Volume of Cube Calculator
Volume
—
Surface Area
—
Space Diagonal
—
How to Calculate the Volume of a Cube
A cube is a three-dimensional shape with six equal square faces. Its volume is V = s³ where s is the side length. The surface area — the total area of all six faces — is SA = 6s². The space diagonal, running from one corner to the opposite corner through the interior, is d = s√3.
Cube calculations are essential in shipping and packaging, construction, and science. For example, knowing the volume helps determine how much material fits inside a cubic container, and the surface area tells you how much wrapping material you need.
To find the side from the volume, take the cube root: s = ∛V. A cube with volume 27 has side length 3. This calculator accepts any unit and results are in corresponding cubic or square units.
Frequently Asked Questions
What is the volume formula for a cube?
Volume = s³, where s is the side length. A cube with side 4 has volume 64 cubic units.
How do you find the surface area of a cube?
Surface area = 6s². A cube has 6 faces, each with area s². A cube with side 3 has surface area 54 square units.
What is the space diagonal of a cube?
The space diagonal runs from one corner to the opposite corner through the interior: d = s√3. For side 5, the diagonal is about 8.66.
How is a cube different from a rectangular prism?
A cube is a special rectangular prism where all three dimensions (length, width, height) are equal. All six faces of a cube are identical squares.
How do I find the side length if I know the volume?
To find the side length from the volume, take the cube root: s = volume raised to the power of 1/3, or equivalently s = the cube root of V. For example, if the volume is 343 cubic units, the side length is the cube root of 343 = 7 units. On a calculator, use the cube root function or raise the volume to the power of (1/3). For volumes that are not perfect cubes, the result will be a decimal -- for instance, a volume of 100 cubic cm gives a side length of approximately 4.642 cm.
What is the ratio of a cube inscribed in a sphere?
When a cube is inscribed in a sphere (all 8 vertices touch the sphere), the sphere diameter equals the space diagonal of the cube: d = s times the square root of 3. The volume ratio is cube volume divided by sphere volume = approximately 0.3675. This means the cube fills about 36.75% of the enclosing sphere. Conversely, a sphere inscribed in a cube (touching all 6 faces) has diameter equal to the side length, filling approximately 52.36% of the cube volume.