Cube Calculator

How to use the Cube Calculator

1. Leave Cube (shape) selected to work with a solid cube, or choose Cube of a number (x³) to raise a number to the third power.
2. In I know the, pick the measurement you have: edge length, volume, surface area, face diagonal or space diagonal.
3. Type it into Value and choose the Length unit (inches, feet, yards, centimeters, meters or millimeters). A volume is read in cubic units and a surface area in square units of that length unit, as shown next to the box.
4. Keep Also show the volume in US gallons and liters checked if you want a capacity estimate.
5. Press Calculate to get every other measurement, with the steps.

Cube formulas

A cube has 6 identical square faces, 12 equal edges and 8 corners. Everything about it follows from the edge length a:

Both diagonals come from the Pythagorean theorem. Across a face, d² = a² + a² = 2a². The space diagonal is the hypotenuse of a right triangle with legs d and a, so D² = 2a² + a² = 3a².

Example: a 3-foot cube (one cubic yard)

A storage bin, planter or water tank shaped like a cube has 3-foot edges.

Because 3 feet equals 1 yard, this cube is exactly one cubic yard: 1 yd³ = 27 ft³ = 46,656 in³. As a watertight tank with these inside dimensions it would hold about 202 US gallons.

Working backward: will it fit?

The space diagonal is the longest straight line that fits inside a cube. To check whether a 40-inch rod fits in a box with 24-inch inside edges, choose Edge length, enter 24 with the unit set to inches, and read the space diagonal: 24 × √3 ≈ 41.57 in. The rod fits, corner to corner. Going the other way, if a cube must hold 1,000 in³, choose Volume: the edge is ∛1,000 = 10 in.

Cube of a number (x³)

"Cubing" a number means multiplying it by itself three times: x³ = x × x × x. That is also the volume of a cube whose edge is x. A negative number cubed stays negative, because (−2) × (−2) × (−2) = −8, and a decimal works the same way: 1.5³ = 3.375.

The result also lists the square and the cube root, so you can go back and forth: ∛1,728 = 12.

How to read the result

• Lengths (edge, diagonals, total edge length) are in the unit you chose; areas are squared units; volume is cubic units.
• Scaling matters: doubling the edge multiplies the surface area by 4 and the volume by 8.
• Gallons are US liquid gallons (231 cubic inches each). A liter is 1,000 cm³.
• The inscribed sphere (radius a ÷ 2) is the largest ball that fits inside; the circumscribed sphere (radius a√3 ÷ 2) passes through all eight corners.

Assumptions and limitations

• The shape is a perfect cube: all edges equal and all angles 90°. For a box with different length, width and height, the cube formulas don't apply.
• Containers have wall thickness. Use inside dimensions for capacity and outside dimensions for space taken up or material needed.
• Gallon and liter figures describe geometric volume, not a safe fill level.
• Results are rounded for display, normally to four decimal places.

Common mistakes

• Converting cubic units with a linear factor. One foot is 12 inches, but one cubic foot is 12³ = 1,728 cubic inches, and one square foot is 144 square inches.
• Mixing units. Measure every edge in the same unit before entering it, or the volume will be off by a large factor.
• Confusing one face with the whole surface. A 3-foot cube has 9 ft² per face but 54 ft² in total.
• Using the face diagonal when you need the space diagonal. The diagonal across a face (4.24 ft for a 3-foot cube) is shorter than the diagonal through the center (5.20 ft).

Need the area of a curved slice instead? Try the Area of a Sector Calculator. Planning a masonry project? The Brick Calculator estimates how many bricks a wall needs.

Formulas and content last reviewed on October 13, 2026. Last updated October 13, 2026. Results are estimates for general information only. Spotted a problem? Tell us and we will check it.