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.

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

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 cm².

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 m² to cm² as 100 x 100 = 10,000 cm².

From here, we can see that the relationship between square meters and square centimeters is, that 1 m² is equivalent to 10,000 cm².

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

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.

m^2 = cm^2 * 0.0001 

An alternative point of view would be to simply divide the cm² by 10,000, which creates the following formula.

m^2 = cm^2  \div 10,000

When converting square meters into square centimeters, we must multiply the m² by 10,000, leading to the following formula.

cm^2 = m^2 * 10,000

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

EXAMPLE 1: What is the equivalent area in m² of a cardboard sheet that has 4,576 cm²?

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 cm² for squared centimeters.

m^2 = cm^2 * 0.0001 \\= 4,567 * 0.0001 \\= 0.4567 ~m^2

m^2 = cm^2 \div 10,000 \\= 4,567 \div 10,000 \\= 0.4567 ~m^2

EXAMPLE 2: A sheet of textile has an area of 2.77 m². What is the equivalent area of this sheet in cm²?

Applying the second formula will lead to a quick solution to this problem after we substitute 2.77 instead of m² and solve.

cm^2 = m^2 * 10,000 \\= 2.77 * 10,000 \\= 27,700 ~cm^2

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 cm² to m²) or we multiply by 10,000 (when converting m² to cm²).

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 cm² to m²), 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 m² to cm²), 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 cm² to m².

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 m² as the result of this conversion.

EXAMPLE 2: Convert 0.231 m² to cm².

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 cm².

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.