Calculating volume is essential for construction, manufacturing, science, and everyday applications. Our free volume calculator computes the space inside any three-dimensional shape - cubes, spheres, cylinders, cones, tanks, and more. Whether you're planning concrete pour, sizing an aquarium, calculating packaging, or solving geometry problems, get instant results with clear formulas and unit conversions.
Volume measures the three-dimensional space enclosed within a solid object, measured in cubic units (cm³, m³, ft³). Unlike area (2D) or length (1D), volume quantifies space in all three dimensions. For simple shapes, volume is calculated using geometric formulas. For complex shapes, volume may require calculus (integration), displacement methods, or approximations. Volume is fundamental to understanding density (mass/volume), buoyancy, and material quantities.
Calculate volume for multiple 3D shapes: cube, sphere, cylinder, cone, rectangular tank, Automatic conversion between cubic units, Converts to gallons and liters for liquid measurements, Step-by-step solutions showing formulas, Handles decimals and fractions, Mobile-friendly responsive design, No registration required, Copy results easily, Educational explanations, Supports any measurement units.
Select your 3D shape: Cube: V = s³ (side cubed), Sphere: V = (4/3)πr³, Cylinder: V = πr²h (circular area × height), Cone: V = (1/3)πr²h (1/3 of cylinder volume), Rectangular box: V = l × w × h. The calculator multiplies the appropriate dimensions using the geometric formula, rounds based on precision settings, and displays results in various units for convenience.
Construction and Engineering - Concrete volume for foundations, slabs, columns. Excavation and earthwork volumes. Storage tank sizing. Swimming pool volumes. Packaging and Shipping - Box sizing for products. Freight volume calculations. Container optimization. Storage planning. Science and Education - Density experiments (mass ÷ volume). Buoyancy studies. Phase change calculations. Geometry lessons. Aquariums and Pools - Fish tank water volume. Pool chemical dosing. Pump sizing. Filtration calculations. Cooking and Food - Recipe scaling by volume. Container sizing. Storage planning. Manufacturing - Material requirements. Mold volumes. Product sizing. HVAC - Duct volume. Air handling calculations.
Manual volume calculations require remembering formulas and careful arithmetic. Our calculator eliminates errors, handles multiple shapes and units, provides instant accurate results, shows the formula and steps, converts between units automatically, helps with material estimation, and serves as an educational tool. Accurate volume calculations prevent costly mistakes in construction, shipping, and manufacturing.
Construction workers and contractors, Engineers and architects, Manufacturers and product designers, Scientists and lab technicians, Aquarium and pool owners, Shipping and logistics professionals, Students learning geometry, Teachers preparing lessons, Homeowners doing DIY projects, Anyone needing 3D space calculations.
Select your 3D shape from the list, Enter the required dimensions (radius, height, side lengths), Choose your preferred units if desired, Click Calculate, Review volume in cubic units, Check conversions to gallons/liters, Copy results for your records.
Always use consistent units for all measurements, Use the same unit throughout (don't mix cm and inches), For partial fills, calculate percentage of total volume, Double-check radius vs diameter (radius = half diameter), Rounding: Keep extra precision until final answer, For construction, add 10% extra for waste, Verify calculations for critical applications.
Calculator handles standard geometric shapes, Complex irregular shapes require approximation or calculus, Very large or small numbers use scientific notation, Precision limited by floating-point arithmetic, Does not account for material thickness in hollow objects.
Volume is the amount of three-dimensional space occupied by a solid object, liquid, or gas. It's measured in cubic units (cm³, m³, ft³). Example: Cube with side 2 cm has volume V = 2³ = 8 cm³. Cylinder with radius 3 cm, height 5 cm: V = π × 3² × 5 = 141.37 cm³. Volume differs from capacity - capacity refers to how much a container can hold.
Formula: V = (4/3)πr³ where r = radius. Example: Sphere with radius 5 cm. V = (4/3) × π × 5³ = (4/3) × π × 125 = 523.6 cm³. If given diameter, first divide by 2 to get radius. Basketball (diameter 9.4 inches): r = 4.7 in, V = (4/3)π(4.7)³ ≈ 434.9 cubic inches.
V = πr²h where r = radius, h = height. The cylinder volume equals the base area (πr²) times height. Example: Soda can (r = 3.25 cm, h = 12 cm). V = π × 3.25² × 12 = 398.2 cm³ = 398.2 mL. That's about 13.5 fluid ounces.
V = (1/3)πr²h where r = radius, h = height. A cone's volume is exactly 1/3 of a cylinder with same base and height. Example: Ice cream cone (r = 3 cm, h = 12 cm). V = (1/3) × π × 3² × 12 = 113.1 cm³. This is why filling a cone takes 1/3 the material of filling a cylinder the same size.
V = length × width × height. Example: Shipping box 20 x 16 x 12 inches. V = 20 × 16 × 12 = 3,840 cubic inches. Convert to cubic feet: 3,840 ÷ 1,728 = 2.22 ft³. This helps determine shipping costs and storage requirements.
Common conversions: 1 m³ = 1,000 liters = 1,000,000 cm³. 1 liter = 1,000 mL = 1,000 cm³. 1 gallon (US) = 3.785 liters. 1 cubic foot = 7.48 gallons. 1 cubic meter ≈ 264 gallons. Example: Fish tank 100 liters = 100,000 cm³ = 26.4 gallons.
Construction: Concrete amounts, soil volume, excavation calculations. Manufacturing: Tank sizing, packaging volume, material requirements. Science: Density calculations (mass ÷ volume), phase changes. Medicine: Dosage by body volume. Shipping: Cargo space, freight calculation. Cooking: Recipe scaling. Aquariums: Tank sizing for fish. HVAC: Air volume calculations. Agriculture: Fertilizer, irrigation water.
Volume: Space occupied by a solid object itself. Capacity: Amount a container can hold (usually for liquids/gases). Example: A hollow cube has capacity equal to its interior volume. A solid cube has volume but zero capacity. In practice, they're often used interchangeably for containers. Capacity usually refers to maximum content volume.