Hip Roof Angle Calculations

Quote of the Day

The only hope of a pure mathematician is to die before their work is applied.

— Pure mathematician stunned to hear that his work found an application in string theory.

I am considering building a small structure at my lake cabin that has a hip roof. The structure will look a little bit like the one shown in Figure 1 (source), but with a steeper roof pitch.

Figure 1: Small Shed with Hip Roof.

Figure 1: Small Shed with Hip Roof.

To build this structure, I need to compute a few angles and, unfortunately, I have forgotten how to determine them using a steel square. To derive formulas for the critical angles, we need to define some terms, which I do in Figure 2. Using these angle definitions, I will  derive formulas for the sheathing (θS) and hip pitch angle (θH) given the common pitch angle (which I call the roof pitch [θR]) and plan angle (θP).


Figure 2: Illustration of Hip Roof Angles.

Figure 3 shows my derivation. The derivation uses basic geometry, so I will just let the drawing stand for itself. If more detail is needed, send me a note. I will use this post to document formulas as I need them.


Figure 3: Derivation of Hip Roof Angle Formulas.

I did find formulas for these angles presented on this web page, but no derivation was given − that's no fun at all!

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5 Responses to Hip Roof Angle Calculations

  1. David Little says:

    It seems it's difficult to calculate the Hip roof area

  2. Gaz says:

    Surely it must be possible to apply a simple multiplier to the pitch angle, say 30 deg., to derive the hip angle ??? like .75, so 30 x .75 = 22.5deg. Does anyone know what the 'normal' multiplier might be, where the hip pitch is the same as the main pitch?

    We know all you maths nerds are geniuses, thanks a lot, but just give us the number, not the symbols!!

    What carpenter will use trig to work it out!!!

    Site work is practical, not a maths workout!!


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