Volume Calculator

Calculate the volume of various 3D geometric shapes.

cube

V = a³

Side (a)

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.

Frequently Asked Questions

What is the difference between volume and capacity?

Volume is the amount of 3D space an object occupies. Capacity is the amount of substance (usually a liquid or gas) that a container can hold. They are related concepts and often use the same units (like liters), but volume refers to the object itself, while capacity refers to its interior.

How are liquid volume (liters) and solid volume (cubic meters) related?

The metric system was designed to link them directly. One liter is defined as the volume of one cubic decimeter (a cube 10cm x 10cm x 10cm). This means 1 liter = 1000 cubic centimeters (cm³), and 1000 liters = 1 cubic meter (m³).

How do you calculate the volume of an irregular object?

A common method is water displacement. You fill a container (like a graduated cylinder) with a known volume of water, submerge the irregular object completely, and then measure the new volume. The difference between the new and old volume is the volume of the object.

Why is volume measured in 'cubic' units?

Volume is a three-dimensional measurement (length × width × height). When you multiply three units of length together (e.g., meter × meter × meter), the resulting unit is 'cubic meters' (m³), reflecting its three-dimensional nature.