Cube Calculator
Two modes in one tool. Use "Cube a number" to find n³ = n × n × n instantly, or switch to "Cube geometry" to enter any one property of a cube (edge length, volume, surface area, or a diagonal) and calculate all the others, with metric or imperial units.
Formula
Worked example
For n = 3 (number mode): 3³ = 3 × 3 × 3 = 27. For a cube with edge a = 5 cm: volume = 125 cm³, surface area = 150 cm², face diagonal = 5√2 ≈ 7.071 cm, space diagonal = 5√3 ≈ 8.660 cm. Reverse: if you know the volume is 125 cm³, the edge = ∛125 = 5 cm.
What it means to cube a number
Cubing a number means multiplying it by itself three times, written n³ and read as "n cubed" or "n to the power 3." For example, 4³ = 4 × 4 × 4 = 64, and 10³ = 1,000. The exponent 3 records how many copies of the base are multiplied together. Cubing is the inverse of taking a cube root: if you cube a number and then take the cube root, you return to where you started, which is why this calculator shows both values side by side. Unlike squaring, cubing preserves the sign of the input, so negative inputs stay negative: (−5)³ = −125.
Cube geometry: five properties from one
A perfect geometric cube has six square faces, twelve equal edges, and eight vertices. Every property follows from the single edge length a. The volume is a³ (which is why cubing and volume are so tightly linked). The total surface area is 6a² because there are six identical square faces, each of area a². The face diagonal, the line from one corner of a face to the opposite corner of that same face, has length a times the square root of 2 (by the Pythagorean theorem in two dimensions). The space diagonal, the line from one vertex of the cube to the opposite vertex through the interior, has length a times the square root of 3 (by applying the Pythagorean theorem in three dimensions). Switch to any geometry mode and the calculator reverse-solves the edge from whichever single property you know, then outputs all five.
Reverse-solve: find the edge from volume, surface area, or a diagonal
In real problems you often know the volume, not the edge. If the volume is V, the edge is the cube root of V: a = V^(1/3). If you know the surface area SA, the edge is the square root of SA divided by 6: a = √(SA/6). From the face diagonal f: a = f / √2. From the space diagonal d: a = d / √3. This calculator handles all four reverse cases. Select the mode that matches your known measurement, enter it, and get the complete set of cube properties instantly.
Negatives, fractions, and signs in number mode
Fractions and decimals shrink when cubed if they lie between 0 and 1: (1/2)³ = 1/8, and 0.4³ = 0.064. Numbers greater than 1 grow rapidly: 10³ = 1,000 and 100³ = 1,000,000. In geometry mode only positive edge lengths are meaningful, but in number mode the full real-number line is supported. The calculator keeps full internal precision and rounds only the displayed result to six significant digits.
Common perfect cubes and their geometric properties
| Edge a (cm) | n³ (Volume, cm³) | Surface area (cm²) | Face diagonal (cm) | Space diagonal (cm) |
|---|---|---|---|---|
| 1 | 1 | 6 | 1.414 | 1.732 |
| 2 | 8 | 24 | 2.828 | 3.464 |
| 3 | 27 | 54 | 4.243 | 5.196 |
| 4 | 64 | 96 | 5.657 | 6.928 |
| 5 | 125 | 150 | 7.071 | 8.660 |
| 6 | 216 | 216 | 8.485 | 10.392 |
| 7 | 343 | 294 | 9.899 | 12.124 |
| 8 | 512 | 384 | 11.314 | 13.856 |
| 9 | 729 | 486 | 12.728 | 15.588 |
| 10 | 1000 | 600 | 14.142 | 17.321 |
Edge lengths in cm and their cube properties. Face diagonal = a√2, space diagonal = a√3.
Frequently asked questions
What does it mean to cube a number?
Cubing a number means multiplying it by itself three times, written n³. For example, 5³ = 5 × 5 × 5 = 125. It is the same as raising the number to the power of 3, and it gives the volume of a cube whose edge length equals that number.
Can you cube a negative number?
Yes. Cubing a negative number gives a negative result because multiplying three negatives together stays negative. For example, (−3)³ = −27. This differs from squaring, where a negative input always produces a positive result.
What is the difference between face diagonal and space diagonal?
The face diagonal connects two opposite corners of one square face (length a√2), staying entirely on that face. The space diagonal cuts through the interior of the cube from one vertex to the opposite vertex, passing through the centre (length a√3). The space diagonal is always longer.
How do I find the edge of a cube if I know its volume?
Take the cube root of the volume: a = ∛V. For example, if the volume is 64 cm³, the edge is ∛64 = 4 cm. Select "Cube geometry: from volume" in this calculator and enter the volume to get the edge and all other properties instantly.
How do I find the edge of a cube if I know its surface area?
Divide the surface area by 6 (since there are six equal square faces) and then take the square root: a = √(SA / 6). For example, if the surface area is 150 cm², the edge is √(150/6) = √25 = 5 cm.
What is a perfect cube?
A perfect cube is an integer that equals another integer cubed. For example, 8 is a perfect cube because 2³ = 8, and 27 is a perfect cube because 3³ = 27. The calculator checks this automatically in number mode and tells you the cube root if the result is whole.