This calculator works out the volume of seven common three-dimensional solids: sphere, cylinder, cone, cube, rectangular box (cuboid), triangular prism, and rectangular pyramid. Volume tells you how much space a shape encloses, and getting it right matters whether you are ordering concrete for a post hole, sizing a water tank, working out shipping space, or checking a geometry homework answer. Start by choosing your shape from the dropdown and selecting a unit of measurement (centimetres, metres, millimetres, inches, or feet), then enter the dimensions the shape needs, such as radius and height for a cylinder, or length, width, and height for a box. The result updates instantly and shows the volume in your chosen cubic unit, the exact formula used, the shape selected, and the value in scientific notation for large or small results. A calculation detail panel confirms the inputs used, and a unit conversion table automatically shows the same volume in cubic metres, cubic centimetres, litres, cubic feet, and cubic inches, so you do not need to convert by hand. Make sure every dimension you enter is in the same unit before calculating; mixing centimetres and metres will give a wrong answer. The maths is exact for the numbers you provide, but if you are ordering materials like concrete, soil, or gravel, add a margin for wastage and compaction on top of the calculated figure.
V = π × r² × h
Volume measures the amount of three-dimensional space enclosed by a shape. It is expressed in cubic units (cm3, m3, litres, etc.). The table below lists the standard formula for each solid supported by this calculator.
| Solid | Formula | Variables |
|---|---|---|
| Sphere | V = (4/3) x pi x r3 | r = radius |
| Cylinder | V = pi x r2 x h | r = base radius, h = height |
| Cone | V = (1/3) x pi x r2 x h | r = base radius, h = height |
| Cube | V = a3 | a = side length |
| Rectangular box (cuboid) | V = l x w x h | l = length, w = width, h = height |
| Triangular prism | V = (1/2) x b x h_t x l | b = triangle base, h_t = triangle height, l = prism length |
| Rectangular pyramid | V = (1/3) x l x w x h | l = base length, w = base width, h = height |
Select the 3D solid from the Shape dropdown, choose the unit of measurement for your dimensions, then enter the required values. The volume updates instantly and the formula used is shown below the inputs. The unit conversion panel at the bottom converts your result into cubic metres, cubic centimetres, litres, cubic feet, and cubic inches automatically.
All dimensions must be in the same unit. If your radius is in centimetres and your height is in metres, convert one before entering values.
1 cubic metre (m3) = 1,000 litres = 1,000,000 cm3. For everyday use, litres are convenient for liquids and small volumes; cubic metres for building materials. The conversion panel below your result shows all common units automatically.
Sources and method: Standard Euclidean geometry formulae as taught in NCEA Level 1 to 3 Mathematics and widely referenced in engineering handbooks (e.g. Machinery's Handbook). Pi is taken as 3.141592653589793 (double-precision floating point).
Results are mathematically exact for the inputs provided, subject to floating-point precision. Ensure all dimensions are in the same unit before calculating.