Square Millimeters and Square Meters Converter

Using the Square Millimeters and Square Meters Converter

This converter can help with finding equivalent values between 2 metric units of area, the square millimeters, and the square meters.

Start by choosing the spelling of the word ‘meter’ throughout the text, which will also affect how the word millimeter is spelled. Your choice consists of the British spelling (metre) or the American spelling (meter). The choice can be made right at the top of the converter.

The next task is to correctly choose your input and output units.

The input units are the units from which the value you are trying to convert comes. This unit is selected in the ‘CONVERT FROM’ section of the converter. You can choose between square millimeters ($mm^2$) and square meters ($m^2$).

A similar choice, but for the output units (the units your result will be in) can be made in the ‘CONVERT TO’ section. The same 2 units can be chosen here.

You can also keep the default setting of the units, or you can choose to swap them by clicking on the icon with the 2 arrows headed in opposite directions. 

Once you are happy with your choice of input and output values, you can move towards the ‘VALUE TO CONVERT’ part of the converter, where you simply type in the input value as a decimal number (using the decimal dot).

Select the number of decimal places you want your result rounded toward, and click on ‘CONVERT’.

Your result will appear below the converter as a decimal number rounded to the desired number of decimal places, alongside the conversion rate between your input and output units. 

A ‘COPY’ icon will appear with the result as well, allowing for simple copying and pasting of the result, if you need to use it in another piece of writing elsewhere. 

Converting Square Millimeters and Square Meters Manually

The easiest way to convert between 2 units manually is to define conversion formulae, which are derived from conversion rates.

The conversion rates you see included along your results were derived from the original units of length (in this case the millimeter and the meter) and their conversion rates. The process starts by stating that 1 meter is equal to 1,000 millimeters. 

If we put this relationship to the power of 2, we get the conversion rate for the square version of the units.

The said relationship would be $1,000^2$ $mm^2$ = 1,000,000 $mm^2$ = 1 $m^2$.

Based on this relationship, we define the conversion rate of $m^2$ to $mm^2$ as 1:1,000,000. From here, we can derive 2 simple formulae that can help us convert the units manually.

The following 2 examples will demonstrate the usage of these formulae in practice. 

EXAMPLE 1: A sheet of textile with an area of 2.98 $m^2$ needs to have its area converted into $mm^2$ in order for us to be able to design a pattern on it with a computer. What is the area of this sheet in $mm^2$?

This problem has $m^2$ as the input and $mm^2$ as the output. That means that we will be using the first formula, as the subject is the output value. Using formulae where your output is the subject makes calculations much easier. We substitute 2.98 for $m^2$ and count as follows.

EXAMPLE 2: What is the area in $m^2$ of a tile with an area of 400,700 $mm^2$?

Here we see our input is in $mm^2$ and output is in $m^2$. That makes the second formula the most suitable one, where we simply substitute $mm^2$ with 400,700 and then calculate the $m^2$ as follows.

Converting Square Millimeters and Square Meters from Memory

Converting between metric units of area is fairly easy to do even from memory, as the conversion rate is defined by the number 1,000,000.

This means, that to get the output values we desire, we simply multiply or divide by 1,000,000.

The following 2 tips can help you divide or multiply a number by a million from memory.

• When multiplying by 1,000,000, we must move the decimal dot 6 positions to the right, while filling any missing tailing digits with zeroes.
• When dividing by 1,000,000, we must move the decimal dot 6 positions to the left, while filling any missing digits at the front with zeroes, alongside an extra zero before the decimal dot (in the position of ones), unless a digit is available for this position.

The 2 examples below will demonstrate this technique.

EXAMPLE 1: Convert 56,830 $mm^2$ into $m^2$.

This problem calls for dividing 56,830 by a million. Hence we move the decimal dot 6 positions to the right. However, we do not see the decimal dot (meaning we should imagine it after the last digit), hence we put all 5 digits after the decimal dot. The movement must be done for 6 positions, so we fill both the position of tenths and ones with an extra zero. We get 0.056830 $m^2$ as the result. 

EXAMPLE 2: Convert 4.22 $m^2$ into $mm^2$.

Here we multiply 4.22 by 1,000,000, hence we move the decimal dot 6 positions to the right. We see only 2 digits after the decimal dot, hence we fill the remaining 4 with zeroes. This results in 4,220,000 $mm^2$.