In automotive and mechanical engineering, understanding the relationship between engine speed (RPM), gear ratios, and output speed is crucial for performance, efficiency, and diagnostics. This calculator helps you determine the output shaft speed or the vehicle's speed based on known parameters.
Key Concepts:
RPM (Revolutions Per Minute): This measures how fast a shaft (like an engine crankshaft or a drive axle) is rotating.
Gear Ratio: This is the ratio of the number of teeth on the driven gear to the number of teeth on the driving gear. In simpler terms, it defines how much a gear (or set of gears) changes the speed and torque. A higher gear ratio (e.g., 4.0) means the output shaft spins slower but with more torque compared to the input shaft. A lower gear ratio (e.g., 0.75) means the output shaft spins faster with less torque. A direct drive (1:1) means no speed or torque change through the gears.
Wheel Diameter: This is the diameter of the tire. It's essential for converting rotational speed into linear speed (vehicle speed).
The Math Behind the Calculator:
The calculation involves a few steps to find the output speed (often corresponding to the wheel speed if the gear ratio represents the entire drivetrain from engine to wheels).
1. Calculating Output Shaft RPM:
The fundamental relationship between input RPM, gear ratio, and output RPM is:
Output RPM = Input RPM / Gear Ratio
This formula tells you how fast the driven shaft will spin relative to the driving shaft, considering the gear reduction or overdrive.
2. Calculating Vehicle Speed (MPH):
To convert the output shaft RPM (assuming it's connected to the drive wheels) into vehicle speed, we use the wheel diameter and the circumference of the tire.
Tire Circumference: Circumference = π × Diameter
Tire Circumference (in inches): C = π × Wheel Diameter
Revolutions Per Hour (RPH): Output Shaft RPM × 60 minutes/hour
Distance per Hour (in inches): RPH × Circumference (in inches)
Distance per Hour (in miles): (Distance per Hour in inches) / (63360 inches/mile)
Combining these, the formula for speed in Miles Per Hour (MPH) is:
*(Note: The constant 0.00295 is derived from (π × 60) / 63360)*
Use Cases:
Performance Tuning: Understanding how different gear ratios affect acceleration and top speed.
Engine Swaps: Estimating how a new engine's RPM range will interact with the existing drivetrain.
Diagnostic Work: Verifying speedometer accuracy or diagnosing drivetrain issues.
Off-Roading: Calculating suitable gearing for specific terrains and tire sizes.
Efficiency Analysis: Determining the optimal gear and RPM for cruising to save fuel.
This calculator assumes a direct connection between the input RPM source and the final gear reduction, leading to the wheel. In complex transmissions, the 'Gear Ratio' might represent the effective ratio of the selected gear.
function calculateSpeed() {
var inputRPM = parseFloat(document.getElementById("inputRPM").value);
var gearRatio = parseFloat(document.getElementById("gearRatio").value);
var wheelDiameter = parseFloat(document.getElementById("wheelDiameter").value);
var resultDiv = document.getElementById("result");
// Clear previous results and errors
resultDiv.innerHTML = "–";
// Input validation
if (isNaN(inputRPM) || inputRPM <= 0) {
resultDiv.innerHTML = "Error: Please enter a valid Input RPM.";
return;
}
if (isNaN(gearRatio) || gearRatio <= 0) {
resultDiv.innerHTML = "Error: Please enter a valid Gear Ratio.";
return;
}
if (isNaN(wheelDiameter) || wheelDiameter <= 0) {
resultDiv.innerHTML = "Error: Please enter a valid Wheel Diameter.";
return;
}
// Calculations
var outputRPM = inputRPM / gearRatio;
var wheelCircumferenceInches = Math.PI * wheelDiameter;
var speedMPH = (outputRPM * wheelCircumferenceInches * 60) / 63360;
// Display result
resultDiv.innerHTML = speedMPH.toFixed(2) + " MPH (Vehicle Speed)";
// Optionally display output RPM as well
// resultDiv.innerHTML += "(Output Shaft RPM: " + outputRPM.toFixed(1) + ")";
}