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

Please enter a positive value to calculate cube properties

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

🔲
6 Faces: All squares of equal area
📏
12 Edges: All equal in length
📍
8 Vertices: Corner points where edges meet
⚖️
Regular: All faces, edges, and angles are identical

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