How is a cone’s volume related to a cylinder’s?

A cone with the same base radius and height as a cylinder holds exactly one third of the cylinder’s volume, which is why the cone formula is (1/3)πr²h. The same one-third relationship links a pyramid to its enclosing prism.

What units does the volume use?

Volume is reported in cubic units of whatever you input — cubic centimetres if your lengths were in centimetres, cubic inches if in inches. To convert cubic units into litres or gallons you would apply the appropriate capacity conversion afterward.

What is the difference between a cube and a rectangular prism?

A cube is a special rectangular prism whose length, width, and height are all equal, so its volume simplifies to s³. The rectangular prism option lets you enter three different edge lengths for a general box shape.

How does volume relate to surface area?

Volume measures the space inside a solid in cubic units, while surface area measures the outer skin in square units. For the same shapes you can compute the outer area with the surface area calculator.

Volume Calculator

Shape

Side Length

Volume125.0000

Volume is the amount of three-dimensional space a solid occupies, measured in cubic units. This calculator finds the volume of a cube, sphere, cylinder, cone, or rectangular prism from its dimensions, applying the standard geometric formula for each shape so you can size tanks, boxes, and containers quickly.

Formula

Cube s³ · Sphere (4/3)πr³ · Cylinder πr²h · Cone (1/3)πr²h · Box l·w·h

s: Side length of the cube
r: Radius of the sphere, cylinder, or cone
h: Height of the cylinder or cone
l, w, h: Length, width, and height of the rectangular prism

How it works

Pick a shape and supply its dimensions: cube (side), sphere (radius), cylinder (radius and height), cone (radius and height), or rectangular prism (length, width, height).
The calculator plugs those numbers into the matching formula — for instance s³ for a cube, (4/3)πr³ for a sphere, and πr²h for a cylinder.
The result is the volume in cubic units of whatever measurement you entered. Any non-positive dimension is invalid and returns no result.

Worked examples

Find the volume of a cone with radius 3 and height 9.

Volume = (1/3)πr²h = (1/3)π × 3² × 9.
= (1/3)π × 9 × 9 = 27π.
27π ≈ 84.823.

Volume ≈ 84.82 cubic units

Find the volume of a sphere with radius 5.

Volume = (4/3)πr³ = (4/3)π × 5³.
= (4/3)π × 125 = (500/3)π.
≈ 523.599.

Volume ≈ 523.60 cubic units

Frequently asked questions

How is a cone’s volume related to a cylinder’s?: A cone with the same base radius and height as a cylinder holds exactly one third of the cylinder’s volume, which is why the cone formula is (1/3)πr²h. The same one-third relationship links a pyramid to its enclosing prism.
What units does the volume use?: Volume is reported in cubic units of whatever you input — cubic centimetres if your lengths were in centimetres, cubic inches if in inches. To convert cubic units into litres or gallons you would apply the appropriate capacity conversion afterward.
What is the difference between a cube and a rectangular prism?: A cube is a special rectangular prism whose length, width, and height are all equal, so its volume simplifies to s³. The rectangular prism option lets you enter three different edge lengths for a general box shape.
How does volume relate to surface area?: Volume measures the space inside a solid in cubic units, while surface area measures the outer skin in square units. For the same shapes you can compute the outer area with the surface area calculator.

Related calculators

Surface Area Calculator Circle Calculator Pyramid Calculator Hemisphere Calculator