Find the volume of spheres, cones, cubes, cylinders, pyramids and more.
Volume measures the three-dimensional space enclosed by a solid. Sphere: (4/3)πr³. Cone: (1/3)πr²h. Cube: a³. Cylinder: πr²h. Rectangular prism: l × w × h. Square pyramid: (1/3)a²h where a is the base side. Capsule (cylinder capped by two hemispheres): πr²h + (4/3)πr³.
Sphere
V = (4/3)πr³
Cone
V = (1/3)πr²h
Cube
V = a³
Cylinder
V = πr²h
Rectangular prism
V = l × w × h
Square pyramid
V = (1/3)a²h
Capsule
V = πr²h + (4/3)πr³
V = (4/3)π × 3³ = (4/3) × π × 27 = 36π ≈ 113.097. This is a classic example because 36π has an exact closed form.
Cavalieri's principle and calculus show that stacking infinitely thin circular slices that taper linearly from base to apex gives exactly (1/3)πr²h. Three identical cones exactly fill one cylinder of the same dimensions.
Any consistent length unit works. If you enter centimetres, the volume is in cm³. To convert: 1 m³ = 1 000 000 cm³; 1 litre = 1000 cm³; 1 gallon ≈ 3785 cm³.