Volume Calculator - Volume Measurement

This physics calculator helps you calculate volume of various 3D shapes including cubes, spheres, cylinders, and cones. Volume is the amount of space occupied by a 3D object.

Volume Definition

• Volume: Amount of space occupied by a 3D object
• SI Unit: Cubic meter (m³)
• Common Units: Liters (L), cubic centimeters (cm³)
• Density Relationship: ρ = m/V (density = mass/volume)

Volume Formulas

• Cube: V = l³ (length cubed)
• Cuboid/Rectangular Prism: V = lwh
• Sphere: V = (4/3)πr³
• Cylinder: V = πr²h
• Cone: V = (1/3)πr²h
• Pyramid: V = (1/3)Bh (B = base area)
• Prism: V = Bh (B = base area)

Applications

• Physics: Density, buoyancy, and fluid mechanics
• Engineering: Tank design and capacity
• Chemistry: Molar volume and gas laws
• Architecture: Building volume and space planning
• Manufacturing: Material requirements and packaging
• Medicine: Organ volume and drug dosages

Important Notes

• Volume is always positive
• Volume units are cubic (length³)
• 1 m³ = 1000 L = 1,000,000 cm³
• Volume is additive for non-overlapping objects
• Volume changes with temperature (thermal expansion)

Volume Types

• Regular Solids: Cube, sphere, cylinder, cone
• Irregular Solids: Complex shapes
• Composite Solids: Multiple shapes combined
• Hollow Solids: Outer volume minus inner volume
• Fractal Objects: Self-similar structures

Volume Examples

• 1m Cube: 1 m³ = 1000 L
• Basketball: ~7 L
• Human Body: ~70 L
• Swimming Pool: ~100,000 L
• Olympic Pool: ~2,500,000 L

Volume Relationships

• Density: ρ = m/V
• Mass: m = ρV
• Weight: W = mg = ρVg
• Buoyant Force: F_b = ρ_fluid V_displaced g
• Pressure: P = F/A (related to volume through height)

Volume Measurement

• Direct Measurement: Ruler and formulas
• Displacement Method: Water displacement
• Integration: Calculus for complex shapes
• 3D Scanning: Digital volume measurement
• Archimedes Principle: Buoyancy method

Volume Conversions

• Metric: 1 m³ = 1000 L = 1,000,000 cm³
• Imperial: 1 ft³ = 7.48 gal = 1728 in³
• US Customary: 1 gal = 3.785 L
• Scientific: 1 mL = 1 cm³