## Converting metres & centimetres, length, area and volume

Many people incorrectly assume that as there are 100 cm in a metre then there must also be 100 cm2 in 1 m2 and 100 cm3 and 1 m3. Working through the pictures below should convince you that there are:

100 cm in 1 m but
10,000 cm2 in 1 m2
and 1,000,000 cm3 in 1 m3

1 m = 100 cm

### Area

1 m2    = 100 × 100 = 10 000 cm2

= 104 cm2

### Volume

1 m3    =  100 × 100 × 100 = 1 000 000 cm3

= 106 cm3

one litre = 1000 cm3

1 l = 1000 cm3

1 m3 = 1000 l

Now read this post in conjunction with the one on units for area and volume! The units for area are square metres and the units for volume are cubic metres. Don’t confuse either of these with metres square or metres cubed!

## Difference between Square Metres and Metres Squared

This post is about the mispronounciation of the SI unit for area, (m²). This is said square metre. I am not wrong, I am not daft and I want the world to say it properly.

### Updated 04/09/2024 (thanks Tim)

This is what I’ve been missing to add in! You can’t now say this is wrong.

## 4 m2

The diagram above shows four square metres or 4 m2. If you looked at the length of each side it would be 2 m long! QED!

### Updated 13/05/2023 (see below)

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

For example

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.

The room has an area of 4 square metres, 4 m2.

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.

So if someone asks you the correct area of the room mentioned originally, you should say that the area is 4 square metres  or 2 metres square both of which are correct answers, but the 4 m2, 4 square metres is standard.

• But beware more confusion arises as 1 m × 1 m = 1 square metres while 1 metre squared is also the same size as 12 = 1 metre square. You just get there by different routes.

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

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!

Just to show I am right, here is the page from the NPL site. The people in the UK responsible for measuring.

March 2024

For those in the US, here is the equivalent link https://www.nist.gov/pml/owm/metric-si/si-units-area

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.

For those in the US, https://www.nist.gov/pml/owm/metric-si/si-units-area

# IoP Teachers of Physics award

The Teachers of Physics awards celebrate the success of secondary school physics teachers who have raised the profile of physics and science in schools.

The IoP acknowledge that teachers contribute an immense amount to society and wish to accord them the recognition they deserve.

The IoP Teacher of Physics awards, honour teachers alongside distinguished research scientists and industrialists.

In this way the IoP recognise that without dedicated teachers there would be no physics research community or technological base in society.

### IoP Award 2015- Winner Andrew Ogilvie

#### What are the Key Challenges in Education?

The key challenges for me teaching physics at the moment are threefold. A drop in the number of candidates choosing physics perhaps because of a perception (which is partly real and partly imagined) of the comparative difficulty of the subject , pressures of time due to course content and assessment and also that the rate of technological advance now makes many applications of physics so hidden behind opaque user interfaces as to be invisible.

For the first problem I try to  emphasise that the subject is not only comprehensible ( and can be constructed from our existing experience with a bit of imagination) but that  general principles are both economic ( learn a little understand a lot) and  satisfying.  For the second , well that’s just doing the job,  and for the third I try to make links explicit links from the curriculum to the technology and always  try to recruit the pupils experience and imagination, though Its hard to give a concrete example of this sitting here right now.

I think that contexts for learning are extremely important and I feel I’ve done my job best if I can do good by stealth without the kids noticing that they’ve learned something useful.

#### How do you manage your time?

To be honest in response to your second question I don’t feel that I do manage my time terribly effectively . It would be a very different , and less efficient ,world if I had been recognised for any sort of excellence in time management.  One thing I do think, though, is that if you’re going to try to do something you should try your best and , as a corollary, that its better to do a small thing well than a big thing badly.

#### What concerns you in Education?

I don’t “dread”  teaching anything in the Higher or Advanced Higher but that’s not to say  that there aren’t challenging bits.  I find I enjoy understanding things better myself through teaching them.
My concern for Higher and Advanced Higher is to try to  give students some sort of insight into ideas like Particle Physics, Relativity, Stellar Physics or Cosmology  and making  these areas seem accessible to reason..
While I understand some of the reasons for the inclusion of these topics  I really feel there is a danger of presenting them in an “unscientific” way  just demanding they be  accepted  by virtue of  our authority as teachers with the justification being inaccessible both to them and often to us.  (The inclusion of these topics seems similar to trying to study Finnegan’s  Wake in Higher English or Stockhausen in Higher Music ) It  might be better to defer that particular form of gratification until  such a time as we have acquired the analytical tools to experience it fully but, if we must do it, then it must also be done well.

#### What are your top teaching tips?

Top tips : no particular order

Try to enjoy the privilege we have in spending time with the pupils ;  learn the pupils’ names and make time to say hello to them passing in corridors etc ;

Remember that sometimes the teacher can be wrong.

Always try to explain – if you’re not explaining,  its not Physics ( its “stamp collecting”)

When someone outside of work  learns you’re a teacher and  asks you “how you put up with the wee blighters” stick up for the kids.  95 % of them  are thoroughly admirable and wonderful in their own ways and if you’re not like that when you’re eleven years old its not your fault.

When I was at Jordanhill one of the lecturers said  always say you teach “children” not a particular subject… this sounds glib but is in fact very good advice – the job isn’t to produce the best  exam results  that’s just a by product of trying to develop the best people we can.

No-one’s fond memory of school is doing Ohm’s law calculations so you’ve got to try to make your lessons about more than that, even when its Ohm’s law you’re teaching .

Given the opportunity you should speak truth to power and if not given the opportunity you should probably try to make an opportunity. (The truth,  incidentally, doesn’t always have to be bad news.)

Sometimes, if you like that sort of thing, ( and I do ) you should talk about poetry,  or  music , or mountains, or crocodiles…. (To be honest, the crocodiles only really work  if, like me, you are missing a finger or two and I can’t recommend that as CPD)

I think I could go on and on ( although its equally possible that that is all I know) but its also worthwhile reminding myself that a) I’m just an ordinary teacher with no special insight and b) what works for someone else might be completely different.

I’m very flattered to have been asked my opinions , so thanks for that , but I recognise it as flattery and I’d  be a fool to believe my own hype so neither should anyone else.  Please don’t imagine that I think I’ve got all, or even any, of the answers its quite the reverse.

Today I have been waiting for Godot – and  I have failed. Tomorrow I shall wait for him again- “fail again, fail better”

### IoP Award 2016

###### Mrs Physics

Here is a copy of an interview I gave with Sally Weatherall from Guzled after hearing of me being awarded the Scottish IoP Physics Teacher Award in 2016.

How can I better what Andrew Ogilvie wrote last year? (See above) He summed it up perfectly. If you want to know all about Physics and teaching his answers are there, fully formed and written so much more eloquently than anything I could do.

When I started teaching we worried about telling people what we did. Telling people at a party you were a  teacher was easy but when you got to the “what do you teach” I found the best reply was “children”. If you made the mistake of saying Physics it would lead to a tirade about how bad their Physics teacher was at school and how hard the subject is and how clever you must be. At this point they would leave to talk to someone else. A friend and colleague of mine was so fed up with having no one to talk to at parties when he said that he was a Physics teacher that he either told them he was a basic rocket scientist, or told them he worked for the Government, in a lab. . How times have changed. I think in the old days some teachers were excellent but just didn’t relate to the student. Such cannot be said for my Physics teacher who is a fantastic guy and inspired me.

What key challenges are you facing in teaching physics right now?

I think the crucial two points are the number of students taking the subject and the workload.

When the subjects are limited to five or six then students will often tackle the ones that appear easier. I think that by making students see the relevance of Physics to everyday things then you’re half way there, but too many still want the easy option and the increased likelihood of higher grades. I think it is vital to put Physics into context, even if the information sounds obscure; at least you can show students how to weigh up the arguments and get them to think for themselves. In my classes I always make students feel that it is OK to get things wrong. The worst sin in my class is not putting forward any idea, not thinking anything. Science is all about having an idea, testing it and if it doesn’t work out try something else. What better recipe for life!

As to the work load, the Physics community have been amazing and I am one of those who would have gone under if it wasn’t for the kindness of others who willingly shared their materials on SPTR and GLOW. If you are one of those people who have allowed me to use their materials then I thank you, and I’ll buy you a drink to celebrate your part in this award. If you are someone who has used my stuff, I hope it has helped you. If you are a teacher that has never produced anything I suggest you give it a go. We all need to add our contribution to surviving and I know some feel it isn’t their skill but they will still have something positive to contribute. We all need to give and take.

#### How are you trying to overcome these challenges?

I have mentioned much of this already. We need to get students to see the relevance and importance of choosing Physics. I describe some subjects as a walk in the park, and Physics as climbing the mountain. A walk in the park is very nice but the sense of achievement at climbing the mountain remains with you for much longer. For the students who have found it a mountain to climb, I tell them it will be the one they check first on their certificate- they usually rush back in September and tell me it was, and how good it feels. I think getting the students to see that you appreciate that it will be hard work but worth it can inspire them to at least try it. If students know that it is a team effort, you’re on their side doing your bit, then the mutual respect is there and the synergy is obvious. (Oh can I use that biological word in a physics piece?) . Another important key is to ensure the students know that the teacher doesn’t always get things right. This is a great get out clause for anyone. I can’t understand teachers who tell students they are never wrong. That doesn’t lead to mutual respect.

#### Time constraints affect teachers worldwide. How do you manage your time effectively?

I find this really difficult to manage, but I would rather put something up for the students on my website, or do a little more marking than clean behind the sofa? I do get hung up with minutiae and like things to be just right instead of ok. I think the students appreciate the effort that you put in for them and sometimes it motivates them to try harder. It’s all part of the team work. I am also happy to answer student questions on Edmodo at silly o’clock. I’d rather them manage their homework than make excuses that they couldn’t do it.

#### Do you have any “top tips” for physics teachers who are new to the profession?

• We are teaching the best subject in the school, although many students don’t know it, so we need to get students to realise it’s the best subject. We can do that by showing the relevance to their everyday lives and, if it is an obscure topic, then at least you can get them to think. Think about asking the whys and how things happen.
• If you can make the learning fun and relevant then that will keep down discipline problems. If you still have discipline problems then ask the students if they are following what you’re doing. Bad behaviour is generally a cry for help or boredom.
• I treat all students differently. Each one needs a different amount of boot, carrot, praise laughter, and understanding. Find out what makes each student tick. Try to find out what interests the students and then find examples to fit that interest. If all your speed/ distance calculations need to be about tractors that’s fine!
• If the students know you won’t give up on them they’ll certainly try hard, but also tell them when they’re not delivering what they are capable of. Even Physics can be completed by 95% of students if they really go for it, I mean I’m teaching Physics so it can’t be that difficult.

Oh yes, go and do amazing things! Who would have ever thought as a Physics teacher that I would spend 7 weeks working in a nuclear power station on a Royal Society of Edinburgh Teaching Fellowship? Visiting astronauts in their houses (Scottish Space School), going underground around the LHC, sharing a meal with a Nobel Prize winner (Royal Society Partnership Grant Scheme), speaking at the Edinburgh International Book Festival (Royal Society), being invited around Renault HQ (Yourideasyourinitiative), testing the reaction time of the Queen’s cousin (Summer Science Exhibition), spending two weeks at the Royal Society and getting students produce a Scientific paper published in a special Young Scientist Journal, spending 3 days in a shooting hotel working at the Optoelectronics College, or spending two great weekends with snoring Physics teachers exchanging notes and making IoP rockets in the middle of the forest (I think now the police would be on to us as a terrorist cell) (Regional CPD event). There are so many opportunities for teachers and students. Grasp each one, as it keeps you invigorated and excited by the amazing things around you. As we are in a rural area we don’t have the same access as some of you do to Universities, Science Centres, great speakers and so on, so try to make these opportunities available for students so they can be inspired by the Science around them and realise that Science will bring them great opportunities. I think I sound like a seven year old- maybe that is the secret, be as inquisitive as the students and show it is OK to be curious!

I would also like to mention a guy who really ought to have won this award but didn’t live long enough to see the nomination process through. That is Kevin Bailey from Wallace Hall Academy in D&G. He was an amazing teacher, would give up everything to help his students and had the respect of all those he knew. He is still sorely missed.

## Martyn CrawshawMillburn Academy, InvernessAwarded in 2017 for outstanding contributions to the teaching of physics

Martyn is a dedicated and enthusiastic teacher who instils a thirst for knowledge in his students and enjoys the challenge of presenting new concepts to them. He has made a very significant impact on his school’s science faculty and the wider school community, and is seen as a “go-to” person for physics support in the north of Scotland, particularly by schools with single-teacher departments, new staff or challenging issues. His students appreciate his engaging and encouraging teaching style and his ability to relate physics to life outside the classroom, while he is a supportive and challenging mentor to new teachers. Throughout his extensive efforts in organising visits, links with industry and hosting CPD, his work-rate has been phenomenal while his ability to empathise with students and colleagues has been exceptional.

(from the IoP Website)