RPM Speed and Gear Ratio Calculator
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RPM Speed & Gear Ratio Calculator
Calculate Speeds
Results will appear here.
Understanding RPM, Gear Ratios, and Vehicle Speed
This calculator helps you understand the relationship between the rotational speed of an engine or shaft (RPM), the mechanical advantage provided by a gear system (gear ratio), and the resulting linear speed of a vehicle (MPH or KPH).
Key Concepts:
RPM (Revolutions Per Minute): This measures how fast a shaft is rotating. In an automotive context, it often refers to engine speed.Gear Ratio: This is a ratio that describes how many times the input shaft (e.g., engine crankshaft) must rotate for the output shaft (e.g., driveshaft connected to wheels) to rotate once.
A higher numerical gear ratio (e.g., 4:1) means the input shaft spins more times for each rotation of the output shaft. This provides more torque but lower speed.
A lower numerical gear ratio (e.g., 2:1) means the input shaft spins fewer times for each rotation of the output shaft. This provides less torque but higher speed.
The ratio is typically expressed as Input Teeth / Output Teeth. In our calculator, this is represented by the Numerator and Denominator.
Wheel Diameter: The overall diameter of the tire and wheel assembly. This is crucial for converting rotational wheel speed into linear distance traveled.Tire Circumference: The distance traveled in one full rotation of the wheel. It's calculated using the formula: Circumference = π * Diameter. The offset allows for slight variations in tire size due to manufacturing or load.Vehicle Speed: The linear speed of the vehicle, commonly measured in Miles Per Hour (MPH) or Kilometers Per Hour (KPH).
The Math Behind the Calculator:
The calculation proceeds in several steps:
Calculate the effective circumference of the wheel:
Effective Circumference (inches) = (π * Wheel Diameter) * (1 + Tire Circumference Offset / 100)
Calculate the output shaft RPM: This is the speed of the shaft connected to the wheels.
Output Shaft RPM = Input Shaft RPM / Gear Ratio
Where Gear Ratio = Gear Ratio Numerator / Gear Ratio Denominator
Calculate wheel rotations per minute: This is directly equal to the Output Shaft RPM.
Wheel Rotations Per Minute = Output Shaft RPM
Calculate distance traveled per minute:
Distance Per Minute (inches) = Wheel Rotations Per Minute * Effective Circumference (inches)
Convert distance per minute to MPH:
There are 63,360 inches in a mile and 60 minutes in an hour.
MPH = (Distance Per Minute (inches) * 60) / 63,360
Convert distance per minute to KPH (optional, but good to know):
There are 1000 meters in a kilometer, and 39.37 inches in a meter.
Distance Per Minute (meters) = Distance Per Minute (inches) / 39.37
Distance Per Minute (kilometers) = Distance Per Minute (meters) / 1000
KPH = Distance Per Minute (kilometers) * 60
Use Cases:
Engine Tuning: Understanding how different gear ratios affect engine RPM at a given road speed.Performance Modifications: Predicting the impact of changing tire sizes or gear ratios on acceleration and top speed.Automotive Engineering: Designing drivetrains for optimal performance and efficiency.Hobbyists: Calculating expected speeds for custom builds, go-karts, or RC vehicles.
By inputting your engine's RPM, the gear ratio in use, and your wheel dimensions, you can accurately estimate the resulting vehicle speed.
function calculateSpeeds() {
var inputRpm = parseFloat(document.getElementById("inputRpm").value);
var gearRatioNumerator = parseFloat(document.getElementById("gearRatioNumerator").value);
var gearRatioDenominator = parseFloat(document.getElementById("gearRatioDenominator").value);
var wheelDiameter = parseFloat(document.getElementById("wheelDiameter").value);
var tireCircumferenceOffset = parseFloat(document.getElementById("tireCircumferenceOffset").value);
var resultDiv = document.getElementById("result");
resultDiv.innerHTML = 'Results will appear here.'; // Reset previous results
if (isNaN(inputRpm) || isNaN(gearRatioNumerator) || isNaN(gearRatioDenominator) || isNaN(wheelDiameter) || isNaN(tireCircumferenceOffset)) {
resultDiv.innerHTML = 'Error: Please enter valid numbers for all fields.';
return;
}
if (gearRatioNumerator <= 0 || gearRatioDenominator <= 0 || wheelDiameter <= 0) {
resultDiv.innerHTML = 'Error: Gear ratio components and wheel diameter must be positive.';
return;
}
var gearRatio = gearRatioNumerator / gearRatioDenominator;
var effectiveCircumferenceInches = (Math.PI * wheelDiameter) * (1 + tireCircumferenceOffset / 100);
var outputShaftRpm = inputRpm / gearRatio;
var wheelRotationsPerMinute = outputShaftRpm;
var distancePerMinuteInches = wheelRotationsPerMinute * effectiveCircumferenceInches;
// Constants for conversion
var inchesPerMile = 63360;
var minutesPerHour = 60;
var inchesPerMeter = 39.37;
var metersPerKilometer = 1000;
// Calculate MPH
var mph = (distancePerMinuteInches * minutesPerHour) / inchesPerMile;
// Calculate KPH
var distancePerMinuteMeters = distancePerMinuteInches / inchesPerMeter;
var distancePerMinuteKilometers = distancePerMinuteMeters / metersPerKilometer;
var kph = distancePerMinuteKilometers * minutesPerHour;
resultDiv.innerHTML = '' +
'Output Shaft RPM: ' + outputShaftRpm.toFixed(2) + '' +
'Approx. Vehicle Speed: ' + mph.toFixed(2) + ' MPH / ' + kph.toFixed(2) + ' KPH' +
'';
}