About

A cube is a regular hexahedron - the only Platonic solid bounded by six congruent squares. A single parameter, the edge length a, determines every metric: volume scales as a³, surface area as 6a², and the space diagonal as a⋅√3. Errors in edge measurement propagate cubically into volume - a 2% overestimate of a inflates computed volume by roughly 6%. This matters in concrete pours, container sizing, packaging optimization, and material cost estimation where cubic quantities translate directly to cost.

This calculator derives all geometric properties from a single edge input, including circumscribed and inscribed sphere radii used in sphere-packing and collision-detection problems. The interactive 3D wireframe lets you verify orientation and proportions visually. Note: all results assume a mathematically perfect cube with zero manufacturing tolerance. For real-world objects, account for chamfers, radii, and dimensional variance per ISO 2768 tolerances.

Formulas

All cube properties derive from a single edge length a.

V = a³

Volume V is the cube of the edge length.

S = 6a²

Total surface area S is six identical square faces.

d_f = a ⋅ √2

Face diagonal d_f connects opposite vertices on one face.

d_s = a ⋅ √3

Space diagonal d_s connects opposite vertices through the interior of the cube.

R = a ⋅ √32

Circumscribed sphere radius R passes through all 8 vertices.

r = a2

Inscribed sphere radius r is tangent to all 6 faces.

ρ = a ⋅ √22

Midsphere radius ρ is tangent to all 12 edges.

L = 12 ⋅ a

Total edge length L is the sum of all 12 edges.

Where a = edge length, V = volume, S = surface area, d_f = face diagonal, d_s = space diagonal, R = circumscribed sphere radius, r = inscribed sphere radius, ρ = midsphere radius, L = total edge length.

Reference Data

Edge Length (a)	Volume (V)	Surface Area (S)	Face Diagonal (d_f)	Space Diagonal (d_s)	Circumscribed R	Inscribed r
1	1	6	1.414	1.732	0.866	0.500
2	8	24	2.828	3.464	1.732	1.000
3	27	54	4.243	5.196	2.598	1.500
4	64	96	5.657	6.928	3.464	2.000
5	125	150	7.071	8.660	4.330	2.500
6	216	216	8.485	10.392	5.196	3.000
7	343	294	9.899	12.124	6.062	3.500
8	512	384	11.314	13.856	6.928	4.000
9	729	486	12.728	15.588	7.794	4.500
10	1000	600	14.142	17.321	8.660	5.000
12	1728	864	16.971	20.785	10.392	6.000
15	3375	1350	21.213	25.981	12.990	7.500
20	8000	2400	28.284	34.641	17.321	10.000
25	15625	3750	35.355	43.301	21.651	12.500
50	125000	15000	70.711	86.603	43.301	25.000
100	1000000	60000	141.421	173.205	86.603	50.000

Frequently Asked Questions

Volume scales as a³, so relative error is amplified approximately threefold. If you measure the edge with 1% error, the volume error approaches 3%. For a 10cm cube measured as 10.1cm, true volume is 1000cm³ but computed volume becomes 1030.301cm³ - a 3.03% overestimate. Use calipers with ±0.01mm resolution for precision applications.

Setting 6a² = a³ and solving gives a = 6. At edge length 6 (in any consistent unit), both the surface area and the volume equal 216. Below a = 6, surface area exceeds volume numerically. Above it, volume dominates. This crossover is relevant in heat transfer analysis where the surface-to-volume ratio determines cooling rate.

A cube has three concentric spheres. The inscribed sphere (insphere, radius r = a÷2) touches all 6 faces. The midsphere (radius ρ = a⋅√2÷2) touches all 12 edges at their midpoints. The circumscribed sphere (circumsphere, radius R = a⋅√3÷2) passes through all 8 vertices. The ratio r : ρ : R = 1 : √2 : √3 holds for all cubes.

Multiply the volume V by the material density ρ_m: mass m = ρ_m × V. For example, a steel cube (ρ_m = 7850 kg/m³) with edge 0.1m has volume 0.001m³ and weighs 7.85kg. Ensure you convert edge length to meters before computing if density is in kg/m³.

No. This tool assumes a mathematically perfect cube where all 12 edges are equal and all 6 faces are perfect squares. If your object is a rectangular parallelepiped (cuboid) with differing edge lengths a, b, c, the volume formula becomes V = a × b × c and the space diagonal becomes √(a² + b² + c²). Use a cuboid calculator for those cases.

The surface-to-volume ratio is 6a² ÷ a³ = 6÷a. As the cube grows, this ratio decreases - large cubes have proportionally less surface area per unit volume. This governs heat dissipation rates, chemical reaction speeds in catalysis, drug dissolution rates in pharmacology, and structural load distribution. A 1cm cube has a ratio of 6cm⁻¹. A 1m cube has 0.06cm⁻¹ - 100 times less relative surface.