A Guide to Calculating Volume

Volume is the measure of the three-dimensional space occupied by a substance or enclosed by a surface. It's a fundamental concept in geometry and has countless practical applications, from calculating the amount of water in a swimming pool to determining the capacity of a shipping container. This calculator provides an easy way to compute the volume of the most common 3D shapes.

1. Cube

A cube is a three-dimensional solid object bounded by six square faces, with three meeting at each vertex. It is the 3D equivalent of a square.

Formula: V = a³, where a is the side length.

2. Cuboid (Rectangular Prism)

A cuboid is a solid shape with six rectangular faces. It's a generalization of a cube, where the sides can have different lengths.

Formula: V = l × w × h, where l is length, w is width, and h is height.

3. Sphere

A sphere is a perfectly round geometrical object in three-dimensional space.

Formula: V = (4/3)πr³, where r is the radius.

4. Cylinder

A cylinder consists of two parallel circular bases joined by a curved surface.

Formula: V = πr²h, where r is the radius of the base and h is the height.

5. Cone

A cone is a three-dimensional shape that tapers smoothly from a flat circular base to a point called the apex.

Formula: V = (1/3)πr²h, where r is the radius of the base and h is the height.

6. Pyramid (Rectangular Base)

A pyramid is a polyhedron formed by connecting a polygonal base and an apex.

Formula: V = (1/3) × Base Area × Height. For a rectangular base, this is V = (1/3)lwh.

7. Right Triangular Prism

A prism is a polyhedron comprising an n-sided polygonal base, a second base which is a translated copy of the first, and n other faces joining corresponding sides of the two bases. For a right triangular prism, the base is a triangle.

Formula: V = (½ × base × height of triangle) × Length of prism

8. Conical Frustum

A conical frustum is the portion of a solid cone that lies between two parallel planes cutting it. It's like a cone with the tip sliced off.

Formula: V = (1/3)πh(r₁² + r₁r₂ + r₂²), where h is the height, r₁ is the radius of the top base, and r₂ is the radius of the bottom base.

9. Pyramidal Frustum

A pyramidal frustum is a frustum made by chopping the top off a pyramid. For a square base:

Formula: V = (1/3)h(A₁ + A₂ + √(A₁A₂)), where h is height, and A₁ and A₂ are the areas of the two square bases.