Calculate output RPM, input RPM, or gear ratio based on your inputs.
revolutions per minute (RPM)
Ratio (e.g., 3.5:1 means input turns 3.5 times for 1 output turn)
revolutions per minute (RPM)
Your calculated value will appear here.
Understanding RPM, Speed, and Gear Ratios
In mechanical systems, understanding the relationship between rotational speed (RPM), gear ratios, and output speed is crucial for performance, efficiency, and proper operation. This calculator helps demystify these relationships.
Key Concepts:
RPM (Revolutions Per Minute): This measures how fast a shaft or component is rotating. Higher RPM indicates faster rotation.
Gear Ratio: This is the ratio of the number of teeth on the driven gear to the number of teeth on the driving gear. It dictates how the input speed is transformed into output speed and torque. A higher gear ratio (e.g., 4:1) means the output shaft rotates slower but with more torque compared to the input shaft. A lower gear ratio (e.g., 1:2) means the output shaft rotates faster with less torque.
Torque: While this calculator focuses on speed and ratio, it's important to remember that gear ratios also inversely affect torque. If the speed is reduced by a factor of 'X' (e.g., 4:1), the torque is increased by approximately the same factor 'X' (minus mechanical losses).
How the Calculator Works:
This calculator uses fundamental physics principles governing gear systems. The core relationships are:
To find Output RPM: If you know the input RPM and the gear ratio, the output RPM is calculated as:
Output RPM = Input RPM / Gear Ratio
To find Input RPM: If you know the output RPM and the gear ratio, the input RPM is calculated as:
Input RPM = Output RPM * Gear Ratio
To find Gear Ratio: If you know both input and output RPM, the gear ratio is calculated as:
Gear Ratio = Input RPM / Output RPM
Use Cases:
This calculator is invaluable for various applications, including:
Automotive Engineering: Calculating transmission gear speeds, differential ratios, and their effect on vehicle speed and engine RPM.
Robotics: Determining motor speed requirements for specific joint movements or actuator speeds.
Machinery Design: Setting up appropriate speeds for conveyor belts, industrial equipment, and other rotating machinery.
Hobbyists: Understanding the relationship between motor speed and wheel speed in RC cars, drones, or custom-built devices.
By accurately calculating these parameters, engineers and enthusiasts can optimize performance, ensure components operate within their intended speed ranges, and achieve desired mechanical advantages.
function calculateSpeed() {
var inputRpm = parseFloat(document.getElementById("inputRpm").value);
var gearRatio = parseFloat(document.getElementById("gearRatio").value);
var outputRpm = parseFloat(document.getElementById("outputRpm").value);
var resultDiv = document.getElementById("result");
resultDiv.style.backgroundColor = "var(–success-green)"; // Reset to default green
// Check which values are provided to determine calculation
if (!isNaN(inputRpm) && !isNaN(gearRatio) && isNaN(outputRpm)) {
// Calculate Output RPM
var calculatedOutputRpm = inputRpm / gearRatio;
if (calculatedOutputRpm < 0) calculatedOutputRpm = 0; // RPM cannot be negative
resultDiv.innerHTML = "Calculated Output RPM: " + calculatedOutputRpm.toFixed(2) + " RPM";
} else if (!isNaN(outputRpm) && !isNaN(gearRatio) && isNaN(inputRpm)) {
// Calculate Input RPM
var calculatedInputRpm = outputRpm * gearRatio;
if (calculatedInputRpm < 0) calculatedInputRpm = 0; // RPM cannot be negative
resultDiv.innerHTML = "Calculated Input RPM: " + calculatedInputRpm.toFixed(2) + " RPM";
} else if (!isNaN(inputRpm) && !isNaN(outputRpm) && isNaN(gearRatio)) {
// Calculate Gear Ratio
if (inputRpm === 0) {
resultDiv.innerHTML = "Cannot calculate Gear Ratio if Input RPM is 0.";
resultDiv.style.backgroundColor = "#dc3545"; // Error red
return;
}
var calculatedGearRatio = inputRpm / outputRpm;
if (calculatedGearRatio < 0) calculatedGearRatio = 0; // Ratio cannot be negative
resultDiv.innerHTML = "Calculated Gear Ratio: " + calculatedGearRatio.toFixed(2) + ":1";
} else if (!isNaN(inputRpm) && !isNaN(gearRatio) && !isNaN(outputRpm)) {
resultDiv.innerHTML = "Please clear one field to calculate.";
resultDiv.style.backgroundColor = "#ffc107"; // Warning yellow
} else {
resultDiv.innerHTML = "Please enter at least two valid values.";
resultDiv.style.backgroundColor = "#dc3545"; // Error red
}
}