A cube is a box whose length, width and height are all equal, so six identical square faces meet at right angles. Dice, sugar cubes, storage cubes and the cubic units we measure volume in are all cubes. Because one number, the edge length, settles everything, this cube calculator can start from the edge, either diagonal, the surface area or the volume and work out the rest, including capacity in liters and US gallons.
How to use the cube calculator
- Under I know the, choose Edge, Face diagonal, Space diagonal, Surface area or Volume.
- Enter the number in Value. Surface area is in square units and volume in cubic units.
- Pick the Units for lengths; areas and volumes follow automatically.
- The headline shows the volume, or the edge length if you started from a volume. The list adds surface area, the area of one face, both diagonals, the radii of the inscribed and circumscribed spheres, and the capacity in liters and US gallons.
Cube formulas
| Measure | From the edge a | Back to the edge |
|---|---|---|
| Volume | V = a3 | a = ∛V |
| Surface area | S = 6a2 | a = √(S ÷ 6) |
| Face diagonal | f = a√2 | a = f ÷ √2 |
| Space diagonal | d = a√3 | a = d ÷ √3 |
| Inscribed sphere radius | a ÷ 2 | — |
| Circumscribed sphere radius | a√3 ÷ 2 | — |
Worked example: a 100-gallon cube tank
You want to build a cube-shaped water tank that holds 100 US gallons. How long should each edge be, and how much sheet material does it need?
- A US gallon is exactly 231 in³, so 100 gallons is 23,100 in³.
- Choose Volume, enter 23100 and set the units to inches.
- Edge: ∛23,100 ≈ 28.48 in. The capacity rows confirm 100 gal, or about 378.54 L.
- Each face is about 811.10 in². An open-top tank needs five faces, about 4,055.5 in² (28.16 ft²); a closed tank needs all six, 4,866.6 in² (33.80 ft²).
- The space diagonal is 49.33 in, the longest rod that would fit inside.
These are inside dimensions. Add the wall thickness to get the outside size.
Diagonals come from Pythagoras
The face diagonal crosses one square face. It is the hypotenuse of a right triangle with two edges as legs, so f² = a² + a², which gives f = a√2. The space diagonal runs through the solid from one corner to the opposite one. It forms a second right triangle with a face diagonal and an upright edge: d² = 2a² + a² = 3a², so d = a√3.
That makes the space diagonal useful for a practical question: will it fit? A cube box with 2 ft edges takes a rod or pole up to about 3.46 ft long, laid corner to corner. Working the other way, if a 6 ft pole must fit diagonally, choose Space diagonal and enter 6: the box needs edges of at least 3.46 ft. The same idea for any box is the 3D distance calculator.
Cube roots and doubling the cube
Going from a volume back to the edge needs a cube root, which is why perfect cubes such as 8, 27, 64, 125 and 1,000 are worth recognizing: their edges are 2, 3, 4, 5 and 10. For anything else, the calculator or a cube root calculator does the work.
Cube roots also explain why doubling a cube’s volume grows it less than you might expect. The edge only grows by ∛2 ≈ 1.2599, so a 4 ft cube (64 ft³) becomes a 5.04 ft cube (128 ft³). Doubling the edge instead multiplies the volume by eight. The ancient Greeks knew this as the Delian problem, after a legend in which an oracle demanded that an altar on Delos be doubled. Geometers tried for centuries to construct an edge ∛2 times as long using only a straightedge and compass; Pierre Wantzel proved in 1837 that it cannot be done.
Common cubes and their capacity
| Edge | Volume | Liters | US gallons |
|---|---|---|---|
| 1 in | 1 in³ | 0.0164 | 0.0043 |
| 10 cm | 1,000 cm³ | 1 | 0.2642 |
| 1 ft | 1,728 in³ | 28.3168 | 7.4805 |
| 1 yd | 27 ft³ | 764.5549 | 201.974 |
| 1 m | 1 m³ | 1,000 | 264.1721 |
The cubic yard is the unit for concrete, mulch and gravel orders; the cubic feet to cubic yards converter handles the factor of 27. For boxes whose sides differ, use the rectangular prism calculator.
Frequently asked questions
What is the formula for the volume of a cube?
V = a³, the edge length multiplied by itself three times. A cube with 4 ft edges has a volume of 4 × 4 × 4 = 64 ft³, which is about 478.75 US gallons.
How do I find the edge of a cube from its volume?
Take the cube root: a = ∛V. Choose Volume under 'I know the' and the calculator does it for you. A 1,000 cm³ cube (one liter) has 10 cm edges.
What is the space diagonal of a cube?
It is the straight line from one corner through the middle of the cube to the opposite corner, a√3 long. It is the longest straight object that fits inside a cube-shaped box: about 3.46 ft for a box with 2 ft edges.
How much bigger is a cube with twice the volume?
Only about 26% bigger along each edge, because the edge must grow by ∛2 ≈ 1.2599. A 64 ft³ cube has 4 ft edges, while a 128 ft³ cube has edges of about 5.04 ft.
Why does the volume field want cubic units instead of gallons?
The calculator measures everything in the length unit you choose, so volume has to be in that unit cubed. Convert first: 1 US gallon is exactly 231 in³ and 1 liter is 1,000 cm³. The capacity rows then convert back to liters and gallons for you.