Volume Calculator

The most frequently used volume formulas: Cube: V = s³ (a 2-foot cube holds 8 cubic feet or 59.8 gallons). Rectangular prism: V = l × w × h. Cylinder: V = πr²h — a 4-foot diameter, 3-foot tall cylindrical tank holds π(2²)(3) = 37.7 ft³ = 282 gallons. Sphere: V = (4/3)πr³. Cone: V = (1/3)πr²h — exactly one-third of a cylinder with the same base and height. Pyramid: V = (1/3) × base area × h. For irregular shapes, break them into simpler components, calculate each separately, and sum the results. A swimming pool with a shallow end (3ft) and deep end (8ft) can be approximated as a rectangular prism with average depth: V = length × width × (3+8)/2.

Key conversion factors: 1 cubic foot = 7.481 US gallons = 28.317 liters. 1 cubic yard = 27 cubic feet = 202 gallons — the standard unit for ordering concrete, mulch, and gravel. 1 cubic meter = 264.2 gallons = 35.31 cubic feet. Quick estimation shortcuts: a standard bathtub holds 40-60 gallons, a hot tub 300-500 gallons, and an average swimming pool 10,000-20,000 gallons. For landscaping, mulch and soil are sold by the cubic yard — a 2-inch layer over a 10×20 foot area requires (10 × 20 × 2/12) / 27 = 1.23 cubic yards. Concrete trucks typically carry 8-10 cubic yards. Always add 10-15% waste factor when ordering materials — irregular shapes, spillage, and settling inevitably consume more material than the pure mathematical volume.

Shipping costs often depend on dimensional weight rather than actual weight. Dimensional weight = (L × W × H in inches) / dimensional factor (typically 139 for domestic US, 166 for international). A 24×18×12 inch box has dimensional weight of 24×18×12/139 = 37.3 lbs — if the actual package weighs only 15 lbs, you pay for 37.3 lbs. This makes efficient packaging critical: reducing box dimensions by just 2 inches in each direction (22×16×10) drops dimensional weight to 25.3 lbs — a 32% cost reduction. Cubic capacity utilization matters for truckload shipping: a standard 53-foot trailer holds approximately 3,489 cubic feet or 2,390 cubic feet of palletized freight (accounting for air gaps). Stackability, pallet patterns, and void fill all affect how much of that theoretical capacity you actually use.

A cube's volume is V = s³ — the side length cubed. A 5 cm cube holds 5³ = 125 cm³. A rectangular box (rectangular prism) uses V = length × width × height: a 30 × 20 × 15 cm box holds 9,000 cm³ = 9 litres. These two shapes cover most everyday containers, rooms, and shipping boxes. Select 'Cube' or 'Rectangular Prism', enter the dimensions, and the calculator returns volume plus surface area and liquid capacity.

A cylinder's volume is V = πr²h — the circular base area (πr²) times the height. A tank 4 ft across (radius 2 ft) and 3 ft tall holds π × 2² × 3 = 37.7 ft³ ≈ 282 US gallons. Use this for water tanks, pipes, cans, and silos. Enter the radius (half the diameter) and the height; the tool converts the result to litres and gallons automatically.

A sphere's volume is V = (4/3)πr³. A ball of radius 10 cm holds (4/3)π × 10³ ≈ 4,189 cm³ ≈ 4.19 litres. A hemisphere (half a sphere) is exactly half of that: V = (2/3)πr³. Spheres enclose the most volume for the least surface area, which is why bubbles and pressure tanks are round. Enter the radius or diameter to compute it.

A cone holds exactly one-third of the cylinder that surrounds it: V = (1/3)πr²h. A pyramid follows the same one-third rule over its base: V = (1/3) × base area × height. An ice-cream cone 3 cm across (radius 1.5 cm) and 12 cm tall holds (1/3)π × 1.5² × 12 ≈ 28.3 cm³. Pick 'Cone' or 'Pyramid' and enter the base dimensions and the height.

To size a tank or container, compute its volume in cubic units, then convert to capacity: 1 ft³ = 7.481 US gallons = 28.32 litres, and 1 m³ = 264.2 gallons = 1,000 litres. A cylindrical tank 5 ft tall and 6 ft in diameter holds π × 3² × 5 = 141.4 ft³ ≈ 1,058 gallons. The calculator shows litres and gallons alongside the cubic result so you can order or fill accurately.

Volume scales with the cube of the linear unit. Key factors: 1 m³ = 35.31 ft³ = 1,000 litres; 1 cubic yard = 27 ft³ = 202 gallons (the unit for ordering concrete, mulch, and gravel); 1 ft³ = 1,728 in³. To order concrete for a 10 × 12 ft slab 4 inches thick: 10 × 12 × (4/12) = 40 ft³ ÷ 27 = 1.48 cubic yards — round up and add a 10% waste factor.

Two methods handle irregular objects. Water displacement: submerge the object and measure the water it pushes up — the displaced volume equals the object's volume. Decomposition: split the shape into cubes, cylinders, and cones, compute each, and add them (subtracting any hollows). A bottle, for instance, is a cylinder body plus a cone neck. This is how you estimate volume for real-world objects the standard formulas don't directly cover.