Many people incorrectly assume that as there are 100 cm in a metre then there must also be 100 cm^{2} in 1 m^{2} and 100 cm^{3} and 1 m^{3}. Working through the pictures below should convince you that there are:

100 cm in 1 m but 10,000 cm^{2} in 1 m^{2} and 1,000,000 cm^{3} in 1 m^{3}

Length

1 m = 100 cm

Area

1 m^{2} = 100 × 100 = 10 000 cm^{2}

= 10^{4} cm^{2}

Volume

1 m^{3} = 100 × 100 × 100 = 1 000 000 cm^{3}

= 10^{6} cm^{3}

one litre = 1000 cm^{3}

1 l = 1000 cm^{3}

1 m^{3} = 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!

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

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 m^{2}

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.

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!

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

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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.