# Cube Calculator

## Cube Shape

a = side lengths

f = face diagonal

d = solid diagonal

S = surface area

V = volume

## Calculator Use

Enter any 1 known variable for a cube into this online calculator to calculate 4 other unknown variables. A cube is a special case where l = w = h for a rectangular prism.

**Units:** Note that units are shown for convenience but do not affect the calculations. The units are in place to give an indication of the order of the results such as ft, ft^{2} or ft^{3}. For example, if you are starting with a in mm, your calculations will result with V in mm^{3}, S in mm^{2} and d in mm.

## Formulas for a cube:

**Volume of a cube:****V = a**^{3}

**Surface area of a cube:**- the area of each face (a x a) times 6 faces
**S = 6a**^{2}

**Face diagonal of a cube**:- By the pythagorean theorem we know that
- f
^{2}= a^{2}+ a^{2} - Then f
^{2}= 2a^{2} - solving for f we get
**f = a√2**

**Diagonal of the solid cube**:- Again, by the pythagorean theorem we know that
- d
^{2}= a^{2}+ f^{2} - substituting f into this equation we get
- d
^{2}= a^{2}+ (a√2)^{2}= a^{2}+ 2a^{2}= 3a^{2} - solving for d we get
**d = a√3**

A cube is a special case of a rectangular prism where l = w = h.

For more information on cuboids see: Weisstein, Eric W. "Cuboid." From
*MathWorld*--A Wolfram Web Resource, Cube.