Volume Calculator
Use our free online volume calculator to calculate the volume of any three-dimensional shape. Select your shape, enter the dimensions, and get the volume instantly using the correct volume formula.
How to Use This Volume Calculator
Using this calculate volume tool is simple:
- Select the shape you want to calculate.
- Enter the required dimensions for that shape.
- Select your preferred unit of measurement.
- Click Calculate to instantly see the volume result in cubic units.
What Is a Volume Calculator?
A volume calculator is an online tool that calculates the amount of three-dimensional space occupied by a shape. It applies the correct volume equation for each shape based on the dimensions you enter.
People use this tool to calculate volume for geometry problems, construction projects, tank capacity, packaging, and everyday measurements. Instead of applying formulas manually, you can calculate volume online in seconds by entering just the dimensions of the shape.
This calculator covers the most common shapes, including cylinders, cubes, rectangles, spheres, cones, and more.
What Is Volume?
Volume is the measure of the three-dimensional space that a substance or shape occupies. It is expressed in cubic units such as cubic centimeters (cm³), cubic meters (m³), cubic feet (ft³), or liters.
For regular shapes, volume is calculated using well-defined formulas based on the dimensions of the shape. For irregular shapes, volume can be estimated by dividing the shape into simpler parts and adding their volumes together.
Volume of a Cube
A cube has six equal square faces. All edges are the same length.
Volume Formula:
Where a is the length of one edge.
Example: A cube with an edge length of 5 cm.
- Step 1: Apply the formula: V = 5³
- Step 2: V = 5 × 5 × 5 = 125 cm³
Volume of a Rectangle (Rectangular Prism)
A rectangular prism, also called a rectangular box or cuboid, has six rectangular faces. It is defined by its length, width, and height.
Volume Formula:
Where l is the length, w is the width, and h is the height.
Example: A box measuring 8 cm long, 5 cm wide, and 4 cm tall.
- Step 1: Apply the formula: V = 8 × 5 × 4
- Step 2: V = 160 cm³
Volume of a Cylinder
A cylinder has two circular bases connected by a curved surface. It is one of the most commonly used shapes in volume calculations for tanks, pipes, and containers.
To find the volume of a cylinder, you first need the area of its circular base, then multiply it by the height.
Cylinder Volume Formula:
Where r is the radius of the circular base, and h is the height of the cylinder.
Since the base is a circle, the volume of a circle (circular cross-section) forms the foundation of this formula. The area of the circular base is π × r².
Example: For a cylinder with a radius of 4 cm and a height of 10 cm, the volume is calculated by first finding the area of the circular base: π × 4² = π × 16 = 50.27 cm². Multiplying this area by the height (50.27 × 10) results in a final volume of 502.65 cm³
Example using diameter: If you know the diameter instead of the radius, divide it by 2 first. A cylinder with a diameter of 8 cm has a radius of 4 cm.
Volume of a Sphere
A sphere is a perfectly round three-dimensional shape. Every point on its surface is the same distance from its center.
Volume Formula:
Where r is the radius of the sphere.
For a sphere with a radius of 6 cm, the volume is calculated by applying the formula V = (4/3) × π × 6³, which simplifies to V = (4/3) × π × 216, resulting in a final volume of 904.78 cm³.
Volume of a Cone
A cone has a circular base and tapers to a point called the apex. Its volume is one-third of the volume of a cylinder with the same base and height.
Volume Formula:
Where r is the radius of the base and h is the height.
For example, if you have a cone with a base radius of 3 cm and a height of 9 cm, applying the formula V = (1/3) × π × 3² × 9 results in V = (1/3) × π × 9 × 9, which simplifies to V = (1/3) × 254.47, yielding a final volume of 84.82 cm³.
Volume of a Square Prism (Square Box)
A square prism has a square base. When all three dimensions are equal, it becomes a cube. When the height differs from the square base, use the rectangular prism formula with equal length and width.
Volume Formula:
Where a is the side length of the square base, and h is the height.
For a square prism with a base side of 5 cm and a height of 8 cm, you apply the formula V = a² × h by calculating 5² × 8, which simplifies to 25 × 8, resulting in a volume of 200 cm³.
Volume of a Square Pyramid
A square pyramid has a square base and four triangular faces meeting at a single apex.
Volume Formula:
Where a is the side length of the square base, and h is the height.
For a square pyramid with a base side of 6 cm and a height of 9 cm, applying the formula V = (1/3) × a² × h gives V = (1/3) × 6² × 9, resulting in a final volume of 108 cm³.
Volume Formulas Reference Table
| Shape | Volume Formula |
|---|---|
| Cube | V = a³ |
| Rectangular Prism | V = l × w × h |
| Cylinder | V = π × r² × h |
| Sphere | V = (4/3) × π × r³ |
| Cone | V = (1/3) × π × r² × h |
| Square Prism | V = a² × h |
| Square Pyramid | V = (1/3) × a² × h |
| Ellipsoid | V = (4/3) × π × a × b × c |
| Capsule | V = π × r² × (h + (4/3) × r) |
FAQs
What is a volume calculator?
A volume calculator is an online tool that calculates the three-dimensional space occupied by a shape using the correct volume formula based on the dimensions you enter.
What is the volume formula for a cylinder?
The volume of a cylinder is V = π × r² × h, where r is the radius of the circular base, and h is the height of the cylinder.
How do I calculate the volume of a rectangle?
Multiply the length by the width by the height: V = l × w × h. For example, a box measuring 8 × 5 × 4 cm has a volume of 160 cm³.
How do I find the volume of a cube?
Raise the edge length to the power of three: V = a³. A cube with an edge of 5 cm has a volume of 125 cm³.
What is the volume of a circle?
A circle is a two-dimensional shape and does not have volume. However, the area of a circle (π × r²) is used to calculate the volume of three-dimensional shapes with circular bases, such as cylinders and cones.
How do I calculate cylinder volume?
Multiply π by the square of the radius and then by the height: V = π × r² × h. For a cylinder with radius 4 cm and height 10 cm, the volume is approximately 502.65 cm³.
What is the volume equation for a sphere?
The volume of a sphere is V = (4/3) × π × r³, where r is the radius.
What is the difference between volume and area?
Area measures the two-dimensional space of a flat surface, expressed in square units. Volume measures the three-dimensional space of a solid shape, expressed in cubic units.
Can I calculate volume in different units?
Yes. This volume calculator supports multiple units, including centimeters, meters, inches, and feet. The result is given in the corresponding cubic unit.
Is this volume calculator free?
Yes. Our online volume calculator is completely free with no sign-up required.