Difference between Square Metres and Metres Squared

Metre is the unit of length in the SI system and square metres is the SI units for calculating area.  The confusion arises when we see metres squared written or spoken. People cannot make out the difference between square metres and metres squared and assume they are the same, which they are not!

For example

The correct size of the room

If a square room has a length of 2 metres and is 2 metres in breadth, you can easily calculate its area with this formula.

Area= Length x Breadth A=l × b
2 metres x 2 metres A = 2 m × 2 m
4 square metres A = 4 m2

The room has an area of 4 square metres

If you say that this is 4 metres squared what you mean is an area which has the length of 4 metres and you are multiplying it by a breadth of 4 metres which would give you an area of 16 square metres and not 4 square metres. That gives you a very different area.

Overestimating the size of the room by giving the wrong units.
An Area = 4 metres squared
4 metres x 4 metres
16 square metres

So if someone asks you the correct area of the room mentioned above, you should say that the area is 4 square metres both of which are correct answers.

But beware more confusion arises as 1 m x 1 m= 1 square metres while 1 metre squared is also the same size as 1 × 1 = 1. You just get there by different routes.

Even though the unit looks like it is written as metres squared you pronounce it square metres.

Hope this clears any confusion you might have on this one!

Actually I ought to put a post script in!

The same applies to volumes
The correct SI unit for volume is cubic metres, (or in Chemistry they might use cubic centimetres). If you say metres cubed you mean that this is the length of one side and you need to cube this value to get the volume.

This cube could be described as 125 cubic centimetres or 5 centimetres cubed.

I wasn’t sure that I ought to have posted this, but it looks like it is less well understood than I imagined, definitely my only popular post!

Signature

Thanks to Andy and Gareth Lewis Maths tuition for these additional thoughts.

Hi, the examples that you have given for metre square and square metre are incorrect.
2 metre square = 4 square metre (2×2=4)
2 square metre = 1 metre x 2 metre (1×2=2)

Andy

XxxxxxxxxxxxxxxxxxxxxxxxX

Good article. Andy’s alternative examples are also correct.

As well as the difference in size between square metres and metres squared (except when you have zero of each or one of each) there is a difference in shape. A metre square is a square with sides one metre in length – it refers to the shape and the side length, not the area. By contrast, a square metre is an area and can be any shape. A square metre could, for example, be in the shape of an oblong of dimensions 50cm x 2m, or in the shape of an A0 sheet, or 16 A4 sheets in any pattern.


26 thoughts on “Difference between Square Metres and Metres Squared”

  1. Hi, the examples that you have given for metre square and square metre are incorrect.
    2 metre square = 4 square metre (2×2=4)
    2 square metre = 1 metre x 2 metre (1×2=2)

    1. Hmm, I agree with you Andy. But this is where the problem starts 2m x 1m = 2 square metres but we agree that a square of side 2m x 2m would be 4 square metres (4m2) that is why it is better to use the correct term and use square metres for area! Thank you for your help! What would you say to a square of side 1.414 m?

    2. Good article. Andy’s alternative examples are also correct.

      As well as the difference in size between square metres and metres squared (except when you have zero of each or one of each) there is a difference in shape. A metre square is a square with sides one metre in length – it refers to the shape and the side length, not the area. By contrast, a square metre is an area and can be any shape. A square metre could, for example, be in the shape of an oblong of dimensions 50cm x 2m, or in the shape of an A0 sheet, or 16 A4 sheets in any pattern.

      1. The problem is trying to find out what is the legal aspect of ordering something that is written as 2 m squared and then recieving something that is only 2 square meters ?

        1. If I was the customer I’d want it clear in the order.
          I think I need another blog post on why it is written and said differently.

  2. I always thought that to write 4 square metres,
    It was written as 4 sq mtrs ( 2×2 ) = 4
    And 4 mtrs square is written as 4 mtrs 2. (4×4) = 16

      1. This is not the SI (Standard Internationale) the world standard of writing out square metres and metres squared. The SI symbol for m is m and m^2 is square metres.

    1. ”I always thought that to write 4 square metres, it was written as 4 sq mtrs ( 2×2 ) = 4”

      Square metres, sq m and sometimes sq mtrs are all used to denote the same thing, a unit of area. The symbol for that unit is – by international agreement – m followed by a superscript 2, which admittedly looks like it should be pronounced “metres squared” but is actually still pronounced “square metres”.

      “And 4 mtrs square is written as 4 mtrs 2. (4×4) = 16”

      A square with side length 4m can be described verbally as “4 metres, squared” but not “4, metres squared”. The latter would suggest that there is a unit called “metres squared” which doesn’t exist (it’s just the symbol for “square metres” looks like it should be pronounced “metres squared”).

      In symbols, it’s (4m)^2, not 4m^2 which is pronounced 4 square metres and is only a quarter of the size.

      For those familiar with PSI for measuring pressures in tyres and so on, PSI stands for “Pounds per square inch”. It’s not an SI unit, but follows the same convention when describing the area. It doesn’t matter whether you measure in mm, cm, m, inches or anything else, the corresponding units of area are “square units”, never “units squared” despite the confusing symbols. Some teachers when challenged attempt to justify using the name ”metres squared” for areas by claiming that they do it differently and it’s an alternative. It’s not, it’s wrong.

      The International System was set up so that we all use the same units, names, symbols etc. For area that means square metres. I’m happy to dig out my screenshots from the BIPM if necessary.

      This not straightforward. It’s a bit counterintuitive and I have sympathy for the many students – and many maths teachers even – who get it wrong.

      As well as wanting students and teachers to learn and follow the established international convention in this case, I find that students tend to understand the subjects of area and volume better when they do.

    1. That isn’t a helpful comment! In what ways do you think it is wrong. I don’t like fake news so only publish what I deem to be correct. What is your background that tells me that I am wrong. I am happy to discuss this.

    1. I beg to differ. This is not wrong and it is not scientific to show the difference as Ken has shown, although perfectly OK in ordinary everyday life terms.

  3. Edward Murphy, the original article is correct.

    There is an international consensus documented by the Bureau International des Poids et des Mesures (BIPM).

    If you don’t know, please don’t rubbish a good article on a difficult subject. BIPM have a website and the info is on there. It’s displayed on my Patreon page too if that’s easier. Nobody remotely serious in science would contradict the BIPM on this subject.

    Gareth Lewis
    B.Sc. MathStat (Warwick)

      1. No problem. It can be so counterintuitive that students often don’t believe me if they don’t know me well already. Having experienced the disbelief myself – even in schools where other teachers joined in with the disbelief – I had to help.

        There is no such debate in scientific communities.

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