🎲 Cube Surface Area Calculator
Calculate Surface Area Using 6a² Formula
Perfect cube calculations made easy
Cube Surface Area Calculator
📏 Enter Side Length
🎲 All 6 Faces (Each = a²)
📊 Calculation Steps
Cube Formulas
Surface Area
Where a = side length (edge length)
Volume
Space Diagonal
Face Diagonal
Side from Surface Area
Side from Volume
Cube Properties
| Property | Value | Formula |
|---|---|---|
| Faces | 6 (all squares) | — |
| Edges | 12 (all equal) | — |
| Vertices | 8 | — |
| Surface Area | 6 × face area | 6a² |
| Volume | Side cubed | a³ |
| Space Diagonal | Side × √3 | a√3 |
| Face Diagonal | Side × √2 | a√2 |
| Face-to-Volume Ratio | 6/a | SA/V = 6/a |
Example Calculations
| Side (a) | Face Area (a²) | Surface Area (6a²) | Volume (a³) | Diagonal (a√3) |
|---|---|---|---|---|
| 1 | 1 | 6 | 1 | 1.73 |
| 2 | 4 | 24 | 8 | 3.46 |
| 3 | 9 | 54 | 27 | 5.20 |
| 4 | 16 | 96 | 64 | 6.93 |
| 5 | 25 | 150 | 125 | 8.66 |
| 10 | 100 | 600 | 1000 | 17.32 |
How to Calculate Cube Surface Area
- Measure one edge — All 12 edges of a cube are equal, so measure any one.
- Square the side length — Calculate a² to get the area of one face.
- Multiply by 6 — A cube has 6 identical faces, so SA = 6 × a².
- Include units — Remember to use square units (cm², m², in²).
- Verify — Check your answer: Total SA = 6 × (side)².
Educational Resources
Frequently Asked Questions
The surface area of a cube is SA = 6a², where a is the side length (edge). This formula comes from having 6 identical square faces, each with area a².
Because a cube has 6 faces, not 1. Each face is a square with area a². Total surface area = 6 × a² = 6a². Think of it as wrapping all 6 sides of a box.
A cube has all edges equal (l = w = h = a), so all 6 faces are identical squares. A rectangular prism has rectangular faces that may differ. Cube SA = 6a²; Rectangular prism SA = 2(lw + lh + wh).
Rearrange the formula: a = √(SA/6). For example, if SA = 150 cm², then a = √(150/6) = √25 = 5 cm.
The space diagonal connects two opposite corners through the interior of the cube. Formula: d = a√3 ≈ 1.732a. For a cube with side 5, diagonal = 5 × 1.732 = 8.66.
The face diagonal goes across one square face (corner to corner of a face). Formula: f = a√2 ≈ 1.414a. This is different from the space diagonal which goes through the cube's interior.
A cube has 12 edges, all of equal length. It also has 6 faces (all squares) and 8 vertices (corners).
First find side length: a = ∛V (cube root of volume). Then calculate SA = 6a². For example, if V = 125 cm³, then a = 5 cm, and SA = 6 × 25 = 150 cm².
Yes! The cube (hexahedron) is one of the five Platonic solids — regular convex polyhedra with identical faces. The others are tetrahedron, octahedron, dodecahedron, and icosahedron.
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Last Updated: January 2026