Cube Volume Calculator
Calculate the volume of a cube with our cube volume calculator using side length or surface area. Get results with the cube volume formula and easy steps.
What Is a Cube?
A cube is a symmetrical three-dimensional solid object bounded by six identical square faces, meeting at right angles. It has 8 vertices, 12 edges, and 6 square faces.
Because all three dimensions (length, width, and height) are identical, calculating the volume of a cube is the simplest of all 3D solid shapes.
Volume of a Cube Formula
Formula Variables Explained:
The length of any edge of the cube (all 12 edges are equal).
The distance between two opposite corners through the center (d = a√3).
Total surface area of all six square faces (S = 6a²).
The volume of a cube is calculated by raising the side length (a) to the third power: V = a³. This is why multiplying a number by itself three times is referred to as "cubing" a number.
How to find the volume of a Cube?
- 1Measure the length of any single side (a) of the cube.
- 2Multiply the side length by itself three times: V = a × a × a.
- 3Include cubic units (e.g., cm³, m³, in³, ft³) with your result.
Example: Calculate the Volume of a Cube
Example 1: Find the volume of a cube with side length 5 cm
Problem: Calculate the total volume of a wooden cube whose edge measures 5 centimeters.
- Formula: V = a³
- Substitute a = 5: V = 5 × 5 × 5
- V = 125 cm³
Example 2: Find the volume of a cube from its space diagonal
Problem: A cube has a space diagonal of 6 inches. Find the volume of the cube.
- Use d = a√3 so a = d / √3
- a = 6 / √3 ≈ 3.464 inches
- Formula: V = a³
- V ≈ (3.464)³
- V ≈ 41.57 in³
Example 3: Find the volume of a cube from its surface area
Problem: A cube has a total surface area of 54 cm². Calculate its volume.
- Use S = 6a² so a = √(S / 6)
- a = √(54 / 6) = √9 = 3 cm
- Formula: V = a³
- V = 3³ = 27 cm³
Frequently Asked Questions (FAQ)
Q: How do you find cube volume if you know surface area?
Given surface area S, find side length a = √(S / 6). Then calculate volume V = a³.
Q: What is the relationship between side length and space diagonal in a cube?
The space diagonal d = a × √3 ≈ 1.732a. To get side length from diagonal, use a = d / √3.