Volume formulas by shape
The rectangular prism — any box-shaped object with six rectangular faces — is the simplest. Its volume is the product of its three dimensions. A cube is a special case where all three dimensions are equal, so volume is the side length cubed.
Curved shapes require the mathematical constant π. A sphere's volume depends only on its radius. A cylinder adds height to the circular base. A cone is related to the cylinder but has a triangular cross-section when viewed from the side, giving it one-third the volume of a cylinder with the same base and height.
Surface area is a related but distinct calculation: it measures the total area of all faces or surfaces of the shape. Surface area matters for packaging design, heat transfer calculations, and any application where coating or covering the exterior is the objective rather than filling the interior.
Rectangular prism: V = L x W x H
Multiply length, width, and height to get the volume of any box-shaped solid.
Cube: V = s³
For a cube, volume is the side length raised to the power of three.
Sphere: V = (4/3) x π x r³
Volume of a sphere depends only on its radius, multiplied by 4π/3.
Cylinder: V = π x r² x h
Multiply π by the square of the base radius and by the height to get the cylinder volume.
Cone: V = (1/3) x π x r² x h
A cone has one-third the volume of a cylinder with the same base and height.