Volume Calculator: Find The Volume of Geometrical Shapes

Volume Calculator

Use this volume calculator to calculate the volume for the three-dimensional geometrical shapes. It provides calculations for a volume in different units and also shows the formula to find the volume for a selected shape.

Volume Definition:

“The amount of Space Enclosed by a 3D Object”

Volume is also known as the boundary of an object. The SI unit for volume is cubic meters

How To Calculate The Volume of A Body?

As we know, all the bodies or objects don’t have the same shape. They have different shapes and dimensions. So there are different formulas for calculating the volume of each shape. To find the volume of any object or shape, use the corresponding volume equation.

Volume Formulas:

The formulas that are used to calculate the volume of different objects or geometric solids are as follows:

Volume of A Cube:

All the edges of a cube are of equal length. That’s why the formula that is used for calculating the cube volume is:

Volume = (side length)³

Volume of A Rectangle:

A rectangular shape has equal edges and the rectangular volume is calculated as:

Volume = length × width × height

It is also known as the volume of a box and is calculated in the same way as we calculate the rectangle volume.

Volume of Square:

A square is a two dimensions shape, it does not have any volume so its area can be calculated as:

Area = Side length x Side length

The Volume of Sphere:

A sphere does not have any face, edges, or vertices, it's a circle whose volume is calculated by using the following formula:

Volume = 4 3 × π × radius³

Volume of A Cylinder:

The space enclosed by the cylindrical shape is known as the cylinder volume. Use the following formula to calculate it:

Volume Formula = π × (radius)² × height

The Volume of Cone:

Use the below-mentioned formula to calculate the cone volume:

Volume = 1 3 × π × (radius)² × height

The Volume of Tube:

A tube volume is the same as the volume of a hollow cylinder. Therefore, the formula for tube volume is as follows:

Volume = πh(R² - r²) 4

Volume of A Circle:

A circle is not a three-dimensional shape which is why there is no formula to calculate the volume of circle, it has an area and its formula is:

Area = πr²

The Volume of Hemisphere:

The hemisphere volume is half of the sphere volume and the formula that is used for it is as follows:

Volume = 2 3 × π × (r)³

Volume of Column:

If you have a cylindrical column and you need to calculate its volume then you can use the following formula:

Volume = πr²h

The Volume of A Pyramid:

A pyramid has a polygonal base and triangle sides and they converge at a single point. This point is known as the apex or vertex. Let's take a look at the following formula for calculating volume of a Pyramid:

Volume = 1 3 × base area × height

Truncated Pyramid:

When you cut the top of a cone or a pyramid form parallel to the base, the shape that you get is called the Truncated Pyramid.

V= h 3 (A₁ + A₂ + (A₁ × A₂)

Conical Frustum:

When you cut the cone shape parallel to the base in a way, that the resultant shape has two circular bases and a curved surface connecting them, then it is known as Conical Frustum. See the following formula to calculate its volume:

V= 1 3 πh(R² + r² + Rr)

Ellipsoid:

This shape resembles an elongated or flattened sphere. You can calculate the volume of an ellipsoid with the help of the following formula:

V = 4 3 πabc

Triangular Prism:

It consists of two triangular bases and three rectangular lateral faces. The formula is a as follows:

V= 1 4 h(a+b+c)(b+c-a)(c+a-b)(a+b-c)

Solved Examples:

Example #1:

Let's suppose the side length of a cube is 6 cm, how do you find volume?

Solution:

Side Length = 6 cm

By putting values in the cube volume formula:

Volume = (6)³ = 6 x 6 x 6 = 216 cm³

Example #2:

Suppose you need to get the volume of a cone with a height of 6 cm and a radius of 4 cm.

Solution:

Height = 6 cm

Radius = 4 cm

Put these values in the cone volume formula:

Volume = 1 3 × π × radius² × height

Volume = 1 3 × 3.14 × (4)² × 6

Volume = 1 3 × 3.14 × 16 × 6 = 100.48 cm³

To make complex calculations easier, you can use our online volume calculator for free.

Common Volume Units:

Unit	Cubic Meters	Milliliters
milliliter (cubic centimeter)	0.000001	1
cubic inch	0.00001639	16.39
pint	0.000473	473
quart	0.000946	946
liter	0.001	1,000
gallon	0.003785	3,785
cubic foot	0.028317	28,317
cubic yard	0.764555	764,555
cubic meter	1	1,000,000
cubic kilometer	1,000,000,000	1015

Applications of Volume Calculator:

The calculator is widely used in various fields, including:

DIY And Home Improvement: It helps to calculate the amount of material (paint, concrete, etc) required for renovations
Construction and Engineering work: The calculator helps in estimating the volume of concrete, and measuring the capacity of various tanks, or storage containers
Science and Research: It helps the scientist in finding the volume of cells or organs, and determine the density of compounds

FAQ's:

What Is The Difference Between Surface Area And Volume?

Surface Area: It is a two-dimensional (2D) measure. Surface area refers to the total area of all the external faces of the object
Volume: This is a three-dimensional (3D) measure, which represents the amount of space enclosed within the boundaries of an object

How Much Liquid Can A Container Hold?

Determine the container’s shape
Measures the dimensions of the container
Use the appropriate formula to calculate the volume of the shape
If you don't know the dimensions of the container, then use the water displacement method to find the volume

What Are The Methods Used To Measure Volume?

The three common methods are as follows:

Geometric Formulas: It is used for regular shapes like spheres, cubes, cylinders, cones, or prisms
Water Displacement: This method involves dipping the object in a water container and measuring the water level increase. The rise in the water is equal to the object's volume
Mass and Density: This method is useful when the object's density (mass per unit volume) is already known. The volume is calculated by dividing the mass of the object by its density

References:

From the source of Wikipedia.org: Volume.