Your essential tool for understanding weight span dynamics.
Weight Span Calculator
Enter the total weight of the object in kilograms.
Enter the distance from the pivot point to the point where the weight is applied, in meters.
Enter the angle between the lever arm and the direction of the force, in degrees (0-180).
Calculation Results
—
Moment: — |
Force Component: — |
Effective Weight: —
Weight Span is often related to the concept of Moment of Force (Torque), calculated as Force × Lever Arm × sin(Angle).
The Force here is the weight of the object.
Weight Span vs. Angle of Application
Visualizing how the effective force changes with the angle of application.
Key Calculation Variables
Variable
Meaning
Unit
Typical Range
Object Weight
The mass of the object being considered.
kg
1 – 10000+
Lever Arm Length
Distance from pivot to force application point.
m
0.1 – 50+
Angle of Application
Angle between lever arm and force vector.
degrees
0 – 180
Moment of Force (Torque)
Rotational effect of the weight.
Nm (Newton-meters)
Varies widely
Force Component
The component of weight acting perpendicular to the lever arm.
N (Newtons)
Varies widely
Effective Weight
The perceived weight considering the angle.
kg
Varies widely
What is Weight Span Calculation?
Weight span calculation, in a physics context, refers to understanding the rotational effect or the effective force exerted by a weight at a certain distance from a pivot point, especially when the force is not applied perpendicularly. It's fundamentally about calculating the moment of force, often referred to as torque. This concept is crucial in engineering, mechanics, and structural analysis where understanding how forces create rotation or stress is paramount.
Who should use it: Engineers, designers, students of physics and mechanics, and anyone involved in rigging, lifting, or structural stability analysis will find weight span calculations essential. It helps in determining the forces that will act on support structures, the ease with which an object can be rotated, or the stability of a system under load.
Common misconceptions: A common misconception is that the weight span is simply the object's weight multiplied by the distance. This ignores the critical factor of the angle at which the force is applied. Another misconception is that weight span is a fixed property of an object; it's a calculated value dependent on the system's geometry (lever arm and angle) and the object's weight. The term "weight span" itself isn't a standard physics term but rather a descriptive phrase for the outcome of moment calculations.
Weight Span Formula and Mathematical Explanation
The core of weight span calculation lies in the principle of Moment of Force (Torque). The formula quantifies the rotational influence of a force applied at a distance from a pivot.
The primary formula used is:
Moment of Force (τ) = F × r × sin(θ)
Where:
τ (Tau) is the Moment of Force (Torque), measured in Newton-meters (Nm). This represents the rotational effect.
F is the magnitude of the Force applied. In our calculator, this is the weight of the object, converted to Newtons (Weight = mass × acceleration due to gravity, approximately 9.81 m/s²).
r is the length of the Lever Arm, the perpendicular distance from the pivot point to the line of action of the force. Measured in meters (m).
θ (Theta) is the Angle of Application, the angle between the lever arm vector and the force vector, measured in degrees and converted to radians for trigonometric functions.
To provide more intuitive results, we also calculate:
Force Component (F_perp) = F × sin(θ): This is the component of the object's weight that acts perpendicularly to the lever arm, thus contributing directly to the rotation.
Effective Weight (W_eff) = Object Weight (kg) × sin(θ): This is a simplified representation, showing how the perceived "pull" or "push" along the lever arm changes with the angle. It's not a true weight but an indicator of rotational tendency.
Variable Table:
Variable
Meaning
Unit
Typical Range
Object Weight (m)
Mass of the object.
kg
1 – 10000+
Lever Arm Length (r)
Distance from pivot to force application.
m
0.1 – 50+
Angle of Application (θ)
Angle between lever arm and force vector.
degrees
0 – 180
Moment of Force (τ)
Rotational effect.
Nm
Varies widely
Force Component (F_perp)
Perpendicular component of weight.
N
Varies widely
Effective Weight (W_eff)
Perceived rotational tendency.
kg
Varies widely
Practical Examples (Real-World Use Cases)
Understanding weight span calculation is vital in various practical scenarios. Here are a couple of examples:
Example 1: Lifting a Beam
Imagine an engineer needs to lift a steel beam weighing 500 kg using a crane. The lifting point on the beam is 3 meters from its center of mass. The crane cable attaches to the beam at an angle, and at the moment of lift, the cable makes an angle of 60 degrees with the beam's length (lever arm).
Inputs:
Object Weight: 500 kg
Lever Arm Length: 3 m
Angle of Application: 60 degrees
Calculation:
Force (F) = 500 kg * 9.81 m/s² = 4905 N
Moment of Force (τ) = 4905 N * 3 m * sin(60°) ≈ 4905 * 3 * 0.866 ≈ 12775 Nm
Force Component (F_perp) = 4905 N * sin(60°) ≈ 4905 * 0.866 ≈ 4248 N
Effective Weight (W_eff) = 500 kg * sin(60°) ≈ 500 * 0.866 ≈ 433 kg
Interpretation: The crane needs to exert a force capable of overcoming a moment of approximately 12775 Nm. The effective weight contributing to rotation is about 433 kg, which is less than the actual weight due to the angle. This information helps in selecting the appropriate lifting gear and understanding the rotational stress on the beam during lifting.
Example 2: Stabilizing a Platform
Consider a platform supported by a single strut. A load of 200 kg is placed on the platform at a distance of 1.5 meters from the base of the strut (pivot). The load is applied at an angle of 30 degrees relative to the horizontal platform, with the strut angled upwards. For simplicity, we consider the lever arm along the platform.
Inputs:
Object Weight: 200 kg
Lever Arm Length: 1.5 m
Angle of Application: 30 degrees
Calculation:
Force (F) = 200 kg * 9.81 m/s² = 1962 N
Moment of Force (τ) = 1962 N * 1.5 m * sin(30°) = 1962 * 1.5 * 0.5 = 1471.5 Nm
Force Component (F_perp) = 1962 N * sin(30°) = 1962 * 0.5 = 981 N
Effective Weight (W_eff) = 200 kg * sin(30°) = 200 * 0.5 = 100 kg
Interpretation: The load creates a moment of 1471.5 Nm around the strut's base. The perpendicular force component is 981 N. This moment contributes to the stress on the strut and the stability of the platform. An effective weight of 100 kg indicates that only half of the actual weight is contributing to the rotational effect in this specific configuration. This is crucial for designing the support structure to withstand the calculated forces and moments.
How to Use This Weight Span Calculator
Our Weight Span Calculator is designed for simplicity and accuracy. Follow these steps to get your results:
Enter Object Weight: Input the total mass of the object in kilograms (kg) into the "Object Weight" field.
Enter Lever Arm Length: Provide the distance in meters (m) from the pivot point (e.g., hinge, fulcrum, support) to where the weight is applied.
Enter Angle of Application: Input the angle in degrees between the lever arm and the direction of the force (weight). A 90-degree angle means the force is perpendicular to the lever arm, maximizing the rotational effect.
Click Calculate: Press the "Calculate" button.
How to Read Results:
Primary Result (Moment of Force): This is the main output, displayed prominently. It represents the total rotational effect (torque) in Newton-meters (Nm). A higher value indicates a greater tendency to cause rotation or stress.
Intermediate Values:
Force Component: Shows the portion of the object's weight acting perpendicularly to the lever arm, in Newtons (N).
Effective Weight: A simplified value in kilograms (kg) indicating the rotational tendency relative to the object's actual weight.
Formula Explanation: A brief description of the underlying physics principle (Moment of Force) is provided.
Chart: The dynamic chart visualizes how the Moment of Force changes as the Angle of Application varies, keeping other inputs constant.
Table: Provides definitions and units for all key variables used in the calculation.
Decision-Making Guidance:
Use the calculated Moment of Force to assess the required strength of supporting structures, actuators, or braking systems.
Compare results for different angles to optimize force application or understand stability under varying conditions.
The intermediate values help in understanding the specific components of the force contributing to the rotational effect.
Use the "Reset" button to clear current inputs and start over. The "Copy Results" button allows you to easily transfer the main result, intermediate values, and key assumptions to other documents or reports.
Key Factors That Affect Weight Span Results
Several factors significantly influence the outcome of a weight span calculation. Understanding these is key to accurate analysis and reliable engineering:
Object Weight (Mass): This is the most direct factor. A heavier object exerts a greater force (F = m × g), leading to a larger moment of force, assuming other variables remain constant. This is fundamental to understanding load-bearing requirements.
Lever Arm Length (Distance): The distance from the pivot point to the point of force application (r) has a linear relationship with the moment. Doubling the lever arm length, for instance, will double the moment of force. This highlights the importance of geometry in mechanical advantage and stress distribution.
Angle of Application (θ): This is a critical trigonometric factor. The moment is proportional to the sine of the angle.
At 90 degrees (perpendicular), sin(90°) = 1, resulting in the maximum possible moment for a given weight and lever arm.
As the angle approaches 0 or 180 degrees, sin(θ) approaches 0, meaning the moment of force diminishes significantly, indicating less rotational effect.
This is crucial in scenarios like opening doors or operating levers.
Gravity (g): While often assumed constant (9.81 m/s² on Earth), variations in gravitational pull (e.g., on different planets) would directly alter the force exerted by the mass, thus changing the moment. For most terrestrial applications, this is a constant.
Pivot Point Location: The choice and stability of the pivot point are paramount. If the pivot is not rigid or shifts under load, the effective lever arm changes, and the calculated moment may not accurately reflect the real-world stress. This relates to structural integrity.
Direction of Force: The angle calculation assumes the force vector is known relative to the lever arm. If the force direction changes (e.g., due to wind, or the object swinging), the angle θ changes, altering the moment. This is relevant in dynamic load calculations.
Friction and Other Resistances: Real-world systems often involve friction at the pivot or air resistance. These forces oppose motion and can effectively reduce the net moment causing rotation. While not part of the basic weight span formula, they are crucial for detailed dynamic analysis.
Frequently Asked Questions (FAQ)
Q1: What is the difference between weight and mass in this calculation?
Mass (in kg) is a measure of inertia. Weight is the force exerted by gravity on that mass (Force = mass × g). Our calculator takes mass as input and implicitly uses the force of gravity (approx. 9.81 m/s²) to calculate the moment of force in Newton-meters (Nm).
Q2: Why is the angle of application so important?
The angle determines how much of the object's weight contributes to rotation. Only the component of the weight perpendicular to the lever arm creates a moment. The sine function in the formula mathematically captures this relationship, showing maximum effect at 90 degrees and zero effect at 0 or 180 degrees.
Q3: Can the lever arm be negative?
In physics, lever arm length (r) is typically treated as a positive distance. The direction of rotation is handled by conventions (e.g., clockwise vs. counter-clockwise moments), but the length itself is a magnitude. Our calculator expects a positive value for lever arm length.
Q4: What does an "Effective Weight" of 0 kg mean?
An effective weight of 0 kg means the object's weight is not contributing to rotation around the pivot. This occurs when the angle of application is 0 degrees or 180 degrees, meaning the force is applied directly along the line of the lever arm, either pushing towards or pulling away from the pivot without causing it to turn.
Q5: How does this relate to real-world engineering problems?
This calculation is fundamental for designing structures like bridges, cranes, doors, levers, and robotic arms. It helps engineers determine the forces on joints, the required torque for motors, and the overall stability of mechanical systems under load.
Q6: Does air resistance affect the weight span?
The basic weight span calculation (moment of force) typically ignores air resistance and friction for simplicity. In high-speed or large-scale applications, these factors can become significant and must be considered in more advanced dynamic analyses.
Q7: What units should I use?
The calculator is set up for standard SI units: kilograms (kg) for mass, meters (m) for distance, and degrees for angles. The primary result is in Newton-meters (Nm), a standard unit for torque.
Q8: Can I use this calculator for weights in pounds or distances in feet?
Currently, this calculator is configured for SI units (kg, m). For imperial units (lbs, ft), you would need to convert your values to kg and meters before inputting them, or use a calculator specifically designed for imperial units. Remember that 1 lb ≈ 0.453592 kg and 1 ft ≈ 0.3048 m.
Related Tools and Internal Resources
Weight Span Calculator Use our interactive tool to instantly calculate moments of force.
Structural Load Calculator (Placeholder URL) Analyze the total load-bearing requirements for your structures.
Torque Conversion Tool (Placeholder URL) Convert torque values between different units easily.
Physics Principles Explained (Placeholder URL) Deep dive into fundamental concepts like force, motion, and energy.
Engineering Design Guides (Placeholder URL) Resources for practical application of physics in design.
Material Strength Analysis (Placeholder URL) Understand how different materials withstand applied forces and moments.
var chartInstance = null; // Global variable to hold chart instance
function calculateWeightSpan() {
// Clear previous errors
document.getElementById('objectWeightError').classList.remove('visible');
document.getElementById('leverArmLengthError').classList.remove('visible');
document.getElementById('angleOfApplicationError').classList.remove('visible');
// Get input values
var objectWeightInput = document.getElementById('objectWeight');
var leverArmLengthInput = document.getElementById('leverArmLength');
var angleOfApplicationInput = document.getElementById('angleOfApplication');
var objectWeight = parseFloat(objectWeightInput.value);
var leverArmLength = parseFloat(leverArmLengthInput.value);
var angleDegrees = parseFloat(angleOfApplicationInput.value);
// — Input Validation —
var isValid = true;
if (isNaN(objectWeight) || objectWeight <= 0) {
document.getElementById('objectWeightError').innerText = "Please enter a valid positive number for object weight.";
document.getElementById('objectWeightError').classList.add('visible');
isValid = false;
}
if (isNaN(leverArmLength) || leverArmLength <= 0) {
document.getElementById('leverArmLengthError').innerText = "Please enter a valid positive number for lever arm length.";
document.getElementById('leverArmLengthError').classList.add('visible');
isValid = false;
}
if (isNaN(angleDegrees) || angleDegrees 180) {
document.getElementById('angleOfApplicationError').innerText = "Angle must be between 0 and 180 degrees.";
document.getElementById('angleOfApplicationError').classList.add('visible');
isValid = false;
}
if (!isValid) {
// Clear results if validation fails
document.getElementById('primaryResult').innerText = "–";
document.getElementById('momentOfForce').innerText = "Moment: –";
document.getElementById('forceComponent').innerText = "Force Component: –";
document.getElementById('effectiveWeight').innerText = "Effective Weight: –";
return;
}
// — Calculations —
var gravity = 9.81; // Acceleration due to gravity in m/s^2
var force = objectWeight * gravity; // Force in Newtons
var angleRadians = angleDegrees * (Math.PI / 180); // Convert angle to radians
var momentOfForce = force * leverArmLength * Math.sin(angleRadians);
var forceComponent = force * Math.sin(angleRadians);
var effectiveWeight = objectWeight * Math.sin(angleRadians); // Simplified effective weight in kg
// — Display Results —
document.getElementById('primaryResult').innerText = momentOfForce.toFixed(2) + " Nm";
document.getElementById('momentOfForce').innerText = "Moment: " + momentOfForce.toFixed(2) + " Nm";
document.getElementById('forceComponent').innerText = "Force Component: " + forceComponent.toFixed(2) + " N";
document.getElementById('effectiveWeight').innerText = "Effective Weight: " + effectiveWeight.toFixed(2) + " kg";
// — Update Chart —
updateChart(leverArmLength, objectWeight);
}
function resetCalculator() {
document.getElementById('objectWeight').value = 100;
document.getElementById('leverArmLength').value = 2;
document.getElementById('angleOfApplication').value = 90;
// Clear errors
document.getElementById('objectWeightError').innerText = "";
document.getElementById('objectWeightError').classList.remove('visible');
document.getElementById('leverArmLengthError').innerText = "";
document.getElementById('leverArmLengthError').classList.remove('visible');
document.getElementById('angleOfApplicationError').innerText = "";
document.getElementById('angleOfApplicationError').classList.remove('visible');
// Reset results
document.getElementById('primaryResult').innerText = "–";
document.getElementById('momentOfForce').innerText = "Moment: –";
document.getElementById('forceComponent').innerText = "Force Component: –";
document.getElementById('effectiveWeight').innerText = "Effective Weight: –";
// Reset chart data if needed (or just var it update on next calculate)
if (chartInstance) {
chartInstance.destroy();
chartInstance = null;
}
// Optionally call calculate to show default state results
calculateWeightSpan();
}
function copyResults() {
var primaryResult = document.getElementById('primaryResult').innerText;
var moment = document.getElementById('momentOfForce').innerText;
var forceComp = document.getElementById('forceComponent').innerText;
var effWeight = document.getElementById('effectiveWeight').innerText;
var assumptions = "Key Assumptions:\n";
assumptions += "- Object Weight: " + document.getElementById('objectWeight').value + " kg\n";
assumptions += "- Lever Arm Length: " + document.getElementById('leverArmLength').value + " m\n";
assumptions += "- Angle of Application: " + document.getElementById('angleOfApplication').value + " degrees\n";
assumptions += "- Gravity: ~9.81 m/s²\n";
var textToCopy = "Weight Span Calculation Results:\n\n";
textToCopy += "Primary Result: " + primaryResult + "\n";
textToCopy += moment + "\n";
textToCopy += forceComp + "\n";
textToCopy += effWeight + "\n\n";
textToCopy += assumptions;
// Use navigator.clipboard for modern browsers, fallback to textarea
if (navigator.clipboard && navigator.clipboard.writeText) {
navigator.clipboard.writeText(textToCopy).then(function() {
alert('Results copied to clipboard!');
}).catch(function(err) {
console.error('Failed to copy text: ', err);
fallbackCopyTextToClipboard(textToCopy);
});
} else {
fallbackCopyTextToClipboard(textToCopy);
}
}
function fallbackCopyTextToClipboard(text) {
var textArea = document.createElement("textarea");
textArea.value = text;
textArea.style.position = "fixed"; // Avoid scrolling to bottom
textArea.style.left = "-9999px";
textArea.style.top = "-9999px";
document.body.appendChild(textArea);
textArea.focus();
textArea.select();
try {
var successful = document.execCommand('copy');
var msg = successful ? 'successful' : 'unsuccessful';
alert('Results copied to clipboard! (' + msg + ')');
} catch (err) {
console.error('Oops, unable to copy', err);
alert('Failed to copy results. Please copy manually.');
}
document.body.removeChild(textArea);
}
function updateChart(leverArm, objectWeight) {
var ctx = document.getElementById('weightSpanChart').getContext('2d');
// Destroy previous chart instance if it exists
if (chartInstance) {
chartInstance.destroy();
}
var angles = [];
var moments = [];
var forceComponents = [];
var gravity = 9.81;
for (var i = 0; i <= 180; i += 5) { // Calculate for every 5 degrees
angles.push(i);
var angleRad = i * (Math.PI / 180);
var force = objectWeight * gravity;
var moment = force * leverArm * Math.sin(angleRad);
var forceComp = force * Math.sin(angleRad);
moments.push(moment);
forceComponents.push(forceComp);
}
chartInstance = new Chart(ctx, {
type: 'line',
data: {
labels: angles,
datasets: [{
label: 'Moment of Force (Nm)',
data: moments,
borderColor: 'rgb(0, 74, 153)', // Primary color
backgroundColor: 'rgba(0, 74, 153, 0.1)',
fill: true,
tension: 0.1
}, {
label: 'Force Component (N)',
data: forceComponents,
borderColor: 'rgb(40, 167, 69)', // Success color
backgroundColor: 'rgba(40, 167, 69, 0.1)',
fill: true,
tension: 0.1
}]
},
options: {
responsive: true,
maintainAspectRatio: false,
scales: {
x: {
title: {
display: true,
text: 'Angle of Application (degrees)'
}
},
y: {
title: {
display: true,
text: 'Value'
},
beginAtZero: true
}
},
plugins: {
legend: {
position: 'top',
},
title: {
display: true,
text: 'Moment of Force vs. Angle of Application'
}
}
}
});
}
// Initial calculation on page load with default values
document.addEventListener('DOMContentLoaded', function() {
calculateWeightSpan();
});
// Simple Chart.js integration (ensure you have Chart.js library included if running standalone)
// For this output, we assume Chart.js is available globally or included separately.
// If not, you'd need to add:
// For a pure HTML/JS solution without external libs, SVG or Canvas API would be needed.
// Given the prompt requires NO external libraries, I'll use Canvas API directly.
// Re-implementing chart logic using Canvas API directly for no external libs
function updateChart(leverArm, objectWeight) {
var canvas = document.getElementById('weightSpanChart');
var ctx = canvas.getContext('2d');
canvas.height = 300; // Set a fixed height for the canvas
// Clear previous drawing
ctx.clearRect(0, 0, canvas.width, canvas.height);
var width = canvas.width;
var height = canvas.height;
var padding = 40; // Padding around the chart area
// Data generation
var angles = [];
var moments = [];
var forceComponents = [];
var gravity = 9.81;
for (var i = 0; i <= 180; i += 5) {
angles.push(i);
var angleRad = i * (Math.PI / 180);
var force = objectWeight * gravity;
var moment = force * leverArm * Math.sin(angleRad);
var forceComp = force * Math.sin(angleRad);
moments.push(moment);
forceComponents.push(forceComp);
}
// Find max values for scaling
var maxMoment = Math.max(…moments);
var maxForceComp = Math.max(…forceComponents);
var maxY = Math.max(maxMoment, maxForceComp);
if (maxY === 0) maxY = 1; // Avoid division by zero
// — Drawing Axes —
ctx.strokeStyle = '#ccc';
ctx.lineWidth = 1;
// Y-axis
ctx.beginPath();
ctx.moveTo(padding, padding);
ctx.lineTo(padding, height – padding);
ctx.stroke();
// X-axis
ctx.beginPath();
ctx.moveTo(padding, height – padding);
ctx.lineTo(width – padding, height – padding);
ctx.stroke();
// — Drawing Labels and Ticks —
ctx.fillStyle = '#333';
ctx.font = '10px Arial';
// Y-axis labels
var numYTicks = 5;
for (var i = 0; i <= numYTicks; i++) {
var yValue = maxY * (i / numYTicks);
var yPos = height – padding – (yValue / maxY) * (height – 2 * padding);
ctx.fillText(yValue.toFixed(0), padding – 30, yPos + 5);
ctx.beginPath();
ctx.moveTo(padding – 5, yPos);
ctx.lineTo(padding, yPos);
ctx.stroke();
}
// X-axis labels
var numXTicks = 4; // e.g., 0, 60, 120, 180
for (var i = 0; i <= numXTicks; i++) {
var angleValue = 180 * (i / numXTicks);
var xPos = padding + (angleValue / 180) * (width – 2 * padding);
ctx.fillText(angleValue.toFixed(0), xPos – 10, height – padding + 15);
ctx.beginPath();
ctx.moveTo(xPos, height – padding);
ctx.lineTo(xPos, height – padding + 5);
ctx.stroke();
}
// — Drawing Data Series —
// Series 1: Moment of Force
ctx.strokeStyle = 'rgb(0, 74, 153)';
ctx.lineWidth = 2;
ctx.beginPath();
for (var i = 0; i < angles.length; i++) {
var angleValue = angles[i];
var momentValue = moments[i];
var xPos = padding + (angleValue / 180) * (width – 2 * padding);
var yPos = height – padding – (momentValue / maxY) * (height – 2 * padding);
if (i === 0) {
ctx.moveTo(xPos, yPos);
} else {
ctx.lineTo(xPos, yPos);
}
}
ctx.stroke();
// Series 2: Force Component
ctx.strokeStyle = 'rgb(40, 167, 69)';
ctx.lineWidth = 2;
ctx.beginPath();
for (var i = 0; i < angles.length; i++) {
var angleValue = angles[i];
var forceCompValue = forceComponents[i];
var xPos = padding + (angleValue / 180) * (width – 2 * padding);
var yPos = height – padding – (forceCompValue / maxY) * (height – 2 * padding);
if (i === 0) {
ctx.moveTo(xPos, yPos);
} else {
ctx.lineTo(xPos, yPos);
}
}
ctx.stroke();
// — Drawing Legend —
ctx.font = '12px Arial';
var legendY = padding / 2;
var legendBoxSize = 10;
// Moment Legend
ctx.fillStyle = 'rgb(0, 74, 153)';
ctx.fillRect(padding, legendY, legendBoxSize, legendBoxSize);
ctx.fillStyle = '#333';
ctx.fillText('Moment of Force (Nm)', padding + legendBoxSize + 5, legendY + legendBoxSize);
// Force Component Legend
var forceLegendX = padding + 150; // Adjust position as needed
ctx.fillStyle = 'rgb(40, 167, 69)';
ctx.fillRect(forceLegendX, legendY, legendBoxSize, legendBoxSize);
ctx.fillStyle = '#333';
ctx.fillText('Force Component (N)', forceLegendX + legendBoxSize + 5, legendY + legendBoxSize);
// — Drawing Title —
ctx.fillStyle = '#004a99';
ctx.font = '16px Arial';
ctx.textAlign = 'center';
ctx.fillText('Moment of Force vs. Angle of Application', width / 2, padding / 2 – 10);
ctx.textAlign = 'left'; // Reset alignment
}
// Initial calculation on page load with default values
document.addEventListener('DOMContentLoaded', function() {
calculateWeightSpan();
});