Volume Calculator Guide: How to Calculate Volume for Any 3D Shape

Cube and rectangular box (cuboid): • Cube: V = side³ • Box: V = length × width × height

Cylinder: • V = π × radius² × height = πr²h

Sphere: • V = (4/3) × π × radius³ = 4πr³/3

Cone: • V = (1/3) × π × radius² × height = πr²h/3

Pyramid: • V = (1/3) × base area × height

Triangular prism: • V = (1/2) × base × height × length = ½bhl

Ellipsoid: • V = (4/3) × π × a × b × c (where a, b, c are semi-axes)

• Box: V = l × w × h | Cube: V = s³
• Cylinder: V = πr²h (radius² × height × 3.14159)
• Sphere: V = 4/3 × π × r³
• Cone: V = 1/3 × π × r² × h (1/3 of cylinder with same dimensions)

Dry volume: • 1 cubic foot = 1,728 cubic inches • 1 cubic yard = 27 cubic feet • 1 cubic meter = 35.315 cubic feet = 1.308 cubic yards

Liquid volume: • 1 gallon (US) = 231 cubic inches = 3.785 liters • 1 cubic foot = 7.481 gallons • 1 liter = 1,000 milliliters = 0.264 gallons • 1 cubic meter = 1,000 liters = 264.2 gallons

Key practical conversion: • Pool volume in gallons = cubic feet × 7.48 • Concrete in cubic yards = cubic feet ÷ 27

Note: 1 liter of water weighs exactly 1 kilogram (at 4°C); 1 US gallon of water weighs approximately 8.34 pounds.

• 1 cubic foot = 7.481 US gallons | 1 cubic yard = 27 cubic feet
• 1 US gallon = 3.785 liters | 1 liter = 1,000 mL
• Pool/tank volume: cubic feet × 7.48 = gallons
• Concrete: calculate cubic feet, divide by 27 for cubic yards

Concrete for a slab: • Measure area in sq ft, determine depth in feet • Cubic feet = area × depth • Cubic yards = cubic feet ÷ 27 • Example: 12' × 20' patio, 4" thick: 12 × 20 × (4/12) = 80 cu ft = 2.96 cu yd ≈ 3 cubic yards

Dirt fill or excavation: • Same formula as concrete: area × depth = cubic yards (÷27) • For excavation: convert cubic yards to truck loads (typical dump truck ≈ 10–14 cu yd)

Gravel for driveway: • Area (sq ft) × depth (ft) ÷ 27 = cubic yards • Typical depth: 4" base + 2" top = 6" = 0.5 ft • 20' × 50' driveway × 0.5 ft = 500 cu ft ÷ 27 = 18.5 cu yd

• Concrete/gravel: (l × w × depth) ÷ 27 = cubic yards
• 4" slab: multiply sq ft by 0.333 (4/12) for cu ft, then ÷ 27
• Add 10% for waste in concrete orders
• Dump truck: ~10–14 cu yd; excavation: calculate loads needed

Rectangular pool: • V (gallons) = length × width × average depth × 7.48 • Example: 20' × 40' pool, 5' average depth: 20 × 40 × 5 × 7.48 = 29,920 gallons

Round pool: • V (gallons) = π × radius² × depth × 7.48 • 16' diameter (8' radius), 4' deep: 3.14159 × 64 × 4 × 7.48 = 6,028 gallons

Oval pool: • V (gallons) = π × (long radius) × (short radius) × depth × 7.48

Chemical dosing for pools typically scales with volume in gallons. Pool volume also determines pump size, filter capacity, and turnover rate (the time to filter the entire volume once — ideal: 6–8 hours).

• Rectangular pool: l × w × avg depth × 7.48 = gallons
• Round pool: π × r² × depth × 7.48 = gallons
• Pool turnover: gallons ÷ pump GPH = turnover hours (target: 6–8 hours)
• Chemical dosing scales with pool volume in gallons or liters

Kitchen volume conversions: • 1 tablespoon = 3 teaspoons = 15 mL • 1 fluid ounce (fl oz) = 2 tablespoons = 30 mL • 1 cup = 8 fl oz = 16 tablespoons = 240 mL • 1 pint = 2 cups = 480 mL • 1 quart = 2 pints = 4 cups = 960 mL • 1 gallon = 4 quarts = 16 cups = 3.785 liters

Note: dry measuring cups (for flour, sugar) and liquid measuring cups give identical volume but are used differently. Dry ingredients are measured level (topped off) while liquids are read at the meniscus.

Baking volume vs. weight: weight (grams) is more accurate for baking because volume can vary with packing density. 1 cup of flour = 120–150g depending on how it's scooped.

• 1 cup = 240 mL = 16 tablespoons = 8 fl oz
• 1 tablespoon = 15 mL | 1 teaspoon = 5 mL
• 1 gallon = 3.785 liters | 1 liter = 4.23 cups
• Weight is more accurate than volume for baking

Volume × density = weight. This is essential for shipping, structural load calculations, and material quantity estimation.

Common material densities: • Water: 62.4 lb/cu ft = 8.34 lb/gallon = 1 kg/liter • Concrete: 145–150 lb/cu ft (2,322–2,403 kg/m³) • Sand: 95–100 lb/cu ft • Gravel: 100–110 lb/cu ft • Topsoil: 75–100 lb/cu ft • Steel: 490 lb/cu ft • Lumber (typical): 30–35 lb/cu ft

Example: weight of a 10 cubic yard concrete pour: • 10 cu yd × 27 cu ft/cu yd = 270 cu ft • 270 × 150 lb/cu ft = 40,500 lbs = 20.25 tons