UPDATED on December 15, 2017 with information on the U-factor alternative.
A roof over a vented, unconditioned attic does not need to include any insulation. However, most cathedral ceilings and low-slope (flat) roofs are insulated roof assemblies: with this kind of roof, the insulation follows the slope of the roof.
Insulated roof assemblies can be vented or unvented. There are lots of different ways to insulate this type of roof, but one of the best methods calls for the installation of rigid foam insulation above the roof sheathing.
There are at least two good reasons why this approach makes more sense than installing the insulation under the roof sheathing:
How much foam do I need?
If you plan to install rigid foam above your roof sheathing, you have two choices:
If you choose Option 1, your rigid foam will be fairly thick:
If you choose Option 2, the code dictates the minimum thickness of your rigid foam layer. According to section R806.4 of the 2009 IRC, this approach requires that “rigid board or sheet insulation shall be installed directly above the structural roof sheathing as specified in Table R806.4 for condensation control.” (In the 2015 IRC, the comparable code requirements can be found in Section R806.5. Table R806.5 is reproduced as Image #5, below.)
According to the relevant code table:
The purpose of the requirement that rigid foam installed above roof sheathing meet certain minimum R-values is to ensure that the roof sheathing stays warm enough during the winter to avoid moisture accumulation and possible sheathing rot. (If the rigid foam layer is too thin and the sheathing is too cold, the sheathing can absorb moisture from the home’s interior. Although this process is often referred to as condensation, it is more accurately referred to as sorption.)
Note that if you follow this path…