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.
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 instantly 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 any geometry homework involving cubes.
This cube calculator reduces manual rework when you need quick checks for assignments, exam prep, and design calculations. You can enter Input mode, Unit and immediately see dependent measurements, validity checks, and geometry relationships in one place. That makes it easier to catch input mistakes early and confirm your final answer before moving to the next step.
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 = 12a
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.
This page is tailored to cube, with outputs tied directly to the form fields (Input mode, Unit). Instead of a one-line formula dump, it consolidates validation, derived metrics, and interpretation so you can solve and verify in one pass.
Use this tool for homework checks, worksheet generation, tutoring walkthroughs, and quick engineering geometry estimates. Presets and visual output blocks make it easier to compare scenarios and understand how each input affects the final result.
Keep units consistent, match each value to the correct field, and watch validity indicators before using the final numbers. If your case looks off, change one input at a time and use the output details to identify the mismatch quickly.
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.