Free volume calculator
Calculate the volume of cubes, spheres, cylinders, cones, and rectangular prisms — enter any dimensions to see the result, updated live, as you type.
On this page10 sections
Standard volume formulas for common 3D shapes.
Results are estimates. Consult a professional.
How the volume calculator works
Volume measures the amount of three-dimensional space a solid occupies, expressed in cubic units (cm³, m³, ft³, litres, etc.). Each shape's formula is derived from its geometry — prisms multiply a base area by height, while spheres and cones use π and fractional coefficients.
Worked example: sphere r = 5 cm and cylinder r = 3 cm, h = 10 cm
Two of the most common 3D shapes solved step by step. The sphere formula contains (4/3)π and cubes the radius; the cylinder formula squares the radius and multiplies by height.
Volume formulas for common 3D shapes
The table summarises six standard solids with their volume formulas and the inputs required. Cones and pyramids hold exactly one-third the volume of the corresponding prism or cylinder with the same base and height.
| Shape | Formula | Required inputs |
|---|---|---|
| Rectangular prism | V = l × w × h | l, w, h |
| Cube | V = s³ | s = side length |
| Cylinder | V = π r² h | r = radius, h = height |
| Sphere | V = (4/3) π r³ | r = radius |
| Cone | V = (1/3) π r² h | r = radius, h = height |
| Pyramid (square base) | V = (1/3) × s² × h | s = base side, h = height |
Source: standard solid geometry formulas
Tips for calculating volume
Volume calculations appear in everyday tasks like filling a fish tank, estimating concrete for a pour, or determining how much liquid a container holds. These tips help avoid the most common errors.
- Cube the radius for spheres — the sphere formula is (4/3)πr³, not (4/3)πr². Squaring instead of cubing the radius gives a result 1/r times smaller than the correct answer.
- Convert units before calculating — mixing metres and centimetres in the same formula produces answers in non-standard units. Always use one unit throughout.
- 1 litre = 1,000 cm³ — to convert a volume in cm³ to litres, divide by 1,000. For fluid-capacity problems (aquariums, tanks), this conversion is essential.
- Hollow containers need subtraction — for a pipe or hollow cylinder, compute the outer volume and inner volume separately, then subtract to find the material or void volume.
- Irregular objects: water displacement — if a shape is too complex for a formula, submerge it in a container of water and measure the rise in water level multiplied by the container's cross-sectional area.
Accuracy and limitations
All calculations use IEEE 754 double-precision floating-point arithmetic with π accurate to 15+ significant digits. Results are reliable to roughly 15 significant digits, which exceeds the precision of any practical measurement. The formulas assume perfect geometric solids; real containers may have rounded corners, wall thickness, or irregular interiors not captured by these equations. For concrete, gravel, or soil estimates, add a 5–10 % overage for compaction and spillage.
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