# Dimensions of length, area and volume

**Dimensions of length, area and volume**

The following rules apply for length, area and volume:

Length: one dimensional, length, units are mm, cm, m, km, inch foot

Area: two dimensional, length x length, units are mm², cm², m², hectare, km², square inch, square foot

Volume: three dimensional, length x length x length, units are mm³, cm³, m³, cubic inch, cubic foot

**Using dimensions to check formulas**

Dimensions can be used to check if a formula is correct to find out if it represents a length, area or volume.

Note: L in brackets [L] represents a dimension of length.

**Length**

When checking the length of a perimeter: the formula is length [L] + length [L] + length [L]

Note: multiple [L] added together will still be [L]

**Area**

Area on the other hand area is two-dimensional, therefore it is derived from multiplying two lengths together.

For example: [L] × [L] = [L²]

If more than two areas are added together, it is still an area, therefore: [L²] + [L²] = [L²]

**Volume**

Volumes is three dimensional and is derived by multiplying three lengths together, therefore [L] × [L] × [L] = [L³]

**Consistency in formulas**

Inconsistent formulas includes an expression where 2 dimensions are added to an expression with 3 dimensions.

Therefore only the following can be added together:

- Lengths to lengths
- Areas to areas
- Volumes to volumes