Calculate the volume of any 3D shape — cube, sphere, cylinder, cone, prism, pyramid, ellipsoid, or torus. Supports metric (cm, m) and imperial (in, ft) units with automatic conversion between litres, gallons, and cubic measurements.
Volume is one of the most practical measurements in everyday life. Whether you are calculating how much concrete you need for a foundation, working out how many gallons an aquarium holds, determining the capacity of a storage tank, or checking whether a recipe will fit in your mixing bowl — understanding volume is essential. This free volume calculator covers all major 3D geometric shapes and supports both metric (centimetres, metres, litres) and imperial (inches, feet, US gallons, UK gallons) units.
One critical difference that catches many people out: the US gallon and the UK (Imperial) gallon are not the same size. One US gallon equals exactly 231 cubic inches, while one UK Imperial gallon equals approximately 277.4 cubic inches — about 20% larger. This matters enormously when planning aquarium volumes, fuel tanks, irrigation systems, or any liquid storage calculation where the US and UK use different standards.
Each 3D shape has its own formula for calculating volume. Below are the formulas used by this calculator, along with worked examples.
A cube has all sides equal. The volume is simply the side length cubed.
Formula: V = s³
| Side (s) | Volume |
|---|---|
| 5 cm | 125 cm³ = 0.125 litres |
| 10 in | 1,000 in³ = 4.33 US gal = 3.60 UK gal |
| 1 ft | 1,728 in³ = 1 ft³ = 7.48 US gal |
A rectangular prism (or cuboid) has length, width, and height. This is the most common shape for boxes, rooms, and tanks.
Formula: V = l × w × h
Example: A fish tank 24 inches long × 12 inches wide × 16 inches tall has a volume of 24 × 12 × 16 = 4,608 in³ = 19.94 US gallons = 16.61 UK gallons.
A sphere's volume depends only on its radius. The formula uses pi (π ≈ 3.14159265).
Formula: V = (4/3) × π × r³
| Radius | Volume |
|---|---|
| 5 cm | 523.6 cm³ = 0.524 litres |
| 1 ft (12 in) | 7,238.2 in³ = 31.3 US gal |
| 10 cm | 4,188.8 cm³ = 4.19 litres |
A cylinder has a circular cross-section. Water tanks, tin cans, and pipes are all cylinders.
Formula: V = π × r² × h
Example: A cylindrical water butt with radius 20 cm and height 80 cm holds π × 400 × 80 = 100,531 cm³ = 100.5 litres = 22.1 UK gallons.
A cone has a circular base that tapers to a point. Its volume is exactly one-third of a cylinder with the same base and height.
Formula: V = (1/3) × π × r² × h
Example: An ice cream cone with base radius 2 cm and height 10 cm has volume = (1/3) × π × 4 × 10 = 41.9 cm³.
A triangular prism has a triangular cross-section extended along a length. Common in roof structures and wedge-shaped containers.
Formula: V = (1/2) × base × height × length
A square pyramid has a square base and four triangular faces meeting at an apex.
Formula: V = (1/3) × b² × h
The Great Pyramid of Giza has a base of approximately 756 feet per side and an original height of about 481 feet, giving an estimated volume of around 91.2 million cubic feet.
An ellipsoid is a stretched sphere with three potentially different semi-axes (a, b, c). A sphere is a special case where a = b = c.
Formula: V = (4/3) × π × a × b × c
A torus is a donut shape defined by a major radius R (from the centre of the tube to the centre of the torus) and a minor radius r (the radius of the tube itself).
Formula: V = 2π² × R × r²
Understanding how to convert between volume units is critical when working across measurement systems. The table below shows the most important conversions used in the US and UK.
| Unit | Equivalent |
|---|---|
| 1 US gallon | 231 in³ = 3.785 litres = 0.833 UK gal |
| 1 UK (Imperial) gallon | 277.4 in³ = 4.546 litres = 1.201 US gal |
| 1 cubic foot (ft³) | 1,728 in³ = 28.317 litres = 7.481 US gal |
| 1 cubic metre (m³) | 1,000 litres = 264.2 US gal = 219.97 UK gal |
| 1 litre | 1,000 cm³ = 61.024 in³ = 0.2642 US gal = 0.2200 UK gal |
| 1 cubic inch (in³) | 16.387 cm³ = 0.01639 litres |
The US gallon and the UK Imperial gallon are frequently confused. The US gallon (exactly 231 in³) was defined in the early days of American independence and is approximately 83.3% the size of a UK Imperial gallon (approximately 277.42 in³). This means:
Always specify which gallon you mean in international contexts. Our calculator labels both US and UK gallon conversions clearly.
Fishkeepers in the US typically size tanks in US gallons, while UK hobbyists use litres or UK gallons. A standard 20-gallon US tank (20 US gal = 75.7 litres = 16.65 UK gal) would be described very differently depending on country. Use the rectangular prism calculator above to find the exact volume of any fish tank by entering its length, width, and water depth.
Concrete is typically ordered in cubic yards (US) or cubic metres (UK). To calculate how much you need for a rectangular slab: volume = length × width × thickness. A 10 ft × 10 ft slab at 4 inches (0.333 ft) thick requires 33.3 ft³ = 1.23 cubic yards. In the UK, a 3 m × 3 m slab at 10 cm (0.1 m) thick requires 0.9 m³. Our calculator computes volume in cubic units that you can then convert using standard factors.
A rectangular swimming pool 25 m long, 10 m wide, and 1.8 m average depth holds 25 × 10 × 1.8 = 450 m³ = 450,000 litres = 118,877 US gallons = 98,999 UK gallons. Knowing your pool volume helps calculate chlorine dosing, heating costs, and pump run times.
US and UK recipes use different volume measurements for liquids. In the US, recipes use cups (1 cup = 237 mL), fluid ounces, pints (473 mL), quarts, and gallons. In the UK, recipes use millilitres, centilitres, and UK pints (1 UK pint = 568 mL — notably larger than a US pint of 473 mL). A US pint of cream is not the same amount as a UK pint.
Vehicle fuel tanks are described in US gallons in America and litres in the UK. A 15 US gallon tank holds 56.8 litres. A 55-litre tank (common in UK cars) holds about 14.5 US gallons or 12.1 UK gallons. Always confirm which unit a vehicle specification uses.
When packing spheres into a rectangular box, you cannot fill 100% of the space due to the gaps between spheres. The densest known random packing of equal spheres fills approximately 64% of available volume. Face-centred cubic packing (like stacked cannonballs) achieves about 74.05% efficiency. This matters in logistics, powder technology, and pharmaceutical manufacturing where understanding packing density determines product quantities and container sizes.
The metric system (used primarily in the UK, Europe, and most of the world) is base-10, making calculations straightforward: 1,000 cm³ = 1 litre, 1,000 litres = 1 m³. The imperial system (still widely used in the US for everyday measurement) has less intuitive conversions: 231 in³ = 1 gallon, 1,728 in³ = 1 cubic foot, 27 cubic feet = 1 cubic yard.
For scientific work, metric is universal. For everyday US construction, real estate, and grocery measurements, imperial remains dominant. Our calculator bridges both systems automatically, displaying results in your chosen primary units with the conversion shown alongside.
The volume of a cylinder is V = π × r² × h, where r is the radius of the circular base and h is the height. For example, a cylinder with radius 5 cm and height 20 cm has volume = π × 25 × 20 = 1,570.8 cm³ = 1.571 litres.
Exactly 231 cubic inches equal one US liquid gallon. This is a defined, exact value. The UK Imperial gallon is larger at approximately 277.42 cubic inches.
A US gallon equals 231 cubic inches (3.785 litres). A UK Imperial gallon equals approximately 277.42 cubic inches (4.546 litres). The UK gallon is about 20% larger than the US gallon. This difference matters significantly for aquarium volumes, fuel capacity, and any liquid measurement comparison between the two countries.
For irregular shapes, the most accurate method is water displacement: submerge the object in a known volume of water and measure how much the level rises. The rise in water level equals the volume of the submerged object. This is the method Archimedes famously used. For approximate calculations, you can model the shape as a combination of standard shapes (spheres, cylinders, cones) and sum their volumes.
Exactly 1,000 litres equal one cubic metre (1 m³). This is because 1 litre = 1 dm³ = 0.001 m³, and 1 m³ = 1,000 dm³ = 1,000 litres. This makes metric volume conversions intuitive: a cube measuring 1 m on each side holds 1,000 litres of liquid.
A standard UK bathtub typically holds around 80–100 litres of water when filled to a normal level (about 18–22 UK gallons / 21–26 US gallons). A US standard bathtub holds approximately 25–45 gallons (95–170 litres) depending on size. Freestanding soaking tubs can hold 50–100 US gallons or more.
Calculate the wall area (perimeter × height minus door and window areas), then divide by the paint coverage rate. Standard paint covers approximately 10–12 m² per litre (US: roughly 400 square feet per gallon). For a room with 40 m² of wall area requiring two coats, you need 40 × 2 ÷ 11 ≈ 7.3 litres. Volume calculations help when mixing custom paint quantities.
A circular above-ground pool 10 feet (120 inches) in diameter with a depth of 30 inches has radius = 60 inches. Volume = π × 60² × 30 = 339,292 in³ ÷ 231 = approximately 1,469 US gallons (5,561 litres or 1,223 UK gallons). Always use the actual water depth, not the pool wall height, for your calculation.
Results are estimates based on standard geometric formulas and the dimensions you provide. Real-world volumes may differ due to shape irregularities, measurement tolerances, and material thickness. Always verify critical measurements with professional tools before construction, engineering, or manufacturing applications.