This calculator works out the volume, surface area, and diagonal lengths of a cube from a single measurement: the length of one side. Because every side, face, and angle in a cube is identical, one number is all you need to describe the whole shape completely. Enter the side length, then choose your unit from millimetres, centimetres, metres, inches, or feet, and the calculator instantly returns four results: the volume (how much space the cube occupies), the surface area (the total area of all six square faces), the face diagonal (the diagonal line across one face), and the space diagonal (the longest line, running from one corner through the interior to the opposite corner). A calculation breakdown shows each step, from side squared through to the final diagonal lengths, alongside the cube's properties: six faces, twelve edges, eight vertices, and ninety-degree angles throughout. It is useful for maths homework, packaging and storage calculations, working out how much material covers a cube-shaped object, or checking how a container will fit through a doorway or gap using the space diagonal. Change the side length or unit at any time and every result updates immediately, so you can compare several sizes without re-entering figures. If you already know the volume and need the side length instead, use the linked cube root calculator.
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Standard formula
Volume = s³ · Surface area = 6s² · Space diagonal = s√3
1. Side Length
cm
2. Unit of Measurement
Cube Measurements
Volume
125
cm³
Surface Area
150
cm²
Face Diagonal
7.071
cm
Space Diagonal
8.66
cm
Calculation Breakdown
Side length (s)5 cm
s² (side squared)25 cm²
s³ (side cubed)125 cm³
6 × s² (surface area)150 cm²
s × √2 (face diagonal)7.0711 cm
s × √3 (space diagonal)8.6603 cm
Properties
Number of faces6
Number of edges12
Number of vertices8
Face shapeSquare
All interior angles90°
SymmetryOh (full octahedral)
Worked Example: side = 5 cm
Volume: s³ = 5 × 5 × 5 = 125 cm³
Surface area: 6 × s² = 6 × 25 = 150 cm²
Face diagonal: s × √2 = 5 × 1.41421 = 7.071 cm
Space diagonal: s × √3 = 5 × 1.73205 = 8.660 cm
How to Calculate the Volume of a Cube
A cube is a three-dimensional solid with six identical square faces, twelve equal edges, and eight vertices. Because all three dimensions (length, width, height) are the same, the volume formula is simply the side length multiplied by itself three times:
V = s × s × s = s³
Where s is the side length in any linear unit. The result is expressed in the corresponding cubic unit. For example, a side of 5 centimetres gives a volume of 125 cubic centimetres (cm³).
Surface Area of a Cube
A cube has six square faces, each with an area of s². The total surface area is therefore:
SA = 6s²
For s = 5 cm: SA = 6 × 25 = 150 cm². Surface area is useful when calculating materials needed to wrap, paint, or coat a cube-shaped object.
Diagonals of a Cube
A cube has two types of diagonal:
Face diagonal: the diagonal across one square face. Length = s × √2. For s = 5 cm, this is approximately 7.071 cm.
Space diagonal: the longest diagonal, running from one corner of the cube to the opposite corner through the interior. Length = s × √3. For s = 5 cm, this is approximately 8.660 cm. This diagonal passes through the centre of the cube.
Cube Volume Reference Table
Side (cm)
Volume (cm³)
Surface Area (cm²)
Space Diagonal (cm)
1
1
6
1.732
2
8
24
3.464
3
27
54
5.196
4
64
96
6.928
5
125
150
8.660
10
1,000
600
17.321
20
8,000
2,400
34.641
50
125,000
15,000
86.603
Finding the Side Length from the Volume
If you know the volume and want to find the side length, take the cube root: s = ³√V. For example, a cube with a volume of 343 cm³ has a side length of ³√343 = 7 cm. You can use the cube root calculator for this.
Frequently Asked Questions
What is the formula for the volume of a cube?
V = s³, where s is the side length. All sides of a cube are equal, so you only need one measurement.
How is a cube different from a rectangular box?
A cube is a special rectangular box where all three dimensions are equal. A rectangular box (cuboid) uses V = l × w × h. For a cube, l = w = h = s, so the formula becomes V = s³.
What is the space diagonal of a cube?
The space diagonal runs corner to corner through the cube's interior. Its length is s × √3. For a 5 cm cube, that is approximately 8.660 cm.
Method: Volume = s³. Surface area = 6s². Face diagonal = s√2. Space diagonal = s√3. Standard Euclidean geometry. Source: NIST Digital Library of Mathematical Functions; Coxeter, H.S.M., Regular Polytopes, 3rd ed., Dover Publications.
All calculations use standard Euclidean geometry. Results are exact for integer inputs and rounded to three decimal places for irrational values. This calculator is intended for educational use.
