Volume Calculator
Pick a solid and enter its measurements to get the volume, surface area and capacity in litres of a cube, box, cylinder, sphere, hemisphere, cone, frustum or pyramid.
- FormulaV = π × r² × h
- Substitutionπ × 30² × 100 = 282,743.3388
- Surface area24,504.4227 cm²
- Capacity (litres)282.7433 L
In other units of volume
How it is calculated
Volume is the amount of three-dimensional space a solid takes up. Where the cross-section is the same at every height (cube, box, cylinder) it is base area × height. Pointed solids (cone, pyramid) hold a third of the prism with the same base and height. A sphere is 4 ÷ 3 × π × r³ and a hemisphere half that. A frustum (a bucket or flowerpot) is π × h × (R² + R × r + r²) ÷ 3, with R the bottom and r the top radius. This gives the geometric volume of a solid; for what a container holds, enter its inside measurements.
V = a × b × h · V = π × r² × h · V = 4 ÷ 3 × π × r³ · V = π × r² × h ÷ 3a, b: base sides · h: perpendicular height · r: radius · π ≈ 3.14159. In order: box, cylinder, sphere and cone. 1 dm³ = 1 litre, 1 m³ = 1,000 litres.- Pick the solid; the calculator asks only for the measurements it needs.
- Enter the measurements in one unit and choose it; the volume comes out in that unit cubed (cm³, m³).
- The capacity is converted to litres: 1,000 cm³ = 1 litre.
- The surface area adds up every outer face (for a cylinder, both ends and the side).
Example
A cylindrical tank 30 cm in radius and 100 cm tall: π × 30² × 100 ≈ 282,743 cm³, about 282.74 litres. A pool 8 m × 4 m × 1.5 m: 8 × 4 × 1.5 = 48 m³ = 48,000 litres. A sphere of radius 4 cm: 4 ÷ 3 × π × 4³ ≈ 268.08 cm³.
Frequently asked questions
How many litres are in 1 m³?
1,000 litres. A litre is a cubic decimetre (1 dm³ = 10 cm × 10 cm × 10 cm), so 1 cm³ = 1 millilitre and 1 m³ = 1,000 litres.
How do I find how many litres a tank holds?
Measure the inside diameter and height of a cylindrical tank, pick “Cylinder”, enter the radius (diameter ÷ 2) and the height; the capacity row gives litres. A tank 1 m across and 1.5 m tall holds π × 0.5² × 1.5 ≈ 1.178 m³, about 1,178 litres.
How does a cone’s volume compare with a cylinder’s?
A cone is exactly a third of the cylinder with the same base and height: π × r² × h ÷ 3. Likewise a pyramid is a third of the matching prism.
Is a cone’s height the same as its slant height?
No. The height is the perpendicular distance from the tip to the base; the slant height runs from the tip to the base’s edge and is √(r² + h²). Volume uses the height; the side surface uses the slant height.
How many litres is a gallon?
A US gallon is 231 cubic inches (NIST SP 1038); with 1 in = 2.54 cm that is exactly 3.785411784 litres. The imperial gallon is defined by law as exactly 4.54609 dm³, i.e. 4.54609 litres (UK Weights and Measures Act 1985, Schedule 1). The table shows both.