Area is used to indicate how large a surface is. For example, it can be the area of a sheet of paper, a floor or a field. The unit of area in the SI system is the square metre \( \text{m}^2 \).

 

 

Common area units

Today, the square metre is used as the standard unit, but there are many practical subunits and multiples that are easier to use depending on the situation.

 

Unit	Symbol	Relation
square millimetre	mm²	\( \large 1\ \text{mm}^2 = 0.000\,001\ \text{m}^2 \)
square centimetre	cm²	\( \large 1\ \text{cm}^2 = 0.0001\ \text{m}^2 \)
square decimetre	dm²	\( \large 1\ \text{dm}^2 = 0.01\ \text{m}^2 \)
square metre	m²	\( \large 1\ \text{m}^2 = 1\ \text{m}^2 \)
square kilometre	km²	\( \large 1\ \text{km}^2 = 1\,000\,000\ \text{m}^2 \)

 

 

What does square metre mean?

A square metre is the area of a square where each side is one metre long.

 

$$ \large 1\ \text{m}^2 = 1\ \text{m} \cdot 1\ \text{m} $$

 

In the same way, a square centimetre \( \text{cm}^2 \) means a square with sides of one centimetre. When converting between area units, you must remember that the length unit appears twice — once for each dimension (width and length).

 

 

Conversion between area units

The conversion between area units follows the same idea as for length, but since there are two dimensions, the conversion factor must be raised to the second power. This means you multiply or divide by \( 10^2 = 100 \) for each step instead of by 10.

 

From metres to centimetres, for example:

 

$$ \large 1\ \text{m} = 100\ \text{cm} $$

 

Therefore:

 

$$ \large 1\ \text{m}^2 = (100\ \text{cm})^2 = 100^2\ \text{cm}^2 = 10\,000\ \text{cm}^2 $$

 

Note that the exponent multiplies itself. When the unit is squared, the conversion factor must also be squared. The same applies when converting from larger to smaller units:

 

$$ \large 1\ \text{dm}^2 = (0.1\ \text{m})^2 = 0.01\ \text{m}^2 $$

 

 

Example

A square has sides of 30 cm. What is the area in square metres?

 

$$ \large 30\ \text{cm} = 0.3\ \text{m} $$

$$ \large A = 0.3 \cdot 0.3 = 0.09\ \text{m}^2 $$

 

The area of the square is therefore \( \large 0.09\ \text{m}^2 \).

 

 

Summary

When converting area units, you should:

 

• remember that the factor must be squared because area has two dimensions
• move the decimal point two places for each step instead of one
• use the same prefixes as for length, but with the square symbol

 

 

In this way, the logic of the metric system provides a clear connection between length and area, because everything is based on powers of ten.