Enter the side length of a cube to instantly calculate its volume, total surface area, face diagonal, and space diagonal. All results update live as you type. Choose your preferred unit of measurement below.
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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
7.07
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)7.071 cm
s × √3 (space diagonal)8.660 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.
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