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Volume Calculator

Volume formulas for common 3D shapes include s³ for cubes, l × w × h for rectangular prisms, (4/3)(pi)r³ for spheres, and (pi)r²h for cylinders. Select a shape and enter dimensions to calculate volume instantly.

Quick Answer

A sphere with radius 5 has a volume of approximately 523.60 cubic units. A cylinder with radius 3 and height 10 has a volume of approximately 282.74 cubic units.

Common Examples

Input Result
Cube: side 4 64 cubic units
Sphere: radius 5 523.60 cubic units
Cylinder: radius 3, height 10 282.74 cubic units
Cone: radius 4, height 9 150.80 cubic units

How It Works

Cube: V = s³

Multiply the side length by itself three times. For a cube with side length 5, the volume is 125 cubic units.

Rectangular Prism: V = l × w × h

Multiply the length by the width by the height. For a prism measuring 4 × 3 × 2, the volume is 24 cubic units.

Sphere: V = (4/3) × π × r³

Multiply four-thirds by π (approximately 3.14159) by the radius cubed. For a sphere with radius 5, the volume is approximately 523.60 cubic units.

Cylinder: V = π × r² × h

Multiply π by the radius squared by the height. This is the area of the circular base multiplied by the height.

Cone: V = (1/3) × π × r² × h

Multiply one-third by π by the radius squared by the height. A cone has exactly one-third the volume of a cylinder with the same base and height.

Worked Example

For a sphere with radius 5: Volume = (4/3) × pi × 5³ = (4/3) × pi × 125 = 500pi/3 ≈ 523.60 cubic units. For a cylinder with radius 3 and height 10: Volume = pi × 3² × 10 = 90pi ≈ 282.74 cubic units. A cone with the same dimensions has 1/3 the volume: (1/3) × 90pi ≈ 94.25 cubic units.

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Frequently Asked Questions

What units does the volume calculator use?
The calculator works with any consistent unit. If you enter dimensions in centimeters, the result is in cubic centimeters (cm3). If you enter dimensions in inches, the result is in cubic inches (in3). The output label shows 'cubic units' as a generic placeholder.
How do I convert between cubic units?
To convert cubic units, cube the linear conversion factor. For example, 1 foot = 12 inches, so 1 cubic foot = 12 x 12 x 12 = 1,728 cubic inches. Similarly, 1 meter = 100 centimeters, so 1 cubic meter = 1,000,000 cubic centimeters.
What is the difference between volume and surface area?
Volume measures the space enclosed inside a 3D shape, expressed in cubic units. Surface area measures the total area of all outer surfaces, expressed in square units. For example, a cube with side length 3 has a volume of 27 cubic units and a surface area of 54 square units.
Why is a cone exactly one-third the volume of a cylinder with the same dimensions?
This relationship can be proven using calculus (integration of cross-sectional areas) or demonstrated experimentally by filling a cone with water and pouring it into a cylinder of the same base and height. It takes exactly three full cones to fill the cylinder.

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