Square Meters and Square Centimeters Converter

Using the Square Meters and Square Centimeters Converter

This converter allows you to find equivalent values between two metric units of area, square meters, and square centimeters. Both units are used commonly in the metric system and being able to convert between them can prove very useful.

Start off by deciding whether you want to use the American spelling or the British spelling of the words ‘meter’ and ‘centimeter’ (spelled ‘metre’ and ‘centimetre’ in the British version).

Then proceed to choose your input and output units.

• You can choose between square centimeters ($cm^2$) and square meters ($m^2$) in the ‘CONVERT FROM’ section of the converter. This will determine the unit of your input value.
• Choosing the unit of your output value takes place in the ‘CONVERT TO’ section. The choice is the same as for the input unit.
• Another way to choose the input and output units is to either stick with the default settings or swap them by clicking on the icon with the 2 arrows headed in opposite directions. 

After you have set your input and output units, it is time to move toward the conversion.

• Write the input value as a decimal number into the ‘VALUE TO CONVERT’ part of the converter. Do not forget to use the decimal dot and not a comma.
• Select the number of decimal places you want your result rounded toward.
• Click on ‘CONVERT’.

You will receive your result as a decimal number rounded toward the desired number of decimal places, alongside a conversion rate between your input and output unit, and a convenient ‘COPY’ button that allows for easy copying and pasting of the result elsewhere. 

Converting Square Meters and Square Centimeters Manually

The conversion rates between metric units are always determined by a multiple of 10, making it fairly simple to convert them manually, in comparison to converting imperial units or imperial and metric units. 

We must first look at the relationship between a meter and a centimeter, as these two units of length define the units of area.

A square centimeter is equivalent in area to a square with a side length of 1 centimeter. This leads to the area being defined as 1 x 1 = 1 $cm^2$.

A square meter is equivalent in area to a square with a side length of 1 meter. Since 1 meter is equivalent to 100 cm, we can easily convert 1 $m^2$ to $cm^2$ as 100 x 100 = 10,000 $cm^2$.

From here, we can see that the relationship between square meters and square centimeters is, that 1 $m^2$ is equivalent to 10,000 $cm^2$.

Due to these relationships between the units, the following conversion rates are established.

• 1 $m^2$ is equivalent to 10,000 $cm^2$, so the conversion rate of square meters to square centimeters is 1:10,000.
• 1 $cm^2$ is equivalent to 1/10,000 $m^2$, or simply 0.0001 $m^2$. This leads to the conversion rate between square centimeters and square meters being 1:0.0001. A simpler way is to express it in reverse order as 10,000:1.

The conversion rates lead to the creation of 2 distinct formulae, that can help us convert manually.

When converting square centimeters to square meters, it is good to have the square meters as the subject of the formula. Hence, we use the following formula.

An alternative point of view would be to simply divide the $cm^2$ by 10,000, which creates the following formula.

When converting square meters into square centimeters, we must multiply the $m^2$ by 10,000, leading to the following formula.

Let’s observe 2 solved examples that demonstrate the usage of these formulae in practice.

EXAMPLE 1: What is the equivalent area in $m^2$ of a cardboard sheet that has 4,576 $cm^2$?

With an input in squared centimeters and output in square meters, the first formula is the best to use for solving this problem, as the output unit is the subject of this formula. We will demonstrate how both versions of this formula (the version using division and the version using multiplication) lead to the same result after substituting 4,567 $cm^2$ for squared centimeters.

EXAMPLE 2: A sheet of textile has an area of 2.77 $m^2$. What is the equivalent area of this sheet in $cm^2$?

Applying the second formula will lead to a quick solution to this problem after we substitute 2.77 instead of $m^2$ and solve. 

Converting Square Meters and Square Centimeters from Memory

Since we are converting two units with a conversion rate defined by the number 10,000, conversion can be done easily from memory, without the need for formulae or calculators.

By looking back at the formulae, we realize that we either divide by 10,000 (when converting from $cm^2$ to $m^2$) or we multiply by 10,000 (when converting $m^2$ to $cm^2$).

Like this, we can offer a simple guide for conversions from memory.

• When we need to divide by 10,000 (in our case when we convert from $cm^2$ to $m^2$), we move the decimal point 4 positions to the left. If there are not enough digits to fill the 4 moves, we add a zero to the left side of the number and then a zero in front of the decimal dot. 
• When we need to multiply by 10,000 (in our case when we convert from $m^2$ to $cm^2$), we move the decimal point 4 positions to the right. If needed, we add zeroes at the end of the number for each position that is not filled with a written down decimal number.

The two examples below will demonstrate the usage of this method when solving problems.

EXAMPLE 1: Convert 17.22 $cm^2$ to $m^2$.

We must move the decimal dot 4 positions to the left. We see only 2 numbers available to the left of the decimal dot, hence we fill in the 2 extra spaces needed with zeroes and then insert one more zero to the left of the decimal dot. This results in 0.001722 $m^2$ as the result of this conversion.

EXAMPLE 2: Convert 0.231 $m^2$ to $cm^2$.

Here, we must move the decimal dot 4 positions to the right. We see only 3 available numbers, so we add a zero at the end. The result of such conversion is then 2,310 $cm^2$.

How Big is a Square Meter?

In order to gain some perspective on the size of a square meter, here is a list of a few everyday items and their approximate areas in square meters.

• The doors of a fridge usually have an area of just a little below 2 $m^2$.
• An average studio apartment has an area of approximately 25 $m^2$.
• Most doors have an area of about 2 to 2.5 $m^2$.
• A doormat has an area of approximately 0.5 $m^2$. Hence, two doormats next to each other have an area of approximately 1 $m^2$.
• A 60-inch TV has an area of a little below 1 $m^2$.