Converting centimeters to meters is easy, but people get confused converting square centimeters to square meters. These two example problems show how to convert cm^{2} to m^{2} and back again.

### cm^{2} to m^{2} Conversion Factor

The conversion factor between cm^{2} to m^{2} is

10,000 cm^{2} = 1 m^{2}

or

10^{4} cm^{2} = 1 m^{2}

How do you get that? Start with the conversion from cm to m.

100 cm = 1 m

A square meter is a square 1 meter wide and 1 meter tall.

1 m^{2} = 1 m x 1 m

Substitute the conversion factor for meter to centimeter

1 m^{2} = (100 cm) x (100 cm)

1 m^{2} = 10,000 cm^{2} = 10^{4} cm^{2}

### cm^{2} to m^{2} Conversion Example Problem

**Question:** How many square meters are in 75,000 square centimeters?

Multiply the conversion factor between cm^{2} and m^{2} by the 75,000 cm^{2}. Put the unit you want to be canceled out in the denominator.

This cancels out the undesired unit, leaving the unit we want.

7.5 m^{2} = x m^{2}

**Answer:** There are 7.5 square meters in 75,000 square centimeters.

### m^{2} to cm^{2} Conversion Example Problem

**Question:** How many square centimeters are in 3 square meters?

Multiply the conversion factor between cm^{2} and m^{2} by the 3 m^{2}. Put the unit you want to be canceled out in the denominator.

This setup allows us to cancel out the unneeded m^{2} units.

30,000 cm^{2} = x cm^{2}

**Answer:** There are 30,000 cm^{2} in 3 m^{2}.