Volume Calculator

How to use?

Pick the solid from the list and type in the measurements in centimeters. The result appears in both cm³ and m³ right away, with the formulas used shown just above the value.

Volume formulas for the six solids

Volume measures the three-dimensional space a solid occupies, in cubic units. Key formulas: cube V = L³; rectangular box V = a·b·c; sphere V = (4/3)π·r³; cylinder V = π·r²·h; cone V = (1/3)π·r²·h; pyramid V = (1/3)·A_base·h. Note the 1/3 factor: a cone fits exactly three times into a cylinder with the same base and height — Archimedes proved this around 250 BC. Unit conversions you'll use constantly: 1 m³ = 1,000 L and 1 cm³ = 1 mL. Cavalieri's principle says two solids with the same cross-sectional area at every height have the same volume — that's how the pyramid and cone formulas extend to any base shape.

Applications

Volume is the workhorse measure for civil construction (m³ of concrete poured, water-tank capacity, swimming-pool fill), logistics and freight (cargo billed by cubic meter, container utilisation), medicine (drug dosing per kg of body mass and IV fluid volumes), cooking (mL ↔ cm³ for liquid measures), and chemistry, where Avogadro's law gives 22.4 L/mol for an ideal gas at standard conditions — a constant you'll meet in every stoichiometry problem.

FAQ

Why is there a 1/3 in the cone and pyramid formulas? Because a cone or pyramid fits exactly three times inside a cylinder or prism with the same base and height — an integration over slices gives ∫₀ʰ A(z) dz, and a linear taper to a point produces the factor 1/3.

How do I convert m³ to litres? Multiply by 1,000: a tank of 0.5 m³ holds 500 L. For small volumes, 1 cm³ = 1 mL.

Does the box formula require a right angle? Yes — V = a·b·c assumes a right rectangular box (all edges perpendicular). For an oblique prism, multiply the perpendicular height by the base area.

How does this relate to mass? Mass = volume × density. Water at 4 °C has density 1 g/cm³, so 1 L of water weighs 1 kg — a handy benchmark for estimating other materials.