Discrepencies in volume calcs

11 Feb 2009
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United Kingdom
I have a Cert of Lawfulness on a hip to Gable Loft conversion, on a semi detached house.
My architects calculations on the plans show an increase of 48.28 cu mt.
The councils 'delegated report' calculates an increase of 40.9 cu mt.

I went to the council - but they refused to run through how they calculated that figure.

I have checked the dimensions of the plans at 1:50, and they look correct.

I cannot work out what my architect has done with the hip to gable volume calc:

7.958 long x 3.210 high = 25.54m2 divide by 2 = 12.77 m2 x 3.927 ridge length = 5.16 m3 divided by 2 = 25.08m3

Its not how I would do it, I'd use:
Finished Gable volume: bhl/2
(ie (7.958x3.210x6.257) divide by 2 = 79.91

Existing Hip Volume: bhl/4
(ie (7.958x3.210x3.297) divide by 4 = 21.05
Plus remaining gable:

Existing Ridged Part Roof Volume:
(7.958x3.210x3.297) divide by 2 = 50.15

So 21.05+50.15=71.20

79.91 less 71.20 = 7.99 cu mt

So I make the hip to gable enlargement 7.99 cu mt, my architect 25.08 ... who is right.

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hi tony,

thanks for your calculation and diagram :)

the problem, (by your calculation and his - 25.08 less 16.09) there is 9.01 cu sq mt's unused in the permitted development, meaning my architect (having incorrectly calculated) has submitted and had approved plans with a lower ceiling height and reduced dormer width.

after now having seen inside an identical development a few doors up, with a greater ceiling height (utilising all available space by building up to the ridge, and a full width dormer ie flush with the flank wall) I knew something wasn't right.

Is there a reference site I can go to to glean these formulas, as I want to check for myself, and present my architect with an argument to make him put it right.

It seems there are so many formulas and ways to calculate the same thing - and without a definitive answer my architect can go on pulling the wool over my ears. My method of calculation is wrong according to your calc. which just makes me more confused !

Your architect should go back to school and learn some basic geometry.

What he has done is;

1. worked out the area of the gable to get 12.77m2 (correct)
2. multiplied this by the ridge length to get a vol. of 50.14m3 for the prism (correct)
3. halved this to get 25.07m3 (totally INcorrect).

The true volume increase is as shown on the calcs. with the little sketch.

However, all is not lost. You can build the dormer up to the ridge, and up to the flank walls each side, under a Bulding Notice, for which you do not need plans. This means that the plans you already have would be useless. Personally, I think your architect is incompetent, and that you should ask him to either 1. re-draw the plans properly or 2. refund your money and get someone else to do the job.

There will be sites giving the volumes of various solids, but for a simple pyramid-shape (which your hip-to-gable is), it is always; one-third the base area multiplied by the height. In your case, the base area is the area of the gable (ie 12.77m2; one-third of this = 4.25; multiply this by the extended ridge length of 3.927, and you get a vol. of 16.7m3. Simples....
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Hi Tony,
Thanks, thats really helped, think I can see where he's wrong.
I'm back at school here trying to learn simple geometry, isosceles triangles, Pythagorean theory etc etc.
I've been working through some examples to get my head round this.

I've been looking at other hip to gable plans and equations, a very simple one to calculate additional volume is:

(base length of gable X height of gable X top width from hip to gable) ÷ 6
7.958 X 3.210 X 3.297 = 84.222 ÷ 6 = 14.03 cu mt

another more complex one (which is what I think my architect was trying to do, and as you point out correctly - he got wrong) is:

Volume of Triangular Prism (area of triangle X length)
7.958 X 3.210 = 25.545 ÷ 2 = 12.77 X (3.297 X 2 = 6.594) = 84.222

Volume of Pyramid Base area x 1/3
7.958 X (3.297 X 2 = 6.594) X (1/3 X 3.210) = 56.148

So Volume of additional segment - hip to gable:
84.222 - 56.148 = 28.074 ÷ 2 = 14.037 cu mt

Can I query your calculation please, sorry - why is yours 16.7 ? when both the above are 14.03 cu mt, surely the height of the the triangular pyramid is not 3.927 as you calculate it, but some other figure - 3.927 is simply another 'leg', or edge of a triangle, and as its not an 'equilateral' triangle I'm stuck on how you'd calculate its height. Excuse me questioning if I'm totally wrong, just need to fully understand this before I engage a conversation with my rather obtuse (excuse the pun) architect.


you've used 3.297m in your calculation, where Tony has used 3.927m...a subtle - but very important - difference :p

You've used 3.927 in some parts of your original post, and 3.297 in others. All of the workings are correct, just the numbers used differ.

Run through your calc again using 3.927, and you will get 16.7m ³ .

You asked why Tony has used 3.927 as the height. It's counterintuitive, but as long as the prism has a base and triangular faces (which it does) the formula (1/3 base area x height) works. It doesn't have to be symmetrical to give the correct answer.
In fact, it's the same formula for cones too, so works as long as the object has a base, and tapers to a point.
You need to be sure in your own mind, so lets take this step-by-step.

(note; I can't find the division symbol on my keboard so I'll use / instead).

1. In your first equation, you wrote;
7.958 x 3.21 x 3.297 / 6 =14.03 cub.m.

The error here is that in the third term you got the '2'and '9' mixed up;
it should be 3.927, not 3.297. If you re-work it out it will come to 16.7.

2. If your architect tried the method in your scond go, it is an a**e about
face way of doing it, but it can be done as follows; (I will re-write the
figures line-by line as you have done them but corrected; follow them
carefully and you will see it);

volume of triangular prism (area of triangle x length)
7.958 x 3.21 = 25.545/2 = 12.77 x 3.927 = 50.14 cub.m.

volume of pyramid = base area x 1/3 height;
7.958 x 3.927 x 3.21/3 = 33.43 cub.m.

so volume of additional segment (ie prism minus pyramid)
50.14 - 33.43 = 16.7 cub.m.

Method 2 is the long-winded way and unnecessarily complex.

In answer to your final point; imagine your house-roof stood up on end. The triangular gable will be the base of the pyramid, and its height will simply be the enlarged length of the ridge. Remember that a pyramid does not have to have a square base like those in Egypt; it can have a triangular base as well.

See if the attached sketch helps with method 2, but I would avoid this if possible in your dealings with your so-called architect. Keep it simple, ie volume = 1/3 base area x height.

(Ronny; You were 25 minutes before me but I wasn't cribbing! - it just took me ages to do that c****y little sketch!)
Very sorry, I am a donkey .. I scratched down a little diagram and wrote 3.297 instead of 3.927, and used that figure in all my calcs :(

Thank you for putting me right, all the figures check out now ...

The second diagram helped me greatly, I can see better (mostly) how the more complex calc works (the shorter one I cant break down, but it checks out the same must trust its correct)

BUT, I have a book that shows examples of calculations - which agree with my architects calculations :( ... (I still think he is wrong, and so do the council by their reckoning, and I wish to prove him so), I have attached the page from the book, and the actual part of my plans (in a lovely 'cloud' image ... umm), and the part of the councils document showing what they have calculated, so you can better see the descrepency I'm trying to resolve.

Total Volume Increase:
My Architects calcs 25.08 + 23.20 = 48.28 cu mt
The Councils calcs: 40.9 cu mt
With your calcs: 16.70 + 23.20 = 39.90cu mt
Using the books calcs: 25.08 + 23.20 = 48.28 cu mt

View media item 47293
View media item 47291
View media item 47292
So as per the books equation:

Gable volume v=bhl/2: (7.958x3.210x3.927)/2=50.15796

Hip Volume v=bhl/4: (7.958x3.210x3.927)/4=25.047

So additional volume is: (Gable volume less Hip volume):
50.15796 less 25.07 = 25.08 cu mt

Now I'm very confused, is the book wrong ??, thanks for all your help so far.

PS didn't use the '/' sign incase it confused anyone.
The author of the book also needs to go back to school.

On the right-hand side, look at the second diagram down; it states the volume incorrectly as bhl/4, when it should be bhl/3. All the subsequent calcs based on the book's method will be wrong, so disregard them completely.

Assuming the dormer dimensions are those in the 'cloud' diagram, then the volume of the dormer part will be;

5.25 x 2.456 x 3.6/2 = 23.2cub.m.

Add to this the correct volume of 16.7 cub.m.for the hio-to-gable, and you get 39,9 cub.m. This accords roughly with the Council's figures, allowing for slight discrepancies in reading off measurements.

I would say that you have another 10 cub.m. to play with, which is why your neighbour has a bigger dormer.

You have all the info. in these figures; remember that the vol. of a pyramid is always 1/3 base area x height, so go and give your 'architect' some earache (and do let us know how you get on).
Hi Tony,

Wow, so the books wrong too, this is a tricky business !

I've gone back to your second diagram, and it all makes sense now ... and yes its /3 - not /4 !!, I have all I need now to prove a case. Many thanks for all.

10 cu mt !! thats 20% less volume than I should have ...

I'm meeting with another architect just for a quick meeting to look over what I've found, and get him to back me in case my architect gets difficult.

I'm now wondering if he is a true architect, and not a building control officer who's got handy with Autocad - umm, should an architect not be registered with any 'licensing' organisation ??

I assume he is responsible for resubmitting both Planning and Building Control plans to the council, and the costs to do so, that may involve his structural engineer re calculating maybe ?
What I dont want is my architect saying 'your out of your depth' which he has done, and then getting really arsy when I start questioning.

I have spoken to my party wall surveyor who we paid £££'s to get an award, and he feels these changes are not 'material', so thats a relief we dont need to go through that again.

I've spoken to trading standards who say he has a case to answer for.
He must have read the Delegated Officers Report showing just 40.9 cu mt's ?? but said nothing, I only uncovered that by going through council documents online, he never made any effort to show me those.
I have checked the ARB (Architects Registration Board) and cannot see my architect registered with them.

Regarding roof volume measurements, I understand it is the external dimensions that are used - it appears my architect has used the external wall measurements, and not measured to the end of the eaves, in his calculations - is that correct.
I have checked the ARB (Architects Registration Board) and cannot see my architect registered with them.

Of itself, that is not important; there are many people who are skilled in preparing drawings and who are not registered architects. Such persons often call themselves architectural technicians or architectural consultants.
However, if he has specifically declared he is an architect, that is a different matter. Proving it, though, would be difficult; it is unlikely that he will put the word 'architect' on his letterhead.

The volume of the roof includes that of the eaves.

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