# Forum Home Renovation Roofing  Calculating roof pitch, rise for trusses

## Malc

Hi All, Planning an extension to my house and want to establish an accurate way to calculate pitch and rise. Current roof on house has trusses that measure 6.6 metre's span (outside of top plate to outside) and a rise of 720mm if you measure from top of truss to underside of bottom chord. I always thought you could calculate by dividing rise by the run so in above case that would be 720mm minus 95 for bottom cord = 625mm then divide this by run 3.3 equals 189mm which I assume is rise per metre. So how do I work out what pitch this is and what is the formula to experiment with different pitchs to work out how roof height will change. Hope I have made myself clear with all above.
Cheers Malc :Confused:

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## harmful81

malc, 
i am no mathemetician, but using limited memory from my school days, tan of the angle equals the division of opposite over adjacent. so in your situation, a shuffeling of the equation means that  
inverse tan (0.625 / 3.3m ) = 10.7244 degrees. 
hope this helps.

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## Bloss

Look here:  http://www.blocklayer.com
and http://www.blocklayer.com/Roof/
and more specifically http://www.visualtrig.com/
and http://www.visualtrig.com/Angles.aspx

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## viiking

> 720mm if you measure from top of truss to underside of bottom chord. I always thought you could calculate by dividing rise by the run so in above case that would be 720mm minus 95 for bottom cord = 625mm then divide this by run 3.
> Cheers Malc

  No this is wrong. The run is 3.3 m or 3300mm. The rise is 720 mm. (Think of the outside of the triangle.) You don't take off the thickness of the chord. 
The tan of an angle is indeed the opposite divided by the adjacent.Therefore the tan of the angle you want is 720/3300 = 0.2182. You want the inverse tan of this number *which equates to an angle of 12.3 degrees*!

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## Bloss

That's why using calculators is a 'good thing'  :2thumbsup:  - you don't have to know or learn trigonometry (although I did) and you shouldn't have to know. Others have already done the work so all you need to know is what measurements are needed as inputs - the calculators (and my dim distant past roofing tables) do the rest. Best to do it the easy way people - and the smart way.   :Biggrin:   
Repeat after me:   :Arrow Down:   :2thumbsup:    

> Look here: http://www.blocklayer.com
> and http://www.blocklayer.com/Roof/
> and more specifically http://www.visualtrig.com/
> and http://www.visualtrig.com/Angles.aspx

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## ausdesign

My calc's for a truss with a 90 top chord comes to 10.78 degrees. With a 70 top chord it would be marginally greater. 11.12 degrees

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## Bloss

> No this is wrong. The run is 3.3 m or 3300mm. The rise is 720 mm. (Think of the outside of the triangle.) You don't take off the thickness of the chord. 
> The tan of an angle is indeed the opposite divided by the adjacent.Therefore the tan of the angle you want is 720/3300 = 0.2182. You want the inverse tan of this number *which equates to an angle of 12.3 degrees*!

  Yep Viiking's on the money. The base of the triangle is 3300mm (1/2 the span) the height is 720mm so the pitch is 12.3 (well 12.31 to be precise). Easy peasy - go to http://www.visualtrig.com/Default.aspx and click on 'Triangles' menu button then fill in the boxes with the information you know - it does the rest (see attached).   :2thumbsup:   :2thumbsup:  
These calculators make it easy without an old fella like me having to recall high school & uni trig - and even offers some quick lessons and tips if you really want to know how the results come about rather than just get them!  :Biggrin:  
For Malc's question all he needs to do is to plug in any measurement for which he wants a result and click on  'Calculate' - voila the numbers all change. I just love the smoke & mirrors of computers!  :brava:

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## ausdesign

All the trig calc's are fine except to my mind the height of the triangle isn't 720mm.
It's 720 minus the vertical height of the top chord.

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## harmful81

I have attached a plan. 
I admit i made an error in the initial post i did. It is wrong to deduct the thickness of the bottom cord. There is a correct way - if you were to deduct the thickness., you have to also reduce the length as ive tried to depict in the first image. The second image shows what happens if you dont - note reduction in pitch.

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## ausdesign

Having trouble opening your PDF harmful, but to go over it again to work out the triangle with a truss you would measure the horizontal (3300) and measure the vertical - from the bottom edge of the bottom chord ( which is the same height position as the bottom of the top chord where it rests on the wall plate ) to the underside edge of the top chord.

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## harmful81

pitch is calculated using overall dimensions. Inverse tan of (overal height divided by overall length) no deductions.
The important relationship here is the rise verses the run. If the rise is reduced, then the run has to be reduced by the same factor (note, NOT the same amount) ( which is dependent of the angle again)

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## ausdesign

I don't think i"m explaining myself very well.
What you're saying with the rise & run is correct, but the height of the triangle can't be 720mm if the measurement has been taken to the top of the top chord.
It should be measured to the bottom of the top chord to form the triangle.

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## zacnelson

Peter (ausdesign) is correct, it would be easy to show in person, maybe a bit confusing in words though!

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## Bloss

> I don't think i"m explaining myself very well.
> What you're saying with the rise & run is correct, but the height of the triangle can't be 720mm if the measurement has been taken to the top of the top chord.
> It should be measured to the bottom of the top chord to form the triangle.

  Yep - I took the 720 from Malc's initial post without properly reading how he derived it.  :Blush7:  The triangle we are looking at is formed by the line drawn across the _underside of bottom chord_ to the outer edge of the top wall plate, the line drawn on the _underside of the top chord_ down to where it meets the bottom cord above the wall plate and the line drawn perpendicularly from the underside of the bottom chord to the _underside of the top chord_. 
So as AusDesign said the 720mm needs to be reduced by the depth of the vertical cut at the ridge join.  :2thumbsup:  In other words Malc needs to measure to that bottom point of the top chord joint. As he wants to then see how changing pitch affects the shape of his roofline he can then just plug in different numbers on the calculator site to see the impact. 
I suggest a better option for Malc is to get in touch with a truss company or talk to his designer/ draftsperson as most nowadays have 3D visualisation software that does all this for you. You give them the right measurements for the existing roof and a few ideas about the planned addition and they can  show you what it will look like very realistically. This is generally a free service although they would not appreciate you using them and buying trusses from someone else (not that they can really do much about it!). 
Clears as mud I suppose?  :Biggrin:

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## barney118

Clear as mud, Imagine the triangle and draw this around the outside of the truss to derive the triangle. Just make note if you are matching into other trusses then there should be limited issues, have a think about the ceiling height and the roof height when battens are fixed as well. You can run into problems if the new battens are different height and or will you be fixing the ceiling to the bottom chord of the truss or using battens to match ceiling heights. 
I have a convential roof and the rafters were birdsmouthed (notched into the top plate) and this can effect the truss as they sit flush on the top plate. A ~12 deg pitch seems a bit low is this off a hip or something.

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## ausdesign

:No:  Not around the outside of the truss.

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