Volume is how much space a solid occupies, always in cubic units. Each common solid has its own formula: a box is length × width × height, a cube is side³, a sphere is 4⁄3 π r³, a cylinder is π r² h (base area × height), and a cone is exactly one third of that, ⅓ π r² h. The companion figure is surface area, the total outer area in square units. Keep every dimension in one unit, and remember the radius is half the diameter.
Reviewed: June 20, 2026 · Author: Naveen P N, Founder — AI Calculator · Verified against: standard solid-geometry volume formulas.
The volume formulas
A box stacks unit cubes, so its volume is simply the product of the three sides. A cylinder is a circular base (π r²) extruded to a height, hence π r² h. A cone tapering to a point from the same base holds exactly a third as much — a result that goes back to Archimedes. The sphere's 4⁄3 π r³ likewise relates a ball to its bounding cylinder. Surface area sums the outer faces, useful for material, paint or heat-loss estimates.
Worked example — a box
Scenario: a box 4 long, 3 wide and 2 high.
The box holds 24 cubic units, with a surface area of 52 square units; if those dimensions were centimetres, that is 24 millilitres or 0.024 litres. Switch solids and the same machinery applies: a cube of side 3 has a volume of 27; a sphere of radius 3 about 113.10; a cylinder of radius 2 and height 5 about 62.83; and a cone with that base and height a third of the cylinder, about 20.94. Volume always comes out in the cube of your chosen unit.
Frequently Asked Questions
length × width × height. 4 × 3 × 2 = 24 cubic units; surface area 52.
4⁄3 π r³. r = 3 → ≈ 113.10. Surface area 4π r² ≈ 113.10.
π r² h. r 2, h 5 → ≈ 62.83. A cone with the same base/height is a third: ≈ 20.94.
cm³ ÷ 1000 = litres. 24 cm³ = 0.024 L. 1 m³ = 1000 L.
Cubic units matching inputs (m → m³). Keep all dimensions in one unit.