Calculate the output speed of a gear system based on input speed and gear ratio.
Calculated Output Speed
— RPM
Understanding Gear Ratio and Speed Calculation
A gear ratio is a fundamental concept in mechanical engineering, describing the relationship between the rotational speeds of two gears or other rotating components (like sprockets and chains). It dictates how torque and speed are transmitted through a system.
What is Gear Ratio?
The gear ratio is typically expressed as a ratio of the number of teeth on the driven gear to the number of teeth on the driving gear. Alternatively, it can be defined as the ratio of the output speed to the input speed, or the ratio of the input torque to the output torque.
In this calculator, we use the ratio of Driven Gear Teeth / Driver Gear Teeth. A ratio greater than 1 means the output shaft rotates slower than the input shaft but with increased torque (a reduction gear). A ratio less than 1 means the output shaft rotates faster than the input shaft but with reduced torque (an overdrive gear).
How the Speed is Calculated
The core principle is that the gear ratio directly affects the speed transmission. If you know the input speed and the gear ratio, you can determine the output speed.
The formula used is:
Output Speed = Input Speed / Gear Ratio
Let's break this down:
Input Speed (RPM): This is the rotational speed of the input shaft or driving gear, measured in revolutions per minute.
Gear Ratio (Driven/Driver): This represents how many times the driver gear must turn for the driven gear to turn once. For example, a 2:1 gear ratio means the driver gear turns twice for every one turn of the driven gear. In our calculator, this is represented as a single number (e.g., 2 for a 2:1 ratio).
Output Speed (RPM): This is the resulting rotational speed of the output shaft or driven gear.
Use Cases
Understanding and calculating gear ratios is crucial in many applications:
Automotive Transmissions: Different gears in a car allow the engine to operate efficiently at various speeds. Lower gears provide high torque for acceleration, while higher gears allow for higher speeds with less engine strain.
Bicycles: Shifting gears on a bike changes the effective gear ratio, making it easier to pedal uphill (lower gear) or achieve higher speeds on flat ground (higher gear).
Robotics: Motors often require specific speed and torque characteristics, which are achieved using gearboxes with carefully selected ratios.
Industrial Machinery: Conveyor belts, pumps, and other industrial equipment use gear systems to control speed and power.
Wind Turbines: Gearboxes increase the slow rotation of the turbine blades to a speed suitable for the generator.
This calculator helps engineers, hobbyists, and students quickly determine the speed changes in their mechanical systems.
function calculateGearRatioSpeed() {
var inputSpeed = parseFloat(document.getElementById("inputSpeed").value);
var gearRatio = parseFloat(document.getElementById("gearRatio").value);
var resultValueElement = document.getElementById("result-value");
// Clear previous results
resultValueElement.textContent = "– RPM";
// Validate inputs
if (isNaN(inputSpeed) || isNaN(gearRatio)) {
resultValueElement.textContent = "Invalid input";
return;
}
if (gearRatio === 0) {
resultValueElement.textContent = "Gear ratio cannot be zero";
return;
}
// Ensure positive values for physical interpretation
if (inputSpeed < 0 || gearRatio < 0) {
resultValueElement.textContent = "Inputs must be non-negative";
return;
}
var outputSpeed = inputSpeed / gearRatio;
// Display the result, formatted to 2 decimal places
resultValueElement.textContent = outputSpeed.toFixed(2) + " RPM";
}