Quadratic Equation Solver (ax² + bx + c = 0)
About Cube Calculator
The 3D Cube (Regular Hexahedron) Geometry Calculator computes Volume ($V = s^3$), Surface Area ($A = 6s^2$), Face Diagonal ($d_f = s\sqrt{2}$), Space / Body Diagonal ($d_s = s\sqrt{3}$), Inradius ($r = s/2$), and Circumradius ($R = s\frac{\sqrt{3}}{2}$) from any single known property.
How to Use Cube Calculator
Step 1
Enter any one known property (Side, Volume, Surface Area, or Space Diagonal).
Step 2
Review computed volume, total surface area, face diagonal, and space diagonal.
Step 3
Inspect inscribed and circumscribed sphere dimensions.
Step 4
Click "Copy Cube Specs".
Practical Use Cases for Cube Calculator
Packaging Box & Shipping Carton Dimensioning
Calculate cubic freight volume and surface cardboard area for cubic shipping boxes and warehouse storage containers.
Crystalline Solid State Physics & Mineralogy (FCC / BCC Lattices)
Calculate unit cell cube volumes, body diagonals, and atomic packing factors for cubic crystal mineral lattices.
Input & Output Examples
Calculating Cube Properties from Side Length = 4m
Side Length (s): `4.0 meters`
Volume: `64.0 m³` | Surface Area: `96.0 m²` | Face Diagonal: `5.657 m (4√2)` | Space Diagonal: `6.928 m (4√3)` | Inradius: `2.0 m`
Key Features & Performance
- ✓Multi-Way Solver: enter Side Length, Volume, Surface Area, Face Diagonal, or Body Diagonal to solve all other dimensions instantly.
- ✓Exact Radical Mode: outputs exact simplified radical expressions ($s\sqrt{2}, s\sqrt{3}$) alongside decimal approximations.
- ✓Computes: Inscribed Sphere Volume ($V_{in} = \frac{\pi}{6} s^3$) and Circumscribed Sphere Volume ($V_{circ} = \frac{\sqrt{3}\pi}{2} s^3$).
- ✓100% Client-Side 3D geometry engine.
- ✓1-Click Copy cube specifications.
Key Terminology & Definitions
Space / Body Diagonal ($s\sqrt{3}$)
The line segment connecting two opposite vertices passing completely through the interior center of the cube ($d_s = \sqrt{s^2 + s^2 + s^2} = s\sqrt{3}$).
Regular Hexahedron
The geometric classification of a cube as one of the five Platonic solids composed of six congruent square faces.