Cube Calculator: Volume, Surface Area, Diagonals and Edge from Any One Value

How it works

V = a³ · S = 6a² · face area = a² · f = a√2 · d = a√3 · a = ∛V = √(S ÷ 6) = f ÷ √2 = d ÷ √3 · inscribed sphere r = a ÷ 2 · circumscribed sphere R = a√3 ÷ 2 · S ÷ V = 6 ÷ a

A cube has 6 square faces, 12 equal edges and 8 corners, so a single measurement fixes everything else. From the edge a: the volume is a³, the surface area is 6a², a face diagonal (corner to corner across one face) is a√2 by Pythagoras, and the space diagonal (corner to opposite corner through the middle) is a√3, since it is the hypotenuse of the face diagonal and one more edge. Each formula can be turned around, so you can start from a volume, an area or either diagonal and the calculator first recovers the edge, then shows every other measure with the steps. Pick a unit to get the capacity in liters and US gallons (useful for a cubic tank, box or planter), and add a material density under More options to get the mass. The results also give the radii of the spheres that fit inside (a ÷ 2) and around (a√3 ÷ 2) the cube, the total edge length and the surface-area-to-volume ratio, which halves each time the edge doubles. The square-and-cube calculator just raises a number to the 2nd or 3rd power, and the rectangular-prism calculator handles boxes whose sides differ. This page solves the solid cube from whichever value you know.

Worked example

A cube has 4 in edges. Volume = 4³ = 64 in³; surface area = 6 × 4² = 96 in², each face 16 in²; face diagonal = 4 × 1.414214 = 5.65685 in; space diagonal = 4 × 1.732051 = 6.9282 in. The 12 edges total 48 in, an inscribed sphere has radius 2 in and a circumscribed sphere 3.4641 in. As a container it holds 64 in³ = 1.04877 L, or 0.277056 US gallons.

Sources: CalculatorSoup: Cube calculator (solve from a, f, d, S or V) · Omni Calculator: Cube calculator (Rubik’s cube example) · RedCrab: Cube formulas and a = 5 example

Frequently asked questions