Cube Calculator
Calculate all properties of a cube: surface area, volume, face diagonal, space diagonal, inscribed and circumscribed sphere radii from side length, diagonal, surface area, or volume.
Cube Volume, Area & Diagonal Calculator
Calculate cube volume, surface area, face diagonal, space diagonal, inscribed and circumscribed sphere properties from side length. Includes scaling table and dimension comparison.
Quick Sizes
cm
Volume⧉
1,000.00 cm³
a³ = 10³
Total Surface Area⧉
600.00 cm²
6a² = 6 × 10²
Face Diagonal⧉
14.14 cm
a√2 = 10 × 1.4142…
Space Diagonal⧉
17.32 cm
a√3 = 10 × 1.7321…
Inscribed Sphere r⧉
5.00 cm
Largest sphere fitting inside (touches all faces)
Circumscribed Sphere R⧉
8.66 cm
Smallest sphere enclosing the cube (through vertices)
Midsphere Radius⧉
7.07 cm
Sphere tangent to all 12 edges at their midpoints
Lateral Area⧉
400.00 cm²
4 side faces only
Single Face Area⧉
100.00 cm²
a² = 100.00
Total Edge Length⧉
120.00 cm
12 edges × a
Face Perimeter⧉
40.00 cm
4a — perimeter of one face
SA : V Ratio⧉
0.60 cm⁻¹
Surface area to volume — decreases with size
Dimension Comparison
Side
10.00 cm
Face diag
14.14 cm
Space diag
17.32 cm
Inscribed r
5.00 cm
Midsphere ρ
7.07 cm
Circum R
8.66 cm
Comprehensive Properties Table
| Property | Formula | Value |
|---|---|---|
| Side length | a | 10.00 cm |
| Volume | a³ | 1,000.00 cm³ |
| Surface area | 6a² | 600.00 cm² |
| Lateral area | 4a² | 400.00 cm² |
| Face area | a² | 100.00 cm² |
| Face diagonal | a√2 | 14.14 cm |
| Space diagonal | a√3 | 17.32 cm |
| Edge total | 12a | 120.00 cm |
| Face perimeter | 4a | 40.00 cm |
| Inscribed sphere r | a/2 | 5.00 cm |
| Midsphere ρ | a√2/2 | 7.07 cm |
| Circumscribed sphere R | a√3/2 | 8.66 cm |
| Inscribed sphere volume | 4πr³/3 | 523.60 cm³ |
| Circumscribed sphere volume | 4πR³/3 | 2,720.70 cm³ |
| Inscribed sphere SA | 4πr² | 314.16 cm² |
| Circumscribed sphere SA | 4πR² | 942.48 cm² |
| SA:V ratio | 6/a | 0.60 cm⁻¹ |
| Vertices | — | 8 |
| Edges | — | 12 |
| Faces | — | 6 |
Scaling Table
| Side (cm) | SA (cm²) | Volume (cm³) | Space Diag (cm) |
|---|---|---|---|
| 1 | 6.00 | 1.00 | 1.73 |
| 2 | 24.00 | 8.00 | 3.46 |
| 5 | 150.00 | 125.00 | 8.66 |
| 10 | 600.00 | 1,000.00 | 17.32 |
| 20 | 2,400.00 | 8,000.00 | 34.64 |
| 50 | 15,000.00 | 125,000.00 | 86.60 |
| 100 | 60,000.00 | 1,000,000.00 | 173.21 |
Planning notes, formulas, and examples
About the Cube Volume, Area & Diagonal Calculator
This all-in-one cube calculator computes every geometric property of a cube from a single measurement: the side length. Enter the edge length in any unit and receive 17+ properties including volume, total and lateral surface area, face and space diagonals, inscribed/midsphere/circumscribed sphere radii and their own volumes and surface areas, plus topological constants.
The cube — also known as a regular hexahedron — is one of the five Platonic solids. Its perfect symmetry makes it the most commonly encountered 3-D shape in architecture, packaging, storage, and manufacturing. Understanding how its properties scale with size is fundamental to physics and engineering: the square-cube law dictates that doubling the side multiplies area by 4 but volume by 8.
The inscribed sphere (insphere) is the largest sphere that fits inside the cube, touching each face at its centre. The midsphere touches each edge at its midpoint. The circumscribed sphere (circumsphere) is the smallest sphere that encloses the cube, passing through all eight vertices. These sphere relationships are important in crystallography, packing problems, and collision detection in computer graphics.
Use the scaling table to explore how properties change across a range of sizes, and the visual bar chart to compare all linear dimensions at a glance.
When This Page Helps
The Cube Volume, Area & Diagonal Calculator is useful when you need fast and consistent geometry results without reworking the same algebra repeatedly. It helps you move from raw measurements to Volume, Total Surface Area, Face Diagonal in one pass, with conversions and derived values shown together.
How to Use the Inputs
- Enter the side length of the cube.
- Select the measurement unit (mm, cm, m, in, ft).
- Use a preset button to quickly load a common size.
- Read all computed properties in the output grid: volume, surface areas, diagonals, sphere radii.
- Compare linear dimensions visually in the bar chart.
- Review the full properties table for formulas and values.
- Check the scaling table to see how properties grow with size.
Formula used
Volume = a³
Surface Area = 6a²
Lateral Area = 4a²
Face Diagonal = a√2
Space Diagonal = a√3
Inscribed Sphere r = a/2
Midsphere ρ = a√2/2
Circumscribed Sphere R = a√3/2
SA:V Ratio = 6/aExample Calculation
Result: Volume = 1000 cm³, SA = 600 cm², Space diagonal ≈ 17.32 cm
A 10 cm cube has volume 10³ = 1000 cm³, surface area 6 × 100 = 600 cm², face diagonal 10√2 ≈ 14.14 cm, space diagonal 10√3 ≈ 17.32 cm, inscribed sphere r = 5 cm, and circumscribed sphere R ≈ 8.66 cm.
Tips & Best Practices
- The space diagonal is the longest straight-line distance inside a cube and equals a√3.
- Doubling the side yields 4× surface area and 8× volume — this is the square-cube law.
- The circumscribed sphere volume is always (π√3/2) ≈ 2.72 times the cube's volume.
- SA:V ratio matters for heat transfer, diffusion, and biology — smaller cubes lose heat faster.
- Use this calculator for estimating shipping box dimensions, concrete volumes, and storage capacity.
How This Cube Volume, Area & Diagonal Calculator Works
Where It Helps In Practice
Cube Volume, Area & Diagonal Calculator 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
Last updated:
Frequently Asked Questions
It computes volume, total and lateral surface area, face and space diagonals, inscribed/midsphere/circumscribed sphere radii and their volumes, edge totals, face perimeter, SA:V ratio, and topological constants.
The space diagonal connects two opposite vertices through the interior of the cube. Its length is a√3, where a is the side length.
The inscribed sphere fits inside the cube touching all faces (r = a/2). The circumscribed sphere encloses the cube touching all vertices (R = a√3/2).
The midsphere (or intersphere) is tangent to every edge of the cube at the midpoint. Its radius is a√2/2.
Surface area grows as a² while volume grows as a³. Dividing gives 6/a, which shrinks as a increases — the square-cube law.
Yes. The cube (regular hexahedron) is one of the five Platonic solids, with 6 square faces, 12 edges, and 8 vertices.
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