Diagonal hides √3
The space diagonal is a√3 because you stack two right triangles: one face diagonal (a√2), then another right angle into 3D.
3D Pythagoras
Cube Calculator — Edge, Surface Area, Volume
Diagram & Inputs
Tip: Enter any one value (a, S, V, or d). The calculator checks consistency if you provide multiple values.
Results
How the Cube Calculator Works
A cube is a regular hexahedron with all edges the same length a. From that single measure you can compute the surface area S = 6a², the volume V = a³, and the space diagonal (corner-to-corner through the interior) d = a√3. This tool solves the cube by inferring a from whatever you provide, then deriving the rest.
Provide any one value—edge length, surface area, volume, or space diagonal—and choose a length unit plus decimal places. If you enter more than one value, the calculator checks for consistency within a small numerical tolerance and warns you if things don’t line up (often due to mixed units or rounding).
- From S:
a = √(S/6) - From V:
a = ³√V - From d:
a = d/√3
Units matter: a uses a length unit (e.g., cm), S uses the squared unit (e.g., cm²), and V uses the cubed unit (e.g., cm³). All computation runs locally in your browser.
Formulas & Relationships
- Surface area:
S = 6a² - Volume:
V = a³ - Space diagonal:
d = a√3 - Face diagonal:
a√2(not required here but useful) - Solve for a:
a = √(S/6) = ³√V = d/√3
Common pitfalls: mixing units between inputs, entering negative values, or rounding too early. If you see an inconsistency warning, double-check your unit labels.
5 Fun Facts about Cubes
Six faces, two formulas
Surface area S = 6a² and volume V = a³ make a cube a rare shape where both 2D and 3D measures come from the same edge.
One edge rules
Dice aren’t perfect cubes
Casino dice have beveled edges and drilled pips. That shifts mass slightly, so manufacturers balance them with paint to keep rolls fair.
Real-world cube
Cube maps your sky
Game engines unwrap environments into six cube faces (a “cubemap”). Your GPU samples those faces to fake a seamless 360° sky.
Graphics hack
Rubik’s math fest
A 3×3×3 Rubik’s Cube has 43 quintillion states, yet God’s number is 20—any scramble can be solved in 20 moves or fewer.
Puzzle lore
Cube Calculator: FAQs
Which inputs are valid to solve a cube?
Any one of edge length (a), surface area (S), or volume (V). Two or more values are also fine.
What formulas are used?
S = 6a², V = a³, and space diagonal d = a√3.
Does the calculator keep my data private?
Yes. Computation is entirely client-side; nothing is uploaded.
Can I change units or decimal places?
Yes. Choose a length unit for a. Surface area uses the squared unit; volume uses the cubed unit.