Geometry Tool
Cube Calculator
Calculate the volume, total surface area, face diagonal, and space diagonal of a cube. Enter any one known property to instantly solve for all other cube dimensions.
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Interactive Cube Calculator Workspace
Solved Cube Values
Edge Length3.0000
Volume27.0000
Surface Area54.0000
Space Diagonal5.1962
Mathematical Proof
• Calculated Edge (s): 3.0000
• Volume: s³ = 3.0000³ = 27.0000
• Surface Area: 6 × s² = 6 × 3.0000² = 54.0000
• Space Diagonal (corner to corner): s × √3 = 3.0000 × 1.732 = 5.1962
Mathematical Formula & Variables
Equation Model
Volume = s³, Surface Area = 6 × s², Space Diagonal = s × √3Calculates all dimensional, surface, and capacity values of a regular six-faced hexahedron (cube) using a single input constraint.
Variable Definitions
| Symbol | Description |
|---|---|
| s (Edge/Side) | The length of any of the 12 equal edges of the cube. |
| V (Volume) | The total 3D space contained inside the cube (s³). |
| SA (Surface Area) | The combined 2D area of all six flat square faces (6 × s²). |
| df (Face Diagonal) | The diagonal length across any single flat square face (s × √2). |
| ds (Space Diagonal) | The diagonal distance across the interior center from one corner to the opposite far corner (s × √3). |
How to Use the Cube Calculator
- Select your starting input criteria (Side Length, Volume, Surface Area, or Space Diagonal) from the dropdown list.
- Enter the numerical value into the input field.
- Watch as all other properties recalculate instantly with high accuracy.
- Follow the worked equations explaining the relationships of double and triple roots.
Practical Example Calculation
Scenario Context: A packaging factory manufactures a cubic box that must have a total volume of 27 cubic feet.
Step 1: Identify given value: Volume (V) = 27 cu ft.
Step 2: Calculate Side Length (s): s = ∛V = ∛27 = 3 feet.
Step 3: Calculate Surface Area (SA): SA = 6 × s² = 6 × 3² = 6 × 9 = 54 square feet.
Step 4: Calculate Face Diagonal (df): df = s × √2 = 3 × 1.4142 ≈ 4.24 feet.
Step 5: Calculate Space Diagonal (ds): ds = s × √3 = 3 × 1.732 ≈ 5.20 feet.
The cubic box will have edge lengths of 3 ft, surface area of 54 sq ft, and space diagonal of 5.20 ft.
Frequently Asked Questions
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