Square Millimeters and Square Feet Converter

Using the Square Millimeters and Square Feet Converter

This converter allows you to convert between the smallest commonly used metric unit of area (the square millimeter) and the commonly used imperial unit of area (the square foot).

Start by choosing the spelling of the word ‘meter’, which directly affects how the word millimeter will be spelled in the converter. The choice is between the American spelling of ‘meter’ or the British spelling of ‘metre’.

Choose your input unit in the ‘CONVERT FROM’ section. Your choice is between the square millimeters ($mm^2$) and the square feet ($ft^2$).

In the ‘CONVERT TO’ section, you choose your output unit out of the same 2 options.

An alternative to manually choosing each unit at a time is to either stick with the default settings or to swap them using the icon with 2 arrows headed in opposite direction. 

Once your input and output units have been selected, type in the value of the input unit. You can write it in the ‘VALUE TO CONVERT’ section of the converter. Type the value as a decimal number using the decimal dot.

The final step requires selecting the number of decimal places we would like our result rounded toward. 

Finish by clicking on the ‘CONVERT’ icon.

Your result will appear below the converter, alongside a convenient ‘COPY’ icon, that allows you to easily copy and paste the result. Additionally, you will also receive a conversion rate between the input and output units to complement your result. 

Converting Square Millimeters and Square Feet Manually

To convert between 2 units of area, we must know their conversion rates. The conversion rates are determined by equivalent values of a unit to the value of 1 for the other unit. 

To find these values for the square units, we start by looking at the units of length, where the following is true.

• 1 foot is equivalent to approximately 304.8 mm.
• 1 mm is equivalent to approximately 0.003281 ft. 

Since our units of area are both square units, the conversion rate between them is going to be determined by the square values of the above-mentioned conversions of units of length.

The following will happen if we put all of the values and units in each expression to the power of 2.

• 1 square foot is equivalent to approximately 304.82 $mm^2$, which is 92,903.04 $mm^2$.
• 1 square millimeter is equivalent to approximately 0.0032812 $ft^2$, which is 0.00001076496 $ft^2$.

We will be working with rounded values of 92,903 and 0.00001 for the sake of convenience. For more accurate results, feel free to use the converter above.

The conversion rates we calculated will now determine the constants in the 2 formulae we will be using.

The choice of the right formula is a matter of observing what is your input and what is your output unit. The first formula is ideal for problems where $ft^2$ is the input, while the second formula is better for problems where $mm^2$ is the input.

The following examples will demonstrate the usage of these formulae in practice.

EXAMPLE 1: What is the area in $mm^2$ of a tablecloth with an area of 1.22 $ft^2$?

This problem requires an input in $ft^2$ and an output in $mm^2$. That makes the first formula the most suitable one for solving this problem quickly by substituting 1.22 for $ft^2$.

EXAMPLE 2: A small shard of glass has a surface area of 28,380 $mm^2$. What is the surface area of this shard in $ft^2$?

Given that our input is in $mm^2$, we will be using the first formula, where we substitute 28,380 for $mm^2$ and calculate as follows.

Approximating Square Millimeters and Square Feet

Although the conversion rates between the 2 units are not expressed in very neat numbers, the truth is that for the use of approximation, both units are fairly close to a round number. 

The conversion rate was determined by the values of 92,903 and 1/92,903 = 0.00001076496.

Since 92,903 is fairly close to 10,000, which results in the inverse relationship of 0.00001, we can safely say, that for the purpose of approximation, the following rules can be used.

• When approximating square feet to square millimeters, we multiply the value by 10,000. This means that we simply move the decimal dot 4 places to the right and fill any missing digits with zeroes.
• When approximating square millimeters to square feet, we divide the value by 10,000. This means that we have to move the decimal dot 4 places to the left and fill any missing digits with zeroes, including the extra digit before the decimal dot.

Let’s look at 2 examples of calculating with the approximation method and then comparing the result with a result from our converter.

EXAMPLE 1: Convert 732 $mm^2$ to $ft^2$.

The converter gives us a value of 0.0079. Our approximation method yields a result of 0.00732. As we can see, the approximation is reasonably close. 

EXAMPLE 2: Convert 2.1 $ft^2$ to $mm^2$.

The converter gives us a value of 195,096.38 $mm^2$. Our method gives us a value of 210,000 $mm^2$ showing, that although being a bit off, for the purpose of approximating, we still get a fairly close result.