# Calculating Volume Of Loft Extension

I am aware that a loft on a detached house needs to be 50 sq m or less to permitted development

My maths from high school and triginometry is not so great - I know that a prism volume is (height * width * depth) / 3 and I ve been trying to calculate the existing volume and the new volume to understand how much additional space I need

A neighbour has done the loft conversion as follows and he did it under permitted development so no planning but I cant understand how he could have done this and I am sure he would not have done this without paperwork

Basically he has taken a detached roof and made it hip to gable on both sides and added a full width dormer

The house is ten metres wide ten metres deep and the height from eaves to roof ridge is 2.2M

By my basic calculation just converting hip to gable results in 36 cubic metres being added and thats before the addition of the full width dormer

Cubic Volume of original roof - Its a prism right? - So current volume is 10 * 10 * 2.2 / 3

Cubic Volume of hip to gable roof excluding rear dormer - Its a triangle right? - So current volume is 10 * 10 * 2.2 / 2

Additional volume created by just doing hip to gable on both sides is (10 * 10 * 2.2 / 3) - (10 * 10 * 2.2 / 2) = 36.66 M

What am I missing? And how can a full width dormer and two hip to gables be less then 50 sq m?!

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Ignoring the calculations, I doubt if that was permitted development, so what are you really querying. Do you want to follow suit, or talk to the council over it.

But work out half the size of the roof front to back, times the width and the height, then add half of that calcultaion for the front - try it that way.

Hi It was definitely permitted development because no planning permission was granted and the neighbour complained and it was deemed fine

I want to do the same on my parents house and the house is identical so understanding how permission was granted would help a lot

Sorry, you'll have to wait till Woody comes along; he's far better at this stuff.

PD is 50m3 additional volume, so you don't need to worry about the existing roof. Any extra bits are just calculated as cuboid or pyramidal shapes.

The rear dormer is a triangular prism, which is really half a cuboid, so LxWxH /2

The gable conversion is again a triangular prism so the volume of that divided by 2 (ie deduct the volume of the existing roof which the new roof (the prism) intersects. The prism is an area of a triangle (the gable) x L (distance from new gable apex to existing ridge)

PD has other criteria, and it looks like the eaves have been raised at the front at least and the whole roof now being higher. Both of these are not PD. Not sure about the rear dormer set back, as it's difficult to make it.

PD is 50m3 additional volume, so you don't need to worry about the existing roof. Any extra bits are just calculated as cuboid or pyramidal shapes.

The rear dormer is a triangular prism, which is really half a cuboid, so LxWxH /2

The gable conversion is again a triangular prism so the volume of that divided by 2 (ie deduct the volume of the existing roof which the new roof (the prism) intersects. The prism is an area of a triangle (the gable) x L (distance from new gable apex to existing ridge)

PD has other criteria, and it looks like the eaves have been raised at the front at least and the whole roof now being higher. Both of these are not PD. Not sure about the rear dormer set back, as it's difficult to make it.

Thanks a lot - The roof has not been raised - I am sure of that - And I am also sure of the fact this is done under PD

Cuboid calc I agree with - I have no questions on that

What I dont see is the gable conversion calculation. Can you explain that? Am I correct that the calc is assume its a prism so (h*l*w/3) - (h*l*w/2) because it is now a triangle!!!

Thanks a lot - The roof has not been raised - I am sure of that - And I am also sure of the fact this is done under PD

Cuboid calc I agree with - I have no questions on that

What I dont see is the gable conversion calculation. Can you explain that? Am I correct that the calc is assume its a prism so (h*l*w/3) - (h*l*w/2) because it is now a triangle!!!

Try this. Although it's two pieces of chocolate long, the extended roof is just one piece as it's half the volume.

Thanks - Thats the picture I have in my mind - Is there a calculation you can share - I have height width length

How do I calc the additional volume ?

What I did before was calc existing volume assuming it was a prism and then calc volume assuming its a triangle and subtracted one from the other

How would you do it?!

I ve tried this now - Comes out with zero !

I set height to be 2.2, width 10, length 10, O=2.2 P=0, Q=0

It's 1/3 triangular area x length along toblerone

So mathematically its originally a prism which means volume is l*h*w/3.

After hip to gable on both sides it becomes a triangle so volume is l*h*w/2.

So the additional volume is l*h*w/2 - l*h*w/3 - Does that formula work for a loft you have worked on?

I ve tried this now - Comes out with zero !
I set height to be 2.2, width 10, length 10, O=2.2 P=0, Q=0

Based upon the pictures above I estimate that the hip-to-gables are as follows:

1x Hip: H=0, W=6, L=5, O=2.2, P=0, Q=5 = 22m3
1x Gable: H=0, W=6, L=5, O=2.2, P=5, Q=0 = 33m3
Increase: +11m2

Dormer: H=2, D=3, L=10 = 30m3

So total= 11m3 + 11m3 + 30m3 =52m3

Based upon the pictures above I estimate that the hip-to-gables are as follows:

1x Hip: H=0, W=6, L=5, O=2.2, P=0, Q=5 = 22m3
1x Gable: H=0, W=6, L=5, O=2.2, P=5, Q=0 = 33m3
Increase: +11m2

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