Difference between Square Metres and Metres Squared

Updated 04/01/2020 (see below)

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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!

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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.

After all the comments on here I decided to contact the people who know this stuff as metrology  is their business. 

So I contacted the NPL (National Physical Laboratory, this is

Andrew Hanson, MBE BSc (Hons) CPhys, Outreach Manager, National Physical Laboratory, Hampton Rd | Teddington | Middlesex | UK | TW11 0LW

From P162 of the SI Brochure (most recent – 9th edition 2019), the area unit definition is:

NAME: square metre

SYMBOL: m2

Almost certainly unchanged from when you first wrote your blog item.

As an example from the definition, spoken ‘9 square metres’, written ‘9 m2‘ are both 9 times the area of the unitary square metre.

The confusion arises from reading m2 as the words ‘metres squared’. These words are NOT defined in the SI system. So with no formal meaning, ‘9 metres squared’ could indeed be taken to mean 9×9 m2 or 9 m2 – there is no definitive statement one way or the other.

I think that m2 should be said out loud as ‘square metres’, so don’t take your blog item down, by all means say I agree.

Actually, if you just do the right/formal thing – use the words ‘square metre’ out loud and write as m2, and never, never even whisper ‘metre squared’, there is NO CONFUSION.

A formal way to do describe things with well defined, precise, scientific language avoids the types of problem you describe.

However, common parlance is commonly improperly used to describe scientific parameters, and these words without clear meaning cause confusion.

Most people don’t discriminate – though metrologists, and people who set and mark exam papers take care to get it right.

I am sure people passionate about English who know dictionary meaning of words are similarly riled by common misuse.


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updated January 2020

54 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.

    1. I’d agree with Andy k for his/her explanation that the correct basis of examples are the 2m x 2m = 4 square metres. “Not a 4 metres square” because the 4 metres square is the only measurements of length sides, Then the 4m x 4m = 16 square metres which is the whole wide sides has a 16 squares divided from 4 metres squares

  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. Edward Murphy is quite correct. You are wrong. You are confusing ‘metre square’ (an square having sides of 1 m), with ‘metre squared’ which can have sides of any dimension giving that area. They are completely different. The SI symbol, ‘m (raised to the power of 2)’ is correctly spoken as ‘square metres’, but it is also correct to speak it as ‘metres squared’. My background? Electrical engineer, engineering lecturer and author, masters degree.

    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.

        1. You are both confusing ‘metre square’ and ‘metre squared’ -completely different. If you are describing an area measuring 3 m by 3 m, then you would say a ‘3-m square’. But its area is ‘9 m(raised to the power of 2)’, spoken EITHER as ‘nine square metres’ (my preference) or ‘nine metres squared’. Similarly with cubes: a ‘three-metre cube’ is a cube having 3-m sides’, but its volume is ’27 m (raised to the power of 3)’ spoken EITHER as ’27 cubic metres’ or ’27 metres cubed’.

          1. Further to my comment, how would you express the unit for acceleration? It’s written as ‘m/s(raised to the power of 2)’, and it’s correct to speak it either as ‘metres per second per second’ or, more commonly actually, as ‘metres per second squared’. The same rule applies to ‘m (raised to the power of 2)’ -it can be spoken as ‘square metres’ OR as ‘metres squared’ (but NOT ‘metres square’, which is something completely different! Once again, I argue that you are confusing ‘metres squared’ and ‘metres square’.

          2. While your logic would make sense in the interest of consistency, pronouncing “27 m² ” as “27 metres cubed” is actually incorrect as per the SI because it is defined as “cubic metres”. This has to do with the fact that geometric units (areas and volumes) have the adjective before, while non-geometric units have the past participle after the underlying unit. This is why, for example, nobody pronounces “9.8 m/s²” as “9.8 metres per square second” because conceptually, a “square second” doesn’t make any sense, but a “second, squared” does. It’s just one of those exceptions in the SI.

  4. 1 square metre is completely different from 1 metre square(d). Not in actual area, but in shape.
    1 square metre could be .5m x 2m, or .25m x 4m
    1 metre square(d) is 1m x 1m.
    Completely different though when it is 2 square metres against 2 metres square(d). One remains 2 square metres, the other is 4 square metres.
    At least, that’s what I was taught at school before I left in April 1973 aged 15. If things have changed in the ensuing almost 48 years, I have no idea.

    1. And before I forget, to forego any further confusion as to what is what, 1 square metre should be written down as 1sqm, 1 metre square(d) should be written 1msq. Preferable it should be written out fully, but what would I know, leaving school at age 15?

        1. Not quite true. The SI derived unit for area is the square metre (at least in English, it may be translated in other languages), and m with a superscript 2 is the symbol for that unit, and such symbols are used internationally, regardless of local language. I’m not aware of any language in which the word for metre doesn’t begin with an m, but for example, in Italian, the word for kilometre begins with a c, but km is still used as it is the internationally agreed symbol for kilometres.

          There is an argument for stating units fully, as is often done in medical contexts to avoid confusion, but using, say, “square metres” is not the convention because it is language-specific, whereas m superscript 2 isn’t.

          1. The SI unit of area, Standard Internationale is the square metre m2, where the 2 is a subscript. If you don’t believe me read the comments from the education officer of the NPL. sqm is NOT a recognised scientific way of writing area.

        1. That’s true, but as an example, I was training prospective teachers to pass the QTS Numeracy Skills Test and regularly encountered student teachers who, for example, didn’t know how many pence there were in a pound. I can’t speak about other subjects, and for sure there will still be some great teachers, but the decline in standards in Maths is as clear as day.

          I’m still yet to discover the minimum qualification in Maths required to teach Maths, but several of my students have claimed that their Maths teachers don’t have a C in GCSE Maths. I didn’t believe them at first but some of the mistakes I’ve seen are just so basic that I’d be disappointed if they were from my students, never mind a teacher.

          Unfortunately in the UK the priority seems to be maintaining a ratio of students to teachers, with inevitable consequences in quality control. The salary doesn’t encourage the best mathematicians to consider teaching either.

          1. Well if that is your experience then it is quite sad. Please note though that the UK doesn’t have one education system. In Scotland to teach Maths you’d have to have a degree or covered the subject for 2 years at degree level, although this is only for maths. My niece has just started teaching in England and she had excellent grades in Maths and further maths A level and did an economics degree.
            The students I’ve taught in the last year don’t appear to know that you turn to the next empty page when continuing with work, choosing instead to start writing at whichever page the jotter falls open. Some students ask for a jotter most periods and when asked “Where’s yours?” I have had the reply “in my bag, but I can’t be botered to get it out!”
            Maybe after covid19, all teachers will be replaced with Google Classrooms and Microsoft Teams and a few computer programmes.

  5. Hmm, SO confusing!!
    Wikipedia says the sq m is annotated m^2, (Where ^ indicates superscript) which goes against my personal grain (which agreed with your initial article), but if I work it out Wikipedia makes sense.
    It’s important to know whether we’re squaring the unit itself or the number of units.
    Or BOTH.
    If it’s m^2 then it’s a square unit, not a square of the number of units.
    so: 2m^2 is two single units of cloth.

    However, if I square the units (2^2 M) is four linear metres… with no area at all.

    In order to get four square metres you would have to square both, the unit AND the quantity: it’s 2^2M^2
    So… according to Wikipedia a square metre is always a metre squared, not the square of the number of units.

    To go off following a fancy:
    This means 100 sq cm remain as 100 little squares = 100*1cm2 equals one linear metre only a centimetre wide.
    However…
    In order to get a square metre you would have to square the NUMBER of units AND have squared units,
    Because 100^2 cm= 10,000 cm but has no area…
    so 100^2 cm2 or 10,000cm2 is a square metre but 100cm2 ISN’T.

    I’m a cartoonist not a mathematician. Am I as confused as I feel or have I just made sense?

    1. Thanks for your contribution to the debate Brendon, and I am certainly more confused by the middle bit of your post! m2 is the unit of AREA and could be your 100 cm x 1 cm squares or it could be a square of sides 10 cm, as 10 cm x 10 cm = 100 cm2. Area can be any shape. You don’t square the m2 by m2 Oh yes I’ve just read your post and the last bit makes sense and yes totally correct. There are indeed 10 000 cm2 in 1 m2.
      Now as a cartoonist, your task is to explain that to the world! This is by far the most popular post of my complete site, so see what you can come up with and hopefully you can get some commissions, should you require them. I’ve seen text books that say metres square instead of square metre (m2) I’d love your interpretation on something that obviously causes lots of trouble with students and the general public. Keep safe!

    2. If I’m understanding correctly, I think the confusion is that it is written differently than it is said. This shouldn’t be too foreign, however, as currencies always have this dissonance (e.g., “$5” is read as “5 dollars”). However, the issue here actually only applies to geometric non-linear units (i.e., areas and volumes). Because powers of 2 and 3 make sense geometrically, they are exceptions to the rule of reading units as ” squared” or ” cubed”. Thus, geometric units are read “square ” and “cubic “, but they are written the same as other units nonetheless. For example, “5 m²” is read as “5 square metres”, but “5 s²” is read as “5 seconds squared”.

      There is no such thing as “sq m”, “sq cm”, or any of the myriad other abbreviations. The SI doesn’t allow abbreviations (https://www.bipm.org/utils/common/pdf/si-brochure/SI-Brochure-9-EN.pdf#page=33), as it uses symbols exclusively. They’re like the per cent symbol (%); they never change based on language, whether the quantity is greater than 1, or based on upper- & lowercase.

  6. Great post and am in complete agreement, but surprised how little material there is online about this surely common mistake.

    The SI brochure states only that”square metre” is acceptable, however the following website (American but trustworthy…) does say for powers, the unit can be said before or after the power. I still think it’s a little ambiguous and the examples are not extensive enough. I think it also raises the possibility of metres square vs metres squared…? It’s not just phonetics here, metres squared and square metres are two different things, assuming the preceding number is greater than 1

    https://www.nist.gov/pml/special-publication-811/nist-guide-si-chapter-9-rules-and-style-conventions-spelling-unit-names

    Thank you for a great blog

    1. Thanks Tom, it’s a shame there isn’t a more widely known website on which to discuss it. Talking to other teachers I think they are not all aware, but I try to correct them.

  7. So what is the abbreviation symbol for metres squared?
    3m x 3m is 9 square metres or 9m^2
    So how is 3m squared annotated? How do you write that as exactly 3 metres by 3 metres or 3m squared, which incorrectly in my mind should be 3m^2? Would it be (3m)^2?

    1. Yes it’s (3m)^2, which has an area of 9 square metres. Note though that 9 square metres indicates the area, not the shape. For example 9 sheets of A0 paper would have also an area of 9 square metres, even if they’re not arranged in the shape of a square.

    1. That’s the problem. There is no correct way to say this. It cannot be (X)^2 m as m is the SI unit for length. Read the comment by Andrew from the NPL. These are the people tasked with defining measurements. I would say it is 3 metres squared, but this is a personal opinion and there is no correct value apart from 9m^2 said, nine square metres! Thanks for your comments Richard. It is a very interesting debate.

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