheel and its circumference, and inversely proportional to the gear ratio.
First, we calculate the rotational speed of the wheel:
Wheel RPM = Engine RPM / Overall Gear Ratio
Next, we determine the wheel's circumference. Since the input is in inches, we'll convert it to miles later.
Circumference = π × Wheel Diameter (inches)
Now, we calculate the distance traveled per minute:
Distance per Minute = Wheel RPM × Circumference (inches)
Finally, we convert this distance per minute into Miles Per Hour (MPH):
A simplified version often used is:
Speed (MPH) ≈ (Engine RPM × Wheel Diameter × 0.00017) / Gear Ratio
(This approximation accounts for π, 60 minutes/hour, and 63360 inches/mile).
Use Cases:
Performance Tuning: Understanding how changing gear ratios (e.g., in a differential) or tire sizes affects acceleration and top speed.
Engine Efficiency: Identifying the optimal gear and RPM for cruising at a certain speed to improve fuel economy.
Diagnostic Checks: Verifying if a vehicle's speedometer reading is accurate compared to its actual speed under specific conditions.
Simulations: Used in automotive design and simulation software.
Note: This calculator provides an approximation. Actual vehicle speed can be affected by factors such as tire slip, drivetrain losses, aerodynamic drag, and the exact tire profile.
function calculateSpeed() {
var engineRpm = parseFloat(document.getElementById("engineRpm").value);
var gearRatio = parseFloat(document.getElementById("gearRatio").value);
var wheelDiameter = parseFloat(document.getElementById("wheelDiameter").value);
var resultContainer = document.getElementById("resultContainer");
var calculatedSpeedElement = document.getElementById("calculatedSpeed");
if (isNaN(engineRpm) || isNaN(gearRatio) || isNaN(wheelDiameter) ||
engineRpm <= 0 || gearRatio <= 0 || wheelDiameter <= 0) {
calculatedSpeedElement.innerText = "Invalid Input";
resultContainer.style.backgroundColor = "#f8d7da"; // Light red for error
resultContainer.style.color = "#721c24"; // Dark red text
resultContainer.style.display = "block";
return;
}
// Constants for conversion
var inchesPerMile = 63360;
var minutesPerHour = 60;
var pi = Math.PI;
// Calculate Wheel RPM
var wheelRpm = engineRpm / gearRatio;
// Calculate Wheel Circumference in inches
var circumferenceInches = pi * wheelDiameter;
// Calculate distance per minute in inches
var distancePerMinuteInches = wheelRpm * circumferenceInches;
// Convert distance per minute to MPH
// (distance per minute * minutes per hour) / inches per mile
var speedMph = (distancePerMinuteInches * minutesPerHour) / inchesPerMile;
calculatedSpeedElement.innerText = speedMph.toFixed(2); // Display with 2 decimal places
resultContainer.style.backgroundColor = "var(–success-green)"; // Success green
resultContainer.style.color = "white"; // White text
resultContainer.style.display = "block";
}