Volume of Cube Calculator – Calculate Cube Volume and Surface Area
Calculate volume and surface area of a cube
Measure the Side Length
A cube has all edges equal. Measure any side – length, width, and height are identical. This single measurement determines all cube properties.
Calculate Volume as s³
Volume equals side length cubed (s × s × s). This represents the 3D space inside the cube. Doubling the side increases volume by 8 times (2³ = 8).
Find Surface Area and Diagonals
Surface area is 6s² (six square faces). Face diagonal is s√2. Space diagonal (corner to opposite corner) is s√3, using the 3D Pythagorean theorem.
**Volume Formula**
V = s³ where s is the side length. A cube with 5 cm sides has volume 125 cm³. Volume scales with the cube of linear dimension – small changes in side cause large volume changes.
**Surface Area Formula**
A = 6s² because a cube has 6 identical square faces. Each face has area s². Total surface area is useful for painting, wrapping, or heat transfer calculations.
**Space Diagonal**
d = s√3 connects opposite corners through the cube interior. Derived from 3D Pythagorean theorem: d² = s² + s² + s². Important for fitting objects inside cubic spaces.
**Face Diagonal**
f = s√2 runs across each square face corner to corner. This is the 2D Pythagorean theorem applied to one face. Face diagonals help in structural bracing calculations.
Cube Measurements Reference Table
| Side Length | Volume (s³) | Surface Area (6s²) | Space Diagonal (s√3) |
|---|---|---|---|
| 1 unit | 1 | 6 | 1.732 |
| 2 units | 8 | 24 | 3.464 |
| 3 units | 27 | 54 | 5.196 |
| 4 units | 64 | 96 | 6.928 |
| 5 units | 125 | 150 | 8.660 |
| 10 units | 1000 | 600 | 17.321 |
What is the formula for volume of a cube?
Volume = s³ (side length cubed). Multiply the side by itself three times. For a cube with 4 cm sides: 4 × 4 × 4 = 64 cm³. All three dimensions are equal in a cube.
How do you find the side length from volume?
Take the cube root of the volume: s = ∛V. If volume is 27 cm³, the side is ∛27 = 3 cm. Most calculators have a cube root function, or use V^(1/3).
What is the difference between a cube and a cuboid?
A cube has all sides equal. A cuboid (rectangular prism) has different length, width, and height. Cube formulas are simpler because there is only one dimension to measure.
Why is the space diagonal s√3?
Using 3D Pythagorean theorem: diagonal² = length² + width² + height². For a cube, all three equal s, so d² = s² + s² + s² = 3s². Therefore d = s√3.
How does doubling the side affect volume?
Doubling the side multiplies volume by 8 (2³ = 8). Tripling multiplies by 27 (3³ = 27). This cubic relationship means small size changes create large volume differences.
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