What is the formula for the volume of a cube?

The volume of a cube is side length cubed: V = s^3. If the side is 5, the volume is 5 x 5 x 5 = 125 cubic units.

How do you find the surface area of a cube?

A cube has six identical square faces. The total surface area is 6 times the area of one face: SA = 6 x s^2. For a cube with side 5, SA = 6 x 25 = 150 square units.

What is the space diagonal of a cube?

The space diagonal runs from one corner of the cube to the opposite corner, passing through the interior. Its length is s times the square root of 3. For a cube with side 5, the space diagonal is 5 x 1.732 = 8.66 units.

Cube Calculator

A cube is the simplest of the three-dimensional solids: every edge has the same length, every face is a square, and every angle is a right angle. Because of that uniformity, all four key measurements follow directly from just one input, the side length. This calculator takes the side length and returns the volume, the total surface area, the face diagonal (the diagonal across one square face), and the space diagonal (the longest straight line from one corner of the cube to the opposite corner, passing through the interior). Volume tells you how much the cube can hold and is used in packaging, shipping, and storage calculations. Surface area is needed whenever you are covering or coating the outside, whether painting a box, wrapping a gift, or calculating material cost. The face diagonal matters in woodworking and engineering when you need to know the clearance across a flat surface. The space diagonal is useful when you need to fit the longest object inside a cube-shaped container. You can enter any positive number and the units are consistent throughout, so if the side is in metres the volume will be in cubic metres and the diagonals in metres. The calculator updates the moment you change the input. Results are exact to two decimal places. Use them as a reference for study, checking your own geometry working, or practical projects.

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Side length (s)

units

125

volume (cubic units)

Surface area150

Face diagonal7.07

Space diagonal8.66

How it works

All formulas use the single side length s. Volume is s cubed (s × s × s). Surface area is 6 times s squared because there are six identical square faces. The face diagonal, the line from one corner of a square face to the opposite corner of the same face, is s times the square root of 2. The space diagonal, from one corner of the cube to the farthest opposite corner through the interior, is s times the square root of 3. These are the four essential measurements for any cube-shaped object.

Worked example

With a side length of 5 units: volume = 5 × 5 × 5 = 125 cubic units. Surface area = 6 × 5² = 6 × 25 = 150 square units. Face diagonal = 5 × √2 = 7.07 units. Space diagonal = 5 × √3 = 8.66 units. These match the pre-filled defaults above.

Related calculators

Cuboid Calculator: volume, surface area and space diagonal for a box with different length, width and height.
Surface Area Calculator: choose from multiple solids including cube, cylinder, cone and sphere.
Pyramid Calculator: volume and surface area of a square-base pyramid.
Sphere Calculator: surface area and volume of a sphere.

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