Understanding Volume
Volume is the measure of three-dimensional space occupied by a substance or object. It quantifies how much space an object takes up and is expressed in cubic units (like cm³, m³, in³, ft³, etc.). The concept is fundamental in many fields, from physics and engineering to everyday tasks. For instance, knowing the volume of a box helps in shipping, and understanding the volume of a container is essential for cooking or chemistry. This volume calculator is a vital tool for a wide range of practical applications, simplifying what can be complex geometric calculations.
Volume vs. Surface Area
It's common to confuse volume with surface area, but they measure different things. Volume measures the space *inside* an object, while surface area measures the total area of the object's exterior surfaces. For example, the volume of a cardboard box tells you how much it can hold, while its surface area tells you how much cardboard is needed to make it. To explore two-dimensional measurements, you can use our Area Calculator.
Volume Formulas for Common Shapes
Each 3D shape has a unique formula to calculate its volume. This calculator uses the standard formulas for many common shapes. For more in-depth mathematical explanations, Khan Academy provides excellent free tutorials on solid geometry.
Cube
A cube has three equal sides (a). Its volume is the side length cubed. V = a³
Cuboid (Rectangular Prism)
The volume is found by multiplying its length (l), width (w), and height (h). V = l × w × h
Sphere
The volume depends on its radius (r), which is the distance from the center to any point on its surface. V = (4/3) × π × r³
Cylinder
Calculated using its radius (r) and height (h). V = π × r² × h
Cone
A cone's volume is one-third that of a cylinder with the same radius and height. V = (1/3) × π × r² × h
Capsule
A capsule is a cylinder with two hemispherical ends. Its volume is the sum of the cylinder's volume and the sphere's volume. V = (π × r² × h) + ((4/3) × π × r³)
Ellipsoid
An ellipsoid has three semi-axes (a, b, c). V = (4/3) × π × a × b × c
Square Pyramid
The volume is calculated from its base side length (a) and its height (h). V = (1/3) × a² × h