mathematics calculator
Cube Surface Area Calculator
Calculate a cube's total and face areas plus its face and space diagonals from one edge length.
Cube Surface Area Calculator
Total surface area
Enter the length of one cube edge.
A cube has six congruent square faces; material thickness, openings, and waste are not included.
Formula version 1.0.0
How to use this calculator
- Enter the cube's positive edge length.
- Select Calculate.
- Read one-face area and total six-face area.
- Review face and space diagonals derived by the Pythagorean theorem.
Symbols and units
| Symbol | Meaning | Unit or domain |
|---|---|---|
a | Cube edge | length |
Af | One face area | square length |
S | Total surface area | square length |
df,ds | Face and space diagonals | length |
Checked examples
Edge three
Inputs: Edge 3
Calculation: Af=3²; S=6×3²; df=3√2; ds=3√3
Result: Face 9; total 54
The six congruent square faces determine total area.
Check: cube-surface-area-core.test.ts
Unit cube
Inputs: Edge 1
Calculation: S=6×1²
Result: 6 square units
Every face has unit area.
Check: cube-surface-area-core.test.ts
Assumptions, rounding, and limits
- All cube edges are equal and positive.
- The cube is ideal and closed.
- Results use the square or linear input unit as labelled.
- Material thickness is excluded.
Frequently asked questions
Why multiply face area by six?
A cube has six congruent square faces.
What is the space diagonal?
It connects opposite vertices through the cube interior and equals a√3.
How does scaling affect area?
Multiplying edge by k multiplies area by k².
Sources and review
- OpenStax: Geometric Formulas — Cube surface area
- OpenStax: The Pythagorean Theorem — Face and space diagonals
- Formula version
- cube.surface-area@1.0.0
- Formula review
- Equatara formula review
- Editorial review
- Equatara editorial review
- Last verified
- 2026-10-25
- Applicability
- Ideal closed cube from one positive edge.
- Next review
- On material formula/source change, or by 2028-10-25.
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Found a problem?
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