Volume Calculator

• Cube: side³ (side length cubed)
• Rectangular Prism: length × width × height
• Sphere: (4/3) × π × r³ (where r is radius)
• Cylinder: π × r² × h (where r is radius, h is height)
• Cone: (1/3) × π × r² × h (where r is radius, h is height)
• Pyramid: (1/3) × base area × height
• Ellipsoid: (4/3) × π × a × b × c (where a, b, c are semi-axes)

• 1 cubic meter (m³) = 1,000 liters (L)
• 1 cubic meter (m³) = 35.3147 cubic feet (ft³)
• 1 liter (L) = 0.001 cubic meters (m³)
• 1 gallon (US) = 3.78541 liters (L)
• 1 cubic foot (ft³) = 28.3168 liters (L)
• 1 cubic foot (ft³) = 7.48052 gallons (US)
• 1 cubic inch (in³) = 16.3871 cubic centimeters (cm³)

For irregular or complex shapes, several methods can be used:

• Decomposition: Breaking down into simpler shapes and adding their volumes
• Displacement Method: Measuring the volume of fluid displaced when an object is submerged
• Integration: Using triple integrals for complex geometric shapes
• 3D Scanning: Using technology to create digital models and calculate volumes
• Cavalieri's Principle: Comparing volumes of objects with equal cross-sectional areas

For objects with cavities or combined shapes:

• Hollow Objects: Outer volume - inner volume
• Composite Objects: Sum of individual component volumes
• Objects with Holes: Total volume - volume of holes
• Truncated Objects: Original volume - removed volume
• Shells: Volume between two similar shapes with different sizes

• Concrete Estimation: Calculating required concrete volume for foundations and structures
• Excavation: Determining soil volume to be removed
• Water Tanks: Designing storage capacity for water systems
• HVAC Systems: Calculating air volume for ventilation design
• Material Requirements: Estimating quantities for construction projects

• Product Design: Optimizing material usage and packaging
• Shipping: Calculating cargo volumes for transportation
• Fluid Dynamics: Designing containers and flow systems
• 3D Printing: Determining material requirements
• Quality Control: Verifying product dimensions and volumes
• Storage Solutions: Designing efficient warehouse systems

• Chemistry: Measuring reagent volumes and solution concentrations
• Biology: Calculating organ volumes and cell densities
• Geology: Estimating mineral deposits and reservoir capacities
• Meteorology: Measuring air masses and precipitation volumes
• Medical Imaging: Analyzing tumor volumes and organ sizes
• Oceanography: Calculating water volumes and displacement

Example 1: Fish Tank Capacity

To calculate the water volume for a rectangular aquarium with dimensions 80cm × 40cm × 50cm:

1. Convert to meters: 0.8m × 0.4m × 0.5m
2. Calculate volume: 0.8m × 0.4m × 0.5m = 0.16m³
3. Convert to liters: 0.16m³ × 1000 = 160 liters
4. Account for decorations and substrate (approx. 10%): 160L × 0.9 = 144 liters actual water capacity

Example 2: Concrete for Garden Path

For a garden path 10m long, 1m wide, with a depth of 10cm:

1. Convert to meters: 10m × 1m × 0.1m
2. Calculate volume: 10m × 1m × 0.1m = 1m³
3. Add 10% for wastage: 1m³ × 1.1 = 1.1m³
4. With concrete sold in 0.25m³ bags: 1.1m³ ÷ 0.25m³ = 4.4 bags (round up to 5)

Example 1: Water Tank Design

For a cylindrical water tank with radius 2m and height 3m:

1. Calculate volume: π × 2² × 3 = 37.7m³
2. Convert to liters: 37.7m³ × 1000 = 37,700 liters
3. Account for 15% safety margin: 37,700L × 0.85 = 32,045 liters usable capacity
4. Calculate flow rate for 4-hour fill: 32,045L ÷ 4h = 8,011 liters/hour needed

Example 2: Shipping Container Capacity

For a standard shipping container with internal dimensions 12.0m × 2.35m × 2.39m:

1. Calculate volume: 12.0m × 2.35m × 2.39m = 67.4m³
2. With average cargo density of 250kg/m³: 67.4m³ × 250kg/m³ = 16,850kg capacity
3. Account for 80% practical fill rate: 67.4m³ × 0.8 = 53.9m³ usable volume
4. Calculate number of standard pallets (1.2m × 0.8m × 1.5m = 1.44m³): 53.9m³ ÷ 1.44m³ = 37 pallets