Volume Calculator
Calculate and convert volumes for seven common prisms, round solids, cubes, and pyramids.
Content updated August 4, 2026
Every entered length must use the selected input unit. The triangular-prism inputs determine its triangular cross-section area and volume, but not its full surface area because the two sloping side lengths are not known. One cubic metre equals 1,000 litres.
Calculate the volume of a rectangular prism, cube, cylinder, sphere, cone, triangular prism, or square pyramid. The selected model requests only the dimensions its formula needs and reports base area and total surface area when those measurements determine them.
All entered lengths share one unit. You can express the result in a different cubic metric or imperial unit, see the equivalent cubic metres and litres, and compare the volume with a cube having the same capacity.
The Volume formula
Prism: V = base area × length · Cylinder: V = πr²h · Sphere: V = 4πr³/3 · Cone: V = πr²h/3 · Square pyramid: V = s²h/3Rectangular-prism base area = lw · triangular-prism base area = bh/2 · r = radius · h = perpendicular height · cubic conversion uses the length factor cubed.
Worked example
A rectangular prism 4 m long, 3 m wide, and 2 m high has volume 4 × 3 × 2 = 24 m³, base area 12 m², and surface area 2(12+8+6) = 52 m². Its volume is 24,000 litres.
Assumptions, rounding, and limitations
Assumptions
- The selected solid is an ideal Euclidean shape and every entered length uses the selected input unit.
- Heights for cylinders, cones, prisms, and pyramids are perpendicular to their bases.
- Circle and sphere inputs are radii; the square-pyramid base has four equal sides.
- Input measurements are treated as exact at the precision entered.
Rounding: The engine retains floating-point precision through shape calculations and cubed unit conversion. Volume, area, litre, and equivalent-edge displays show up to eight decimal places.
Limitations
- Each dimension must be greater than zero and no more than 1 billion; supported length units are mm, cm, m, in, ft, and yd.
- Does not model wall thickness, hollow or truncated solids, irregular shapes, displaced volume, material density, fill level, waste, tolerances, or measurement uncertainty.
- Triangular-prism surface area is unavailable from the selected inputs because the other two triangle sides are not uniquely determined.
Sources
- SI Units — Volume — National Institute of Standards and Technology
- NIST Guide to the SI, Appendix B.9: Conversion Factors — National Institute of Standards and Technology
Base area times perpendicular height
Prisms and cylinders keep a constant cross-section, so their volume is base area multiplied by perpendicular length or height. Cones and pyramids taper to a point, giving one third of that corresponding prism or cylinder volume.
A sphere does not have a flat base; its volume is 4πr³/3. The displayed surface-area formulas use the same entered dimensions, except a triangular prism's base and perpendicular triangle height do not reveal the two sloping triangle sides, so its full surface area is not determined.
Cubic units and litres
Volume has three length dimensions. A length conversion factor k therefore becomes k³ for volume: one metre equals 100 centimetres, so one cubic metre equals 100³ = 1,000,000 cubic centimetres.
NIST identifies the cubic metre as the SI derived unit of volume and notes that one cubic metre equals 1,000 litres. The litre display is derived from the result in cubic metres, not from a U.S. liquid-volume conversion.
Frequently asked questions
▶How do I calculate rectangular-prism volume?
Multiply length × width × height, with all three measurements in the same length unit.
▶Why is cone volume divided by three?
A cone with the same circular base and perpendicular height as a cylinder has one third of that cylinder's volume.
▶How many litres are in one cubic metre?
One cubic metre equals exactly 1,000 litres because one litre is one cubic decimetre.
▶Why is cubic-unit conversion raised to the third power?
Length, width, and height each change by the conversion factor, so their product changes by that factor cubed.
▶Why is triangular-prism surface area unavailable?
Its entered triangle base and perpendicular height determine cross-section area but not the two remaining triangle sides needed for the full boundary and surface.
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Open calculator →Disclaimer: Volume Calculator results are estimates for general information and education only, and are not financial, tax, legal or medical advice. Verify important decisions with a qualified professional.