Cube Surface Area Calculator
Calculate total and lateral surface area of a cube from side length, volume, face diagonal, or space diagonal. Includes formula reference and comparison table.
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.
Presets
cm
Side Length (a)⧉
10.00 cm
Edge length of the cube
Face Diagonal⧉
14.14 cm
a√2 = 10.00 × √2
Space Diagonal⧉
17.32 cm
a√3 = 10.00 × √3
Surface Area⧉
600.00 cm²
6a² = 6 × 10.00²
Volume⧉
1,000.00 cm³
a³ = 10.00³
One Face Area⧉
100.00 cm²
a² = 10.00²
Inscribed Sphere Radius⧉
5.00 cm
r = a/2 — sphere touching all 6 faces
Circumscribed Sphere Radius⧉
8.66 cm
R = a√3/2 — sphere through all 8 vertices
Midsphere Radius⧉
7.07 cm
ρ = a√2/2 — sphere touching all 12 edge midpoints
Total Edge Length⧉
120.00 cm
12 edges × a
Dimension Comparison
Side
10.00 cm
Face diag
14.14 cm
Space diag
17.32 cm
Inscribed r
5.00 cm
Circum R
8.66 cm
Midsphere ρ
7.07 cm
Cube Properties Table
| Property | Formula | Value |
|---|---|---|
| Side length | a | 10.00 cm |
| Face diagonal | a√2 | 14.14 cm |
| Space diagonal | a√3 | 17.32 cm |
| Surface area | 6a² | 600.00 cm² |
| Volume | a³ | 1,000.00 cm³ |
| Face area (one) | a² | 100.00 cm² |
| Total edge length | 12a | 120.00 cm |
| Inscribed sphere radius | a/2 | 5.00 cm |
| Midsphere radius | a√2/2 | 7.07 cm |
| Circumscribed sphere radius | a√3/2 | 8.66 cm |
| Vertices | — | 8 |
| Edges | — | 12 |
| Faces | — | 6 |
Planning notes, formulas, and examples
About the Cube Calculator
A cube is the most symmetric of all three-dimensional Platonic solids — six identical square faces, twelve edges of equal length, and eight vertices. Despite its simplicity, the cube appears everywhere: from dice and sugar cubes to crystallography unit cells and 3-D pixel (voxel) grids.
This comprehensive cube calculator lets you start from any one known quantity — side length, face diagonal, space diagonal, surface area, or volume — and derives every other property. You get the edge length, both diagonals, surface area, volume, total edge length, and three sphere radii: inscribed (tangent to all faces), midsphere (tangent to all edges), and circumscribed (passing through all vertices).
The formulas are straightforward: face diagonal = a√2, space diagonal = a√3, surface area = 6a², volume = a³. From any of these you can solve for the side a and compute the rest. The inscribed sphere radius is a/2, the midsphere radius is a√2/2, and the circumscribed sphere radius is a√3/2.
Useful for packaging calculations, shipping box optimisation, material estimation, crystallography, game design, and geometry homework involving cubes.
When This Page Helps
Use this when you know one cube measurement and need the rest without jumping between separate formulas for volume, area, diagonals, and edge length. It is practical for packaging, fabrication, and geometry work because every cube property comes back to the same side length.
How to Use the Inputs
- Select an input mode: side length, face diagonal, space diagonal, surface area, or volume.
- Enter the known value in the input field.
- Choose a measurement unit (mm, cm, m, in, ft).
- View all derived properties in the output grid.
- Use the bar chart to visually compare linear dimensions.
- Consult the reference table for formulas and topology (faces, edges, vertices).
Formula used
Face diagonal = a√2
Space diagonal = a√3
Surface area = 6a²
Volume = a³
Inscribed sphere r = a/2
Midsphere ρ = a√2/2
Circumscribed sphere R = a√3/2
Total edge length = 12aExample Calculation
Result: For mode=side, val=1, unit=cm, the tool returns the solved cube outputs shown in the result cards.
This example uses a realistic input set from the calculator workflow. After entry, the calculator applies the built-in cube formulas and reports derived values, checks, and classifications automatically.
Tips & Best Practices
- Entering the volume is handy for finding the side length of a container: a = ∛V.
- The space diagonal is the longest straight line that fits inside a cube.
- The circumscribed sphere radius is always √3/2 ≈ 0.866 times the side length.
- For unit cubes (a = 1), surface area = 6, volume = 1, space diagonal = √3 ≈ 1.732.
- Use the surface area mode to figure out how much wrapping paper you need.
When To Use This 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. Use it when you need a repeatable calculation in the math / geometry category and want the setup, result, and supporting values kept together. This is especially helpful when small input changes, unit choices, or rounding decisions can change the final number.
How To Check The Result
Start by confirming that the inputs match the formula shown on the page. Then compare the main output with the worked example and any secondary values shown by the calculator. If the result will be used in another calculation, keep extra precision until the final step and record the assumptions beside the number.
Practical Notes
Treat the result as a calculation aid rather than a substitute for context. For schoolwork, include the formula and substitution steps. For planning, technical, financial, or health-related decisions, verify important numbers against primary records, current rules, or a qualified professional before acting on them.
Sources & Methodology
Last updated:
Frequently Asked Questions
Take the cube root of the volume: a = ∛V. For V = 1000, a = 10.
The face diagonal runs across one face (a√2). The space diagonal runs through the interior from one vertex to the opposite vertex (a√3).
The largest sphere that fits inside the cube, touching all six faces at their centres. Its radius is a/2.
The smallest sphere that contains the entire cube, passing through all eight vertices. Its radius is a√3/2.
A cube has 6 faces, 12 edges, and 8 vertices. It satisfies Euler's formula: V − E + F = 2.
Yes. A cube is a rectangular prism (cuboid) where all three dimensions are equal.
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