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Cube Calculator — Volume, Surface Area & Diagonals
Calculate all properties of a cube from its edge length: volume, surface area, face diagonal, space diagonal, circumscribed and inscribed sphere radii. Reverse-solve from volume, surface area, or d...
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Planning notes, formulas, and examples
About the Cube Calculator — Volume, Surface Area & Diagonals
The cube is the simplest and most symmetric of all three-dimensional solids — six identical square faces, twelve equal edges, and eight vertices. Despite its simplicity, the cube has a rich set of geometric properties that appear throughout mathematics, physics, architecture, and engineering.
Every geometric property of a cube derives from a single measurement: the edge length a. The volume is a³. The total surface area is 6a² (six identical faces). The face diagonal — the line connecting opposite corners of one face — equals a√2. The space diagonal — the longest line you can draw inside the cube, from one vertex to the opposite vertex — equals a√3. Three spheres are naturally associated with every cube: the inscribed sphere (touching all six faces, radius a/2), the midsphere (touching all twelve edges, radius a√2/2), and the circumscribed sphere (passing through all eight vertices, radius a√3/2).
This calculator computes all of these properties from the edge length. Even more useful, it can reverse-solve: give it a known volume, surface area, face diagonal, or space diagonal, and it will determine the edge length and all other properties. Presets for common cube-shaped objects — dice, ice cubes, Rubik's cubes, and shipping boxes — let you explore those relationships quickly.
When This Page Helps
The Cube Calculator — Volume, Surface Area & Diagonals is useful when you need fast and consistent geometry results without reworking the same algebra repeatedly. It helps you move from raw measurements to Edge Length, Volume, Surface Area in one pass, with conversions and derived values shown together.
How to Use the Inputs
- Select what you know: edge length, volume, surface area, face diagonal, or space diagonal.
- Choose the measurement unit (mm, cm, in, m, or ft).
- Enter the known value, or tap a preset to load a common cube.
- View all computed properties: volume, surface area, diagonals, sphere radii, and total edge length.
- Check the property comparison bars for a visual overview.
- Scroll down to the reference table to compare common cube-shaped objects.
Formula used
Volume: V = a³
Surface Area: SA = 6a²
Face Diagonal: d_f = a√2
Space Diagonal: d_s = a√3
Inscribed Sphere Radius: r_in = a/2
Midsphere Radius: r_mid = a√2/2
Circumscribed Sphere Radius: r_out = a√3/2
Total Edge Length: 12aExample Calculation
Result: Volume = 125 cm³, Surface Area = 150 cm², Space Diagonal ≈ 8.66 cm
With edge a = 5 cm: V = 5³ = 125 cm³. SA = 6 × 25 = 150 cm². Face diagonal = 5√2 ≈ 7.07 cm. Space diagonal = 5√3 ≈ 8.66 cm. Inscribed sphere radius = 2.5 cm. Circumscribed sphere radius ≈ 4.33 cm.
Tips & Best Practices
- The space diagonal is always √3 ≈ 1.732 times the edge length.
- Doubling the edge length increases the volume 8× but the surface area only 4×.
- The inscribed sphere touches every face at its center; the circumscribed sphere passes through every vertex.
- A cube is the only Platonic solid that tessellates (tiles) three-dimensional space perfectly.
- For reverse calculations, the edge length from a known volume is simply the cube root: a = ∛V.
How This Cube Calculator — Volume, Surface Area & Diagonals Works
Where It Helps In Practice
Cube Calculator — Volume, Surface Area & Diagonals calculations show up in coursework, drafting, construction layout, packaging, tank sizing, machining, and quality control. Instead of solving each transformation manually, you can test scenarios quickly and verify whether your dimensions remain within tolerance.
Accuracy And Setup Tips
Sources & Methodology
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Frequently Asked Questions
Volume = a³, where a is the edge length. For a 10 cm cube, volume = 1,000 cm³ = 1 liter.
Take the cube root: a = ∛V. For example, ∛125 = 5, so a 125 cm³ cube has 5 cm edges.
The space diagonal connects two opposite vertices through the interior. Its length is a√3, where a is the edge length.
The face diagonal lies on one face (a√2). The space diagonal passes through the cube interior (a√3). The space diagonal is always longer.
The largest sphere that fits inside a cube, touching all six faces at their centers. Its radius is half the edge length (a/2).
A cube has 12 edges, all of equal length. The total edge length is 12a.
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