About the Cube Calculator
A cube has six identical square faces, so a single measurement fixes everything else about it. This cube calculator lets you start from whichever number you actually have — the edge length, the volume, the total surface area, the diagonal across one face, or the space diagonal running corner to corner through the middle — and solves for all the rest.
It is useful for geometry homework, checking how much a cubic box or planter holds, working out how much paint or wrapping a cube-shaped object needs, or finding the longest rod that fits inside a cubic crate (that is the space diagonal). It also reports the radii of the inscribed and circumscribed spheres.
Results are in the same unit you enter: if the edge is in centimeters, areas come out in cm² and volumes in cm³. 1,000 cm³ is one liter, and one cubic foot is about 7.48 US gallons.
With the default inputs, the volume (a³) is 125. Change any value above to recalculate instantly.
How to use the cube calculator
- 1Choose which measurement you already know.
- 2Enter its value — a length, an area or a volume in consistent units.
- 3Read the volume and every other measurement of the cube.
- 4Use the space diagonal to check whether a long item fits inside a cubic box.
Formula and method
Every cube measurement is a fixed multiple of the edge length a. The volume is a × a × a, the surface area is six square faces of a² each, the face diagonal comes from the Pythagorean theorem on one square (√(a² + a²) = a√2), and the space diagonal applies it again across the cube (√(a² + 2a²) = a√3).
To start from another measurement the calculator inverts the matching formula first: a = ∛V, a = √(SA ÷ 6), a = f ÷ √2 or a = d ÷ √3. Then it recomputes everything else from a.
- a
- Edge (side) length
- V
- Volume
- SA
- Total surface area
- f
- Face diagonal
- d
- Space (body) diagonal
Worked examples
Cube with 5 cm edges
A 5 cm cube holds 5³ = 125 cm³ and has six 25 cm² faces for 150 cm² of surface. The face diagonal is 5√2 ≈ 7.07 cm and the corner-to-corner diagonal is 5√3 ≈ 8.66 cm.
One-liter cube (volume 1,000 cm³)
A cube holding exactly one liter (1,000 cm³) has edges of ∛1000 = 10 cm, a surface area of 600 cm² and a space diagonal of about 17.32 cm.
Crate whose space diagonal is 12 ft
If a 12 ft pole just fits corner to corner, each edge is 12 ÷ √3 ≈ 6.93 ft. That gives a volume of about 332.55 ft³ and a surface area of 288 ft²; the circumscribed sphere has radius 6 ft, half the diagonal.
Frequently asked questions
How do you find the volume of a cube?+
Multiply the edge length by itself three times: V = a³. A cube with 4-inch edges has a volume of 4 × 4 × 4 = 64 cubic inches.
How do you find the side of a cube from its volume?+
Take the cube root of the volume: a = ∛V. For example, a cube of 343 cm³ has edges of ∛343 = 7 cm.
What is the surface area formula for a cube?+
SA = 6a², because a cube has six square faces each with area a². A 3 m cube has 6 × 9 = 54 m² of surface area.
How long is the diagonal of a cube?+
The space diagonal from one corner to the opposite corner is a√3 ≈ 1.732 × a. The diagonal across a single face is a√2 ≈ 1.414 × a.
Is a cube a rectangular prism?+
Yes. A cube is a special rectangular prism whose length, width and height are all equal, so every face is a square. Use the rectangular prism calculator when the sides differ.