Calculate the force needed or the distance required to balance a lever.
Your calculation result will appear here.
Understanding the Fulcrum and Lever Balance
A fulcrum is the pivot point around which a lever rotates. In physics, the principle of levers states that for a lever to be in equilibrium (balanced), the sum of the clockwise moments must equal the sum of the anticlockwise moments. A moment (or torque) is the turning effect of a force and is calculated by multiplying the force by the perpendicular distance from the fulcrum to the line of action of the force.
The fundamental formula governing a balanced lever is:
Force 1 × Distance 1 = Force 2 × Distance 2
This calculator helps you determine one of the four variables (Force 1, Distance 1, Force 2, or Distance 2) if the other three are known, or to simply check if a given configuration is balanced.
How to Use This Calculator:
Enter values for any three of the four input fields (Force 1, Distance 1, Force 2, Distance 2).
Leave the field you wish to calculate blank.
Click the "Calculate Balance" button.
The calculator will determine the missing value required for the lever to be in balance.
Use Cases:
Physics Education: Helps students visualize and understand the principle of moments and lever equilibrium.
Engineering Design: Aids in preliminary calculations for simple machines, seesaws, and other lever-based systems.
DIY Projects: Useful for determining forces and distances in simple construction or repair tasks involving levers.
Example: If you have a force of 50 N applied at 2 meters from the fulcrum on one side, and you know the other side has a force of 100 N, this calculator can tell you the exact distance from the fulcrum that the 100 N force must be applied to achieve balance. In this case, 50 N * 2 m = 100 N * Distance 2, so Distance 2 = 100 Nm / 100 N = 1 meter.
function calculateFulcrum() {
var force1Input = document.getElementById("force1");
var distance1Input = document.getElementById("distance1");
var force2Input = document.getElementById("force2");
var distance2Input = document.getElementById("distance2");
var resultDiv = document.getElementById("result");
var force1 = parseFloat(force1Input.value);
var distance1 = parseFloat(distance1Input.value);
var force2 = parseFloat(force2Input.value);
var distance2 = parseFloat(distance2Input.value);
var missingField = "";
var calculatedValue = NaN;
// Determine which field is missing
if (isNaN(force1) && !isNaN(distance1) && !isNaN(force2) && !isNaN(distance2)) {
missingField = "force1";
calculatedValue = (force2 * distance2) / distance1;
} else if (!isNaN(force1) && isNaN(distance1) && !isNaN(force2) && !isNaN(distance2)) {
missingField = "distance1";
calculatedValue = (force2 * distance2) / force1;
} else if (!isNaN(force1) && !isNaN(distance1) && isNaN(force2) && !isNaN(distance2)) {
missingField = "force2";
calculatedValue = (force1 * distance1) / distance2;
} else if (!isNaN(force1) && !isNaN(distance1) && !isNaN(force2) && isNaN(distance2)) {
missingField = "distance2";
calculatedValue = (force1 * distance1) / force2;
} else {
resultDiv.innerHTML = "Please provide exactly three values.";
resultDiv.style.backgroundColor = "#dc3545"; // Red for error
return;
}
// Perform calculation if a value was determined
if (!isNaN(calculatedValue)) {
var unit = "";
if (missingField === "force1" || missingField === "force2″) {
unit = " N";
} else if (missingField === "distance1" || missingField === "distance2″) {
unit = " m";
}
resultDiv.innerHTML = "To balance: " + missingField.replace("force", "Force ").replace("distance", "Distance ") + " = " + calculatedValue.toFixed(2) + unit + "";
resultDiv.style.backgroundColor = "var(–success-green)"; // Green for success
} else {
resultDiv.innerHTML = "Invalid input. Please ensure all inputs are numbers.";
resultDiv.style.backgroundColor = "#dc3545"; // Red for error
}
}