Area, Volume, and Weight Calculator
Calculate dimensions, capacities, and material weights with precision.
Cube
Rectangular Prism
Cylinder
Sphere
Cone
Rectangle (Area)
Circle (Area)
Choose the geometric shape for your calculation.
Calculation Results
—
Dimension 1: —
Dimension 2: —
Dimension 3: —
Material Density: —
Weight per Unit Volume: —
Formula Used:
Key Assumptions: Uniform material density, ideal geometric shape.
Result Trends
Chart showing the relationship between a key dimension and calculated weight.
Calculation Details
| Parameter | Value | Unit |
|---|
{primary_keyword}
The Area, Volume, and Weight Calculator is an indispensable tool designed to help users quickly determine the surface area, enclosed volume, and mass of various geometric shapes. This calculator is crucial for professionals and hobbyists alike, from engineers and architects to DIY enthusiasts and material suppliers. It simplifies complex geometric formulas, allowing for rapid estimations of material requirements, shipping costs, and structural integrity. Understanding these basic physical properties is fundamental in many practical applications, ensuring efficiency and accuracy in planning and execution.
Who Should Use It?
This area, volume, and weight calculator is beneficial for a wide range of individuals and professions:
- Engineers and Architects: For calculating material quantities (concrete, steel, insulation), estimating structural loads, and determining space requirements.
- Construction Professionals: To budget for raw materials like sand, gravel, paint, and bricks, and to understand the weight of structural components.
- Logistics and Shipping Managers: For estimating cargo weight and volume to optimize transportation and calculate shipping costs.
- Manufacturers: To determine material needs for production, calculate product weight for packaging and distribution, and ensure dimensional accuracy.
- DIYers and Homeowners: For home improvement projects, such as calculating the amount of paint for a room, the volume of soil for a garden bed, or the weight of materials for a renovation.
- Students and Educators: As a learning aid to understand geometric principles and practical applications of math and physics.
Common Misconceptions
Several common misconceptions surround area, volume, and weight calculations:
- "Volume and Weight are Interchangeable": While related through density, volume is a measure of space, whereas weight is a measure of mass influenced by gravity. Two objects of the same volume can have vastly different weights if their densities differ.
- "All Shapes of the Same Size Have the Same Weight": This is only true if they are made of the same material. The density of the material is a critical factor.
- "Surface Area Calculations are Only for Painting or Coating": Surface area is also vital for heat transfer calculations, insulation effectiveness, and understanding material exposure.
- Ignoring Material Density: Often, users focus on dimensions alone and forget that the specific material's density significantly impacts the final weight.
{primary_keyword} Formula and Mathematical Explanation
The calculations performed by this area, volume, and weight calculator are based on fundamental geometric formulas and the relationship between mass, volume, and density. For any given shape, we first calculate its relevant geometric property (area or volume), and then use the material's density to determine its weight.
Geometric Formulas:
- Area of a Rectangle: $A = \text{length} \times \text{width}$
- Area of a Circle: $A = \pi \times \text{radius}^2$
- Volume of a Cube: $V = \text{side}^3$
- Volume of a Rectangular Prism: $V = \text{length} \times \text{width} \times \text{height}$
- Volume of a Cylinder: $V = \pi \times \text{radius}^2 \times \text{height}$
- Volume of a Sphere: $V = \frac{4}{3} \times \pi \times \text{radius}^3$
- Volume of a Cone: $V = \frac{1}{3} \times \pi \times \text{radius}^2 \times \text{height}$
Weight Calculation:
Once the volume (for 3D shapes) or area (for 2D materials like sheet metal) is calculated, the weight is determined using the material's density:
Weight = Volume × Density
If calculating the weight of a surface (e.g., a metal plate), the formula is adapted to use area and thickness:
Weight = Area × Thickness × Density
Variable Explanations:
The calculator uses the following variables:
- Dimensions (Length, Width, Height, Side, Radius): These are the linear measurements defining the shape's size.
- Radius: The distance from the center of a circle or sphere to its edge.
- Height: The vertical dimension of a shape.
- Side: The length of one edge of a cube.
- Area (A): The amount of two-dimensional space a shape occupies.
- Volume (V): The amount of three-dimensional space a shape occupies.
- Density ($\rho$): The mass of a substance per unit volume. This is a crucial material property.
- Weight: The force exerted on an object due to gravity. For practical purposes in calculators like this, it's often treated as mass.
- $\pi$ (Pi): A mathematical constant, approximately 3.14159.
Variables Table:
| Variable | Meaning | Unit (Common Examples) | Typical Range |
|---|---|---|---|
| Length, Width, Height, Side, Radius | Linear dimension of the shape | meters (m), centimeters (cm), feet (ft), inches (in) | Positive numerical values (e.g., 0.1 to 1000+) |
| Area (A) | Surface coverage of a 2D shape | square meters (m²), square feet (ft²) | Calculated value based on dimensions |
| Volume (V) | Space occupied by a 3D shape | cubic meters (m³), cubic feet (ft³), liters (L) | Calculated value based on dimensions |
| Density ($\rho$) | Mass per unit volume of a material | kg/m³, g/cm³, lbs/ft³ | Highly variable; e.g., water ≈ 1000 kg/m³, steel ≈ 7850 kg/m³ |
| Weight (Mass) | Total mass of the object | kilograms (kg), pounds (lbs), metric tons (t) | Calculated value based on volume and density |
Practical Examples (Real-World Use Cases)
Let's illustrate the power of the Area, Volume, and Weight Calculator with practical scenarios:
Example 1: Calculating Concrete Needed for a Foundation
A construction manager needs to estimate the amount of concrete required for a rectangular building foundation. The foundation dimensions are:
- Length: 20 meters
- Width: 10 meters
- Height (depth): 0.5 meters
The concrete mix has a standard density:
- Density: 2400 kg/m³
Calculator Inputs:
- Shape: Rectangular Prism
- Length: 20
- Width: 10
- Height: 0.5
- Material Density: 2400
- Density Unit: kg/m³
- Dimension Unit: meters
Calculator Outputs:
- Volume: 100 m³
- Weight: 240,000 kg (or 240 metric tons)
Interpretation:
The manager knows they need exactly 100 cubic meters of concrete. This volume translates to a significant weight of 240,000 kg, which is crucial for planning the delivery logistics (number of concrete trucks) and understanding the load on the ground. This also helps in budgeting for the material cost.
Example 2: Determining the Weight of a Steel Sphere for a Sculpture
An artist is creating a large spherical sculpture with a diameter of 3 meters. They need to know its weight for structural support and transportation planning.
- Diameter: 3 meters (Radius = 1.5 meters)
The sculpture will be made of solid steel:
- Density of Steel: 7850 kg/m³
Calculator Inputs:
- Shape: Sphere
- Radius: 1.5
- Material Density: 7850
- Density Unit: kg/m³
- Dimension Unit: meters
Calculator Outputs:
- Volume: 14.137 m³ (approx.)
- Weight: 111,077 kg (approx.)
Interpretation:
The artist realizes the sculpture will be extremely heavy, weighing over 111 metric tons. This weight impacts decisions about the installation site's load-bearing capacity, the type of crane needed for lifting, and the overall structural design to ensure stability. For more insights into material science, exploring related tools can be beneficial.
How to Use This Area, Volume, and Weight Calculator
Using our Area, Volume, and Weight Calculator is straightforward. Follow these steps to get accurate results for your projects:
Step-by-Step Instructions:
- Select the Shape: In the "Select Shape" dropdown menu, choose the geometric form that best represents the object or area you are calculating (e.g., Cube, Cylinder, Rectangle).
- Input Dimensions: Based on your selected shape, relevant input fields will appear. Enter the precise measurements (length, width, height, radius, side) for your shape. Ensure you use consistent units (e.g., all in meters, or all in feet).
- Specify Material Density: Enter the density of the material you are using. You can select common units like kg/m³ or lbs/ft³. If you don't know the density, search online for the specific material (e.g., "density of aluminum," "density of concrete").
- Choose Units: Select the desired units for your dimensions and the resulting weight. This ensures your final calculation is in a format you understand.
- Click Calculate: Once all inputs are entered, click the "Calculate" button.
How to Read Results:
The calculator will display:
- Primary Highlighted Result: This shows the main output, typically the weight or the primary geometric property (Area/Volume), in a large, easy-to-read format.
- Intermediate Values: These provide key figures used in the calculation, such as the calculated Area or Volume, and dimensions.
- Material Information: Details about the material density and derived weight per unit volume are shown.
- Formula Used: A plain-language explanation of the mathematical formula applied.
- Table View: A detailed table breaks down all parameters, their values, and units for comprehensive review.
- Chart: A visual representation (if applicable) showing how results might change with variations in input dimensions.
Decision-Making Guidance:
Use the results to make informed decisions:
- Material Procurement: Ensure you order enough material by cross-referencing calculated volume/area with supplier quantities.
- Budgeting: Estimate material costs based on the calculated weight and current market prices.
- Logistics: Plan for transportation, storage, and handling based on the object's dimensions and weight.
- Structural Integrity: Verify if structures can support the calculated weight. Consult engineering resources if needed.
Don't forget to use the "Copy Results" button to paste the key figures and assumptions into your reports or planning documents.
Key Factors That Affect Area, Volume, and Weight Results
Several factors can influence the accuracy and interpretation of area, volume, and weight calculations. Understanding these is crucial for realistic project planning:
- Material Density Variations: The assumed density might be an average. Real-world materials can have slight variations due to manufacturing processes, impurities, or composition differences. For critical applications, use precise density data from the manufacturer.
- Geometric Imperfections: Real-world objects are rarely perfect geometric shapes. Slight deviations from flatness, roundness, or straightness can alter the precise volume and surface area.
- Unit Consistency: Inconsistent units are a common source of error. Mixing meters with centimeters, or feet with inches, within the same calculation will lead to dramatically incorrect results. Always ensure all input dimensions and density units are compatible.
- Temperature and Pressure Effects: For some materials, especially gases and liquids, density can change significantly with temperature and pressure. While this calculator assumes standard conditions, significant fluctuations may require adjustments.
- Hollow Structures and Inclusions: The calculator typically assumes solid objects. If an object is hollow (like a pipe or a hollow sphere) or contains voids/inclusions, the calculation needs to be adjusted to account for the internal empty space or different material densities.
- Tolerances and Manufacturing Margins: Engineering and manufacturing involve tolerances – acceptable ranges of variation in dimensions. The calculated weight is based on ideal dimensions; actual weights might differ slightly due to these tolerances. Understanding engineering tolerances can refine estimates.
- Moisture Content: For materials like wood, soil, or grains, moisture content can significantly affect their density and, consequently, their weight. Ensure density values used are appropriate for the expected moisture levels.
Frequently Asked Questions (FAQ)
Q1: Can I calculate the weight of a hollow object like a pipe?
A1: This calculator primarily handles solid shapes. For hollow objects, you would typically calculate the volume of the outer shape and subtract the volume of the inner hollow space to get the material volume, then multiply by density. Some advanced versions might offer this functionality.
Q2: What's the difference between weight and mass?
A2: Mass is the amount of matter in an object, while weight is the force of gravity acting on that mass. On Earth, they are often used interchangeably because gravity is relatively constant. However, density is defined as mass per unit volume.
Q3: How do I find the density of a material?
A3: You can usually find material density in engineering handbooks, material safety data sheets (MSDS), online databases, or by consulting the material supplier. Common materials like water, steel, and concrete have widely available density values.
Q4: What units should I use? Can I mix them?
A4: You must use consistent units for all dimensions (e.g., all meters or all feet) and ensure the density unit matches (e.g., kg/m³ if dimensions are in meters). The calculator allows you to select output units, but input consistency is vital.
Q5: Does the calculator account for material waste?
A5: No, this calculator provides theoretical geometric calculations. It doesn't account for cutting waste, spillage, or over-ordering, which are common in practical construction and manufacturing. Always add a buffer (e.g., 10-15%) for waste.
Q6: Can this calculator be used for liquids?
A6: Yes, if you know the density of the liquid (e.g., water density ~1000 kg/m³ or 1 g/cm³). You can calculate the volume of the container and then multiply by the liquid's density to find its weight.
Q7: What if my shape isn't listed?
A7: For complex or irregular shapes, you might need to approximate them using simpler geometric forms or use more advanced CAD software. For estimation, breaking down the complex shape into simpler components (cubes, cylinders) can sometimes work.
Q8: How accurate are the results?
A8: The accuracy depends entirely on the accuracy of your input dimensions and the material density you provide. The geometric formulas themselves are exact. Real-world factors like tolerances and material variations introduce discrepancies.
Enter the length of one side of the cube.
';
} else if (shapeType === 'rectangular_prism') {
html += 'Enter the length of the prism.
';
html += 'Enter the width of the prism.
';
html += 'Enter the height of the prism.
';
} else if (shapeType === 'cylinder') {
html += 'Enter the radius of the cylinder base.
';
html += 'Enter the height of the cylinder.
';
} else if (shapeType === 'sphere') {
html += 'Enter the radius of the sphere.
';
} else if (shapeType === 'cone') {
html += 'Enter the radius of the cone base.
';
html += 'Enter the height of the cone.
';
} else if (shapeType === 'rectangular_area') {
html += 'Enter the length of the rectangle.
';
html += 'Enter the width of the rectangle.
';
html += 'Enter the thickness for weight calculation (use 0 if only area is needed).
';
} else if (shapeType === 'circle_area') {
html += 'Enter the radius of the circle.
';
html += 'Enter the thickness for weight calculation (use 0 if only area is needed).
';
}
html += 'Enter the density of the material (e.g., kg/m³).
';
html += '' + unitOptions + 'Select the units for your length, width, height, etc.
';
html += '' + (shapeType.includes('area') ? areaDensityUnitOptions : densityUnitOptions) + 'Select the units for the material density.
';
inputSection.innerHTML = html;
// Set default values
document.getElementById('density').value = defaultDensity[shapeType] || ";
document.getElementById('dimensionUnit').value = defaultUnits[shapeType] || 'meters';
document.getElementById('densityUnit').value = defaultDensityUnits[shapeType] || 'kg/m³';
if (shapeType.includes('area')) {
document.getElementById('thickness').value = 0.1; // Default thickness for area shapes
}
calculate(); // Recalculate with new defaults
}
function validateInput(value, inputId, errorId, min = -Infinity, max = Infinity) {
var errorElement = document.getElementById(errorId);
errorElement.style.display = 'none';
var inputElement = document.getElementById(inputId);
if (value === null || value === ") {
errorElement.textContent = 'This field is required.';
errorElement.style.display = 'block';
inputElement.style.borderColor = '#dc3545';
return false;
}
var numValue = parseFloat(value);
if (isNaN(numValue)) {
errorElement.textContent = 'Please enter a valid number.';
errorElement.style.display = 'block';
inputElement.style.borderColor = '#dc3545';
return false;
}
if (numValue max) {
errorElement.textContent = 'Value exceeds maximum limit.';
errorElement.style.display = 'block';
inputElement.style.borderColor = '#dc3545';
return false;
}
inputElement.style.borderColor = '#ccc'; // Reset border color
return true;
}
function getInputValue(id, defaultValue = 0) {
var element = document.getElementById(id);
if (!element) return defaultValue;
var value = element.value;
return (value === " || isNaN(parseFloat(value))) ? defaultValue : parseFloat(value);
}
function convertToSi(value, unit) {
if (unit === 'cm') return value / 100;
if (unit === 'ft') return value * 0.3048;
if (unit === 'in') return value * 0.0254;
return value; // meters
}
function convertDensityToSI(value, unit) {
if (unit === 'g/cm³') return value * 1000; // g/cm³ to kg/m³
if (unit === 'lbs/ft³') return value * 16.0185; // lbs/ft³ to kg/m³
if (unit === 'kg/m²') return value; // already SI for area density
if (unit === 'kg/ft²') return value * 10.7639; // kg/ft² to kg/m²
return value; // kg/m³ or kg/m²
}
function convertToOutputUnits(value, unit, isVolume = false) {
if (unit === 'cm') {
return isVolume ? value * 1000000 : value * 100; // m³ to cm³ or m to cm
}
if (unit === 'ft') {
return isVolume ? value / 0.0283168 : value / 0.3048; // m³ to ft³ or m to ft
}
if (unit === 'in') {
return isVolume ? value / 16387.1 : value / 0.0254; // m³ to in³ or m to in
}
return value; // meters or m³
}
function convertWeightToOutputUnits(value, unit) {
if (unit === 'lbs/ft³' || unit === 'kg/ft²' || unit === 'lbs/ft²') {
// If density was in lbs/ft³ or lbs/ft², convert final weight to lbs
if (document.getElementById('densityUnit').value === 'lbs/ft³' || document.getElementById('densityUnit').value === 'lbs/ft²') {
return value; // Already in lbs if input density was lbs related
} else {
// Convert from kg to lbs
return value * 2.20462;
}
}
return value; // kg
}
function calculate() {
var shapeType = currentShape;
var dimUnit = document.getElementById('dimensionUnit').value;
var densityUnit = document.getElementById('densityUnit').value;
var length = 0, width = 0, height = 0, radius = 0, side = 0, thickness = 0;
var area = 0, volume = 0;
var density = getInputValue('density', 0);
var valid = true;
// Clear previous errors and results
document.getElementById('primary-result').textContent = '–';
document.getElementById('intermediate1').innerHTML = 'Dimension 1: –';
document.getElementById('intermediate2').innerHTML = 'Dimension 2: –';
document.getElementById('intermediate3').innerHTML = 'Dimension 3: –';
document.getElementById('materialDensity').innerHTML = 'Material Density: –';
document.getElementById('materialWeightPerUnit').innerHTML = 'Weight per Unit Volume: –';
document.getElementById('formulaText').textContent = ";
document.querySelector('#resultsTable tbody').innerHTML = ";
document.getElementById('chartSection').style.display = 'none';
// Input Validation and Value Retrieval
if (shapeType === 'cube') {
side = getInputValue('side');
valid &= validateInput(side, 'side', 'sideError', 0);
if (valid) {
var sideSI = convertToSi(side, dimUnit);
volume = Math.pow(sideSI, 3);
density = convertDensityToSI(density, densityUnit);
var weight = volume * density;
// Update intermediate values and results
document.getElementById('intermediate1').innerHTML = 'Side: ' + side.toFixed(3) + ' ' + dimUnit;
document.getElementById('intermediate2').innerHTML = 'Volume: ' + convertToOutputUnits(volume, dimUnit, true).toFixed(3) + (volumeUnitMap[dimUnit.charAt(0)] || 'm³');
document.getElementById('intermediate3').innerHTML = "; // Not needed for cube
document.getElementById('primary-result').textContent = convertWeightToOutputUnits(weight, dimUnit).toFixed(3) + ' ' + (weightUnitMap[dimUnit.charAt(0)] || 'kg');
document.getElementById('formulaText').textContent = 'Volume = side³; Weight = Volume × Density';
// Table population
populateTable([
['Side Length', side.toFixed(3), dimUnit],
['Volume', convertToOutputUnits(volume, dimUnit, true).toFixed(3), volumeUnitMap[dimUnit.charAt(0)] || 'm³'],
['Density', density.toFixed(3), densityUnitMap[densityUnit.charAt(0)] || 'kg/m³'],
['Calculated Weight', convertWeightToOutputUnits(weight, dimUnit).toFixed(3), weightUnitMap[dimUnit.charAt(0)] || 'kg']
]);
updateChart(side, weight); // Update chart
}
} else if (shapeType === 'rectangular_prism') {
length = getInputValue('length');
width = getInputValue('width');
height = getInputValue('height');
valid &= validateInput(length, 'length', 'lengthError', 0);
valid &= validateInput(width, 'width', 'widthError', 0);
valid &= validateInput(height, 'height', 'heightError', 0);
if (valid) {
var lengthSI = convertToSi(length, dimUnit);
var widthSI = convertToSi(width, dimUnit);
var heightSI = convertToSi(height, dimUnit);
volume = lengthSI * widthSI * heightSI;
density = convertDensityToSI(density, densityUnit);
var weight = volume * density;
document.getElementById('intermediate1').innerHTML = 'Length: ' + length.toFixed(3) + ' ' + dimUnit;
document.getElementById('intermediate2').innerHTML = 'Width: ' + width.toFixed(3) + ' ' + dimUnit;
document.getElementById('intermediate3').innerHTML = 'Height: ' + height.toFixed(3) + ' ' + dimUnit;
document.getElementById('primary-result').textContent = convertWeightToOutputUnits(weight, dimUnit).toFixed(3) + ' ' + (weightUnitMap[dimUnit.charAt(0)] || 'kg');
document.getElementById('formulaText').textContent = 'Volume = Length × Width × Height; Weight = Volume × Density';
populateTable([
['Length', length.toFixed(3), dimUnit],
['Width', width.toFixed(3), dimUnit],
['Height', height.toFixed(3), dimUnit],
['Volume', convertToOutputUnits(volume, dimUnit, true).toFixed(3), volumeUnitMap[dimUnit.charAt(0)] || 'm³'],
['Density', density.toFixed(3), densityUnitMap[densityUnit.charAt(0)] || 'kg/m³'],
['Calculated Weight', convertWeightToOutputUnits(weight, dimUnit).toFixed(3), weightUnitMap[dimUnit.charAt(0)] || 'kg']
]);
updateChart(length, weight);
}
} else if (shapeType === 'cylinder') {
radius = getInputValue('radius');
height = getInputValue('height');
valid &= validateInput(radius, 'radius', 'radiusError', 0);
valid &= validateInput(height, 'height', 'heightError', 0);
if (valid) {
var radiusSI = convertToSi(radius, dimUnit);
var heightSI = convertToSi(height, dimUnit);
volume = Math.PI * Math.pow(radiusSI, 2) * heightSI;
density = convertDensityToSI(density, densityUnit);
var weight = volume * density;
document.getElementById('intermediate1').innerHTML = 'Radius: ' + radius.toFixed(3) + ' ' + dimUnit;
document.getElementById('intermediate2').innerHTML = 'Height: ' + height.toFixed(3) + ' ' + dimUnit;
document.getElementById('intermediate3').innerHTML = 'Volume: ' + convertToOutputUnits(volume, dimUnit, true).toFixed(3) + (volumeUnitMap[dimUnit.charAt(0)] || 'm³');
document.getElementById('primary-result').textContent = convertWeightToOutputUnits(weight, dimUnit).toFixed(3) + ' ' + (weightUnitMap[dimUnit.charAt(0)] || 'kg');
document.getElementById('formulaText').textContent = 'Volume = π × radius² × height; Weight = Volume × Density';
populateTable([
['Radius', radius.toFixed(3), dimUnit],
['Height', height.toFixed(3), dimUnit],
['Volume', convertToOutputUnits(volume, dimUnit, true).toFixed(3), volumeUnitMap[dimUnit.charAt(0)] || 'm³'],
['Density', density.toFixed(3), densityUnitMap[densityUnit.charAt(0)] || 'kg/m³'],
['Calculated Weight', convertWeightToOutputUnits(weight, dimUnit).toFixed(3), weightUnitMap[dimUnit.charAt(0)] || 'kg']
]);
updateChart(radius, weight);
}
} else if (shapeType === 'sphere') {
radius = getInputValue('radius');
valid &= validateInput(radius, 'radius', 'radiusError', 0);
if (valid) {
var radiusSI = convertToSi(radius, dimUnit);
volume = (4/3) * Math.PI * Math.pow(radiusSI, 3);
density = convertDensityToSI(density, densityUnit);
var weight = volume * density;
document.getElementById('intermediate1').innerHTML = 'Radius: ' + radius.toFixed(3) + ' ' + dimUnit;
document.getElementById('intermediate2').innerHTML = 'Volume: ' + convertToOutputUnits(volume, dimUnit, true).toFixed(3) + (volumeUnitMap[dimUnit.charAt(0)] || 'm³');
document.getElementById('intermediate3').innerHTML = "; // Not needed for sphere
document.getElementById('primary-result').textContent = convertWeightToOutputUnits(weight, dimUnit).toFixed(3) + ' ' + (weightUnitMap[dimUnit.charAt(0)] || 'kg');
document.getElementById('formulaText').textContent = 'Volume = (4/3) × π × radius³; Weight = Volume × Density';
populateTable([
['Radius', radius.toFixed(3), dimUnit],
['Volume', convertToOutputUnits(volume, dimUnit, true).toFixed(3), volumeUnitMap[dimUnit.charAt(0)] || 'm³'],
['Density', density.toFixed(3), densityUnitMap[densityUnit.charAt(0)] || 'kg/m³'],
['Calculated Weight', convertWeightToOutputUnits(weight, dimUnit).toFixed(3), weightUnitMap[dimUnit.charAt(0)] || 'kg']
]);
updateChart(radius, weight);
}
} else if (shapeType === 'cone') {
radius = getInputValue('radius');
height = getInputValue('height');
valid &= validateInput(radius, 'radius', 'radiusError', 0);
valid &= validateInput(height, 'height', 'heightError', 0);
if (valid) {
var radiusSI = convertToSi(radius, dimUnit);
var heightSI = convertToSi(height, dimUnit);
volume = (1/3) * Math.PI * Math.pow(radiusSI, 2) * heightSI;
density = convertDensityToSI(density, densityUnit);
var weight = volume * density;
document.getElementById('intermediate1').innerHTML = 'Radius: ' + radius.toFixed(3) + ' ' + dimUnit;
document.getElementById('intermediate2').innerHTML = 'Height: ' + height.toFixed(3) + ' ' + dimUnit;
document.getElementById('intermediate3').innerHTML = 'Volume: ' + convertToOutputUnits(volume, dimUnit, true).toFixed(3) + (volumeUnitMap[dimUnit.charAt(0)] || 'm³');
document.getElementById('primary-result').textContent = convertWeightToOutputUnits(weight, dimUnit).toFixed(3) + ' ' + (weightUnitMap[dimUnit.charAt(0)] || 'kg');
document.getElementById('formulaText').textContent = 'Volume = (1/3) × π × radius² × height; Weight = Volume × Density';
populateTable([
['Radius', radius.toFixed(3), dimUnit],
['Height', height.toFixed(3), dimUnit],
['Volume', convertToOutputUnits(volume, dimUnit, true).toFixed(3), volumeUnitMap[dimUnit.charAt(0)] || 'm³'],
['Density', density.toFixed(3), densityUnitMap[densityUnit.charAt(0)] || 'kg/m³'],
['Calculated Weight', convertWeightToOutputUnits(weight, dimUnit).toFixed(3), weightUnitMap[dimUnit.charAt(0)] || 'kg']
]);
updateChart(radius, weight);
}
} else if (shapeType === 'rectangular_area') {
length = getInputValue('length');
width = getInputValue('width');
thickness = getInputValue('thickness', 0); // Optional
valid &= validateInput(length, 'length', 'lengthError', 0);
valid &= validateInput(width, 'width', 'widthError', 0);
valid &= validateInput(thickness, 'thickness', 'thicknessError', 0); // Allow 0 for thickness
if (valid) {
var lengthSI = convertToSi(length, dimUnit);
var widthSI = convertToSi(width, dimUnit);
var thicknessSI = convertToSi(thickness, dimUnit); // Convert thickness too
var area = lengthSI * widthSI;
var areaOutput = convertToOutputUnits(area, dimUnit, false); // Area units
var weight = 0;
var effectiveDensity = density; // Use provided density
if (thickness > 0) {
var volume = area * thicknessSI;
effectiveDensity = convertDensityToSI(density, densityUnit); // Ensure density is SI (kg/m³)
weight = volume * effectiveDensity;
document.getElementById('intermediate2').innerHTML = 'Volume: ' + convertToOutputUnits(volume, dimUnit, true).toFixed(3) + (volumeUnitMap[dimUnit.charAt(0)] || 'm³');
document.getElementById('materialWeightPerUnit').innerHTML = 'Weight per Unit Volume: ' + effectiveDensity.toFixed(3) + ' ' + (densityUnitMap[densityUnit.charAt(0)] || 'kg/m³');
} else {
// If thickness is 0, treat density as surface density (kg/m²)
effectiveDensity = convertDensityToSI(density, densityUnit); // Assume kg/m² if thickness=0
weight = area * effectiveDensity; // Area * surface density
document.getElementById('intermediate2').innerHTML = ";
document.getElementById('materialWeightPerUnit').innerHTML = 'Surface Density: ' + effectiveDensity.toFixed(3) + ' ' + (densityUnitMap[densityUnit.charAt(0)] || 'kg/m²');
}
document.getElementById('intermediate1').innerHTML = 'Length: ' + length.toFixed(3) + ' ' + dimUnit;
document.getElementById('intermediate3').innerHTML = 'Width: ' + width.toFixed(3) + ' ' + dimUnit;
document.getElementById('primary-result').textContent = convertWeightToOutputUnits(weight, dimUnit).toFixed(3) + ' ' + (weightUnitMap[dimUnit.charAt(0)] || 'kg');
document.getElementById('formulaText').textContent = 'Area = Length × Width; Weight = Area × Thickness × Density (or Area × Surface Density)';
populateTable([
['Length', length.toFixed(3), dimUnit],
['Width', width.toFixed(3), dimUnit],
['Thickness', thickness > 0 ? thickness.toFixed(3) + ' ' + dimUnit : 'N/A', thickness > 0 ? dimUnit : "],
['Area', areaOutput.toFixed(3), areaUnitMap[dimUnit.charAt(0)] || 'm²'],
['Density', effectiveDensity.toFixed(3), densityUnitMap[densityUnit.charAt(0)] || 'kg/m³'],
['Calculated Weight', convertWeightToOutputUnits(weight, dimUnit).toFixed(3), weightUnitMap[dimUnit.charAt(0)] || 'kg']
]);
updateChart(length, weight);
}
} else if (shapeType === 'circle_area') {
radius = getInputValue('radius');
thickness = getInputValue('thickness', 0); // Optional
valid &= validateInput(radius, 'radius', 'radiusError', 0);
valid &= validateInput(thickness, 'thickness', 'thicknessError', 0);
if (valid) {
var radiusSI = convertToSi(radius, dimUnit);
var thicknessSI = convertToSi(thickness, dimUnit);
var area = Math.PI * Math.pow(radiusSI, 2);
var areaOutput = convertToOutputUnits(area, dimUnit, false); // Area units
var weight = 0;
var effectiveDensity = density;
if (thickness > 0) {
var volume = area * thicknessSI;
effectiveDensity = convertDensityToSI(density, densityUnit);
weight = volume * effectiveDensity;
document.getElementById('intermediate2').innerHTML = 'Volume: ' + convertToOutputUnits(volume, dimUnit, true).toFixed(3) + (volumeUnitMap[dimUnit.charAt(0)] || 'm³');
document.getElementById('materialWeightPerUnit').innerHTML = 'Weight per Unit Volume: ' + effectiveDensity.toFixed(3) + ' ' + (densityUnitMap[densityUnit.charAt(0)] || 'kg/m³');
} else {
effectiveDensity = convertDensityToSI(density, densityUnit); // Assume kg/m² if thickness=0
weight = area * effectiveDensity;
document.getElementById('intermediate2').innerHTML = ";
document.getElementById('materialWeightPerUnit').innerHTML = 'Surface Density: ' + effectiveDensity.toFixed(3) + ' ' + (densityUnitMap[densityUnit.charAt(0)] || 'kg/m²');
}
document.getElementById('intermediate1').innerHTML = 'Radius: ' + radius.toFixed(3) + ' ' + dimUnit;
document.getElementById('intermediate3').innerHTML = "; // Not needed for circle area
document.getElementById('primary-result').textContent = convertWeightToOutputUnits(weight, dimUnit).toFixed(3) + ' ' + (weightUnitMap[dimUnit.charAt(0)] || 'kg');
document.getElementById('formulaText').textContent = 'Area = π × radius²; Weight = Area × Thickness × Density (or Area × Surface Density)';
populateTable([
['Radius', radius.toFixed(3), dimUnit],
['Thickness', thickness > 0 ? thickness.toFixed(3) + ' ' + dimUnit : 'N/A', thickness > 0 ? dimUnit : "],
['Area', areaOutput.toFixed(3), areaUnitMap[dimUnit.charAt(0)] || 'm²'],
['Density', effectiveDensity.toFixed(3), densityUnitMap[densityUnit.charAt(0)] || 'kg/m³'],
['Calculated Weight', convertWeightToOutputUnits(weight, dimUnit).toFixed(3), weightUnitMap[dimUnit.charAt(0)] || 'kg']
]);
updateChart(radius, weight);
}
}
if (!valid) {
document.getElementById('primary-result').textContent = 'Invalid Input';
}
}
// Unit mapping for display
var volumeUnitMap = {'m':'m³', 'c':'cm³', 'f':'ft³', 'i':'in³'};
var areaUnitMap = {'m':'m²', 'c':'cm²', 'f':'ft²', 'i':'in²'};
var weightUnitMap = {'m':'kg', 'c':'g', 'f':'lbs', 'i':'lbs'};
var densityUnitMap = {'k':'kg/m³', 'g':'g/cm³', 'l':'lbs/ft³', 'm':'kg/m²', 't':'kg/ft²', 's':'lbs/ft²'};
function populateTable(data) {
var tbody = document.querySelector('#resultsTable tbody');
tbody.innerHTML = "; // Clear existing rows
for (var i = 0; i < data.length; i++) {
if (data[i][1] === '' || data[i][1] === 'N/A') continue; // Skip empty or N/A data points
var row = tbody.insertRow();
var cell1 = row.insertCell(0);
var cell2 = row.insertCell(1);
var cell3 = row.insertCell(2);
cell1.textContent = data[i][0];
cell2.textContent = data[i][1];
cell3.textContent = data[i][2];
}
}
function resetCalculator() {
var shapeType = document.getElementById('shapeType').value;
document.getElementById('density').value = defaultDensity[shapeType] || '';
document.getElementById('dimensionUnit').value = defaultUnits[shapeType] || 'meters';
document.getElementById('densityUnit').value = defaultDensityUnits[shapeType] || 'kg/m³';
if (shapeType.includes('area')) {
document.getElementById('thickness').value = 0.1;
}
// Reset specific dimension inputs based on shape
if (shapeType === 'cube') document.getElementById('side').value = 5;
else if (shapeType === 'rectangular_prism') {
document.getElementById('length').value = 10;
document.getElementById('width').value = 5;
document.getElementById('height').value = 3;
} else if (shapeType === 'cylinder') {
document.getElementById('radius').value = 2;
document.getElementById('height').value = 5;
} else if (shapeType === 'sphere') {
document.getElementById('radius').value = 3;
} else if (shapeType === 'cone') {
document.getElementById('radius').value = 4;
document.getElementById('height').value = 6;
} else if (shapeType === 'rectangular_area') {
document.getElementById('length').value = 10;
document.getElementById('width').value = 5;
} else if (shapeType === 'circle_area') {
document.getElementById('radius').value = 3;
}
calculate();
}
function copyResults() {
var primaryResult = document.getElementById('primary-result').textContent;
var intermediate1 = document.getElementById('intermediate1').textContent;
var intermediate2 = document.getElementById('intermediate2').textContent;
var intermediate3 = document.getElementById('intermediate3').textContent;
var materialDensity = document.getElementById('materialDensity').textContent;
var materialWeightPerUnit = document.getElementById('materialWeightPerUnit').textContent;
var formula = document.getElementById('formulaText').textContent;
var assumptions = document.querySelector('.key-assumption').textContent;
var tableRows = document.querySelectorAll('#resultsTable tbody tr');
var tableContent = "Calculation Details:\n";
tableRows.forEach(function(row) {
var cells = row.cells;
tableContent += `- ${cells[0].textContent}: ${cells[1].textContent} ${cells[2].textContent}\n`;
});
var contentToCopy = `— Area, Volume, and Weight Calculation Results —\n\n`
+ `Primary Result: ${primaryResult}\n\n`
+ `Intermediate Values:\n`
+ `${intermediate1}\n`
+ `${intermediate2}\n`
+ `${intermediate3}\n\n`
+ `Material Information:\n`
+ `${materialDensity}\n`
+ `${materialWeightPerUnit}\n\n`
+ `Formula Used: ${formula}\n\n`
+ `${tableContent}\n`
+ `Key Assumptions: ${assumptions}`;
// Use Clipboard API
navigator.clipboard.writeText(contentToCopy).then(function() {
// Success feedback (optional)
var copyButton = document.querySelector('.btn-copy');
copyButton.textContent = 'Copied!';
setTimeout(function() {
copyButton.textContent = 'Copy Results';
}, 2000);
}).catch(function(err) {
console.error('Failed to copy: ', err);
// Fallback for older browsers or if clipboard API fails
alert('Failed to copy results. Please copy manually.');
});
}
// Charting Logic
var chartInstance = null;
function updateChart(primaryInput, calculatedWeight) {
var canvas = document.getElementById('resultChart');
if (!canvas) return;
var ctx = canvas.getContext('2d');
// Generate some sample data points for the chart based on input variation
var dataPoints = [];
var baseInput = primaryInput;
var step = baseInput * 0.1; // Vary input by 10% increments
var numPoints = 10;
var shapeType = currentShape;
var dimUnit = document.getElementById('dimensionUnit').value;
var density = getInputValue('density', 0);
var densityUnit = document.getElementById('densityUnit').value;
var thickness = getInputValue('thickness', 0);
for (var i = 1; i <= numPoints; i++) {
var currentInput = baseInput – step * (numPoints / 2) + step * (i – 1);
if (currentInput 0) {
currentWeight = currentVolumeOrArea * currentInputSI * currentDensitySI; // Area * Thickness * Density
} else {
currentWeight = currentVolumeOrArea * currentDensitySI; // Area * Surface Density
}
} else if (shapeType === 'circle_area') {
currentVolumeOrArea = Math.PI * Math.pow(currentInputSI, 2); // Area
if (currentThicknessSI > 0) {
currentWeight = currentVolumeOrArea * currentInputSI * currentDensitySI; // Area * Thickness * Density
} else {
currentWeight = currentVolumeOrArea * currentDensitySI; // Area * Surface Density
}
}
// Convert weight back to user's chosen unit for display
var displayWeight = convertWeightToOutputUnits(currentWeight, dimUnit);
dataPoints.push({ x: currentInput, y: displayWeight });
}
var labels = dataPoints.map(function(point) { return point.x.toFixed(2); });
var weights = dataPoints.map(function(point) { return point.y.toFixed(2); });
// Destroy previous chart instance if it exists
if (chartInstance) {
chartInstance.destroy();
}
// Create new chart
chartInstance = new Chart(ctx, {
type: 'line',
data: {
labels: labels,
datasets: [{
label: 'Calculated Weight',
data: weights,
borderColor: 'rgba(0, 74, 153, 1)',
backgroundColor: 'rgba(0, 74, 153, 0.2)',
fill: true,
tension: 0.4
}]
},
options: {
responsive: true,
maintainAspectRatio: true,
scales: {
x: {
title: {
display: true,
labelString: capitalizeFirstLetter(shapeType.replace('_', ' ')) + ' (' + dimUnit + ')'
}
},
y: {
title: {
display: true,
labelString: 'Weight (' + (weightUnitMap[dimUnit.charAt(0)] || 'kg') + ')'
}
}
},
plugins: {
tooltip: {
callbacks: {
label: function(context) {
var label = context.dataset.label || ";
if (label) {
label += ': ';
}
label += context.parsed.y + ' ' + (weightUnitMap[dimUnit.charAt(0)] || 'kg');
return label;
}
}
}
}
}
});
document.getElementById('chartSection').style.display = 'block';
}
function capitalizeFirstLetter(string) {
return string.charAt(0).toUpperCase() + string.slice(1);
}
// Initialize calculator on page load
window.onload = function() {
updateInputs();
// Add Chart.js library dynamically (if not already present)
// In a real-world scenario, you'd include this in the
if (typeof Chart === 'undefined') {
var script = document.createElement('script');
script.src = 'https://cdn.jsdelivr.net/npm/chart.js@3.7.0/dist/chart.min.js';
script.onload = function() {
console.log("Chart.js loaded.");
// Ensure calculation happens after chart library is loaded if needed
};
document.head.appendChild(script);
}
// Ensure initial calculation happens after potential script load
setTimeout(calculate, 100); // Small delay to ensure chart.js is available
};