Cube Volume Calculator
Fast, accurate and free online cube volume calculator tool running directly in your browser.
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Other tools you may find usefulHow does the cube volume calculator work and how does it help?
Cube Volume Calculator is a simple but extremely useful online math tool designed to instantly determine the volume of a cube. A cube (hexahedron) is the most regular three-dimensional prism whose all 6 faces are identical squares. In a cube, each edge has the same length and adjacent faces meet at right angles (90°). The shape of a cube has, among others, dice, concrete blocks and decorative containers.
Precise volume calculation allows you to quickly plan the cargo space, determine the weight of objects after taking into account density, or calculate the volume. Our calculator allows you to perform calculations using two methods: based on the edges of the cube or its spatial diagonal.
Formula for the volume of a cube
Determining the volume of a cube is based on the power of the length of its edges. Depending on the measurement data, the following formulas are used:
- Formula from the edge of a cube (a):The simplest formula in three-dimensional geometry: V = a³ Where V is the volume and a is the length of the edges of the cube.
- Formula for the spatial diagonal of a cube (D):The diagonal of a cube is a segment connecting two vertices that are not on one face. Since the geometric relation D = a√(3) holds, the formula for volume using the diagonal is as follows: V = (D³) / (3√(3)) Where D is the length of the diagonal of the cube.
Table of geometric relationships in the cube
| Edge of the cube (a) | Diagonal of the face (d = a√(2)) | Diagonal of the cube (D = a√(3)) | Total surface area (Pc= 6a²) | Volume of the cube (V = a³) |
|---|---|---|---|---|
| 10 cm | 14.14 cm | 17.32 cm | 600 cm² | 1000 cm³ (1 liter) |
| 20 cm | 28.28 cm | 34.64 cm | 2400 cm² | 8000 cm³ (8 liters) |
| 50 cm | 70.71 cm | 86.60 cm | 15,000 cm² (1.5 m²) | 125,000 cm³ (125 liters) |
| 1 m | 1.41 m | 1.73 m | 6 m² | 1 m³ (1000 liters) |
Step by step: how to calculate the volume of a cube? Examples
Let's look at two practical examples of calculating the volume of a cube.
Example 1: Carton for shipping (edge calculations).You have a cubic box with side a = 40 cm (4 dm). You want to calculate its capacity in liters.
- Convert centimeters to decimeters: a = 4 dm.
- We use the volume formula: V = a³.
- We perform the exponentiation: V = 4³ = 64 dm³.
- Conclusion: The box has a capacity of exactly 64 liters.
Example 2: Spatial diagonal measurements.You have measured the distance between opposite vertices of a metal block (the spatial diagonal), which is D = 15 cm. What is the volume of this block?
- We determine the length of the edges of the cube using the formula: a = (D) / (√(3)).
- We substitute the data: a = (15) / (1.732) ≈ 8.66 cm.
- We calculate the volume of the cube: V = a³ ≈ 8.66³ ≈ 649.5 cm³.
Frequently asked questions (FAQ)
What is the difference between the diagonal of a wall and the diagonal of a cube?
The diagonal of face (d) lies in the plane of one of the square faces of the cube. The diagonal of the cube (D) passes through the entire interior of the cube, connecting opposite corners on opposite sides.
How to calculate the edge of a cube from its volume?
To determine the edge (a) from the volume (V), perform the third-degree square root operation: a =3√(V).
What is the total surface area of the cube?
A cube consists of six identical faces, each of which is a square with area a². The total surface area is: Pc= 6 × a².
Is a cube a cuboid?
Yes. A cube is a special type of cuboid in which all three dimensions are equal.
How to convert the volume of a cube to cubic meters (m³)?
If the edge of the cube is given in meters, the result of the exponentiation is already in cubic meters. If given in centimeters, the result in cm³ is divided by 1,000,000.