Volume Calculator (Multi-Solid)
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.
1. Choose a Shape
2. Enter Dimensions
V = π × r² × h
V = π × 3² × 10 = π × 9 × 10 = 282.743 m³
Calculation Detail
Unit Conversions
Volume Formulae for Common Solids
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 |
How to Use This Calculator
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.
Practical Uses
- Concrete and fill: Calculate how many cubic metres of concrete, soil, or gravel you need to fill a cylindrical post hole, rectangular trench, or conical pile.
- Water storage: Estimate the capacity of a cylindrical tank or rectangular reservoir in litres.
- Packaging: Work out how much space a product occupies for shipping calculations.
- Science and engineering: Volume is used in density, pressure, flow rate, and thermodynamics calculations.
- Maths study: Check your homework answers for geometry problems involving 3D shapes.
Understanding Volume Units
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.
Related Calculators
- Maths and Stats Calculators: full hub for geometry and statistics tools.
- Surface Area Calculator (multi-solid): find the surface area of the same set of solids.
- Cube Surface Area and Volume Calculator: dedicated tool for cubes with additional detail.
- Pyramid Volume and Surface Area Calculator: dedicated pyramid tool with slant height.
- Rectangular Box (Cuboid) Calculator: volume, surface area, and diagonal for boxes.
- Area Calculator (multi-shape): calculate the area of 2D shapes.
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.