Surface Area of a Cube Calculator
Calculate cube surface area, volume, and other properties from various measurements
Calculate Cube Surface Area
Length of any edge of the cube
Cube Formulas
Surface Area: A = 6a²
Volume: V = a³
Face Diagonal: d_face = a√2
Space Diagonal: d_space = a√3
Example Calculations
Example 1: From Side Length
Given: Side length = 4 cm
Surface area: 6 × 4² = 96 cm²
Volume: 4³ = 64 cm³
Example 2: From Volume
Given: Volume = 125 cm³
Side length: ∛125 = 5 cm
Surface area: 6 × 5² = 150 cm²
Quick Reference
Key Formulas
Surface Area = 6a²
Volume = a³
Face Diagonal = a√2
Space Diagonal = a√3
Cube Properties
Quick Tips
A cube has 6 identical square faces
Surface area = 6 × (side length)²
All diagonals can be calculated from side length
Perfect for dice because all faces are equal
Understanding Cube Surface Area
What is Surface Area?
Surface area is the total area of all the faces of a 3D object. For a cube, this means calculating the area of all six square faces and adding them together.
Why is the Formula 6a²?
A cube has 6 faces, each being a square with area a². Since all faces are identical, we multiply the area of one face by 6 to get the total surface area.
Calculating by Hand
Step 1: Find Face Area
Area of one face = side × side = a²
Step 2: Multiply by 6
Total surface area = 6 × a²
Example
If a = 4: Surface area = 6 × 4² = 96
Real-World Applications
Packaging:
Calculate material needed to wrap a cubic box
Painting:
Determine paint coverage for cubic structures
Dice Manufacturing:
Ensure all faces have equal area for fairness