Simple is seldom a word you’ll hear used in modern construction—least of all when talking about roofs. It’s not often that today’s estimators and framers will ever come across a simple gabled roof with a consistent pitch, no dormers, hips, or valleys. These features drastically change the design and complexity of the construction and you now have to deal with hip and valley rafters and potentially multiple angles throughout the roof. To make matters more complicated, you often won’t find the exact pitch of hip and valley rafters documented on your plans. So, what is the pitch of hips and valleys—is it the same as the main rafter pitch?
The simple answer is no. Hips and valleys always have a shallower pitch than the main rafters of the roof. So why aren’t they the same? And how do I calculate the pitch of hip and valley rafters if it’s not in the plans?
In the industry, pitch is a fraction that describes the “steepness” of a roof. Mathematically, it refers to the rise over the span:
Without simplifying that fraction, that number is not particularly useful information. Particularly if the ridge isn’t in the middle of the span. In the industry we typically see pitch expressed as a rise in inches per foot.
This example has a roof with all faces at a 6/12 pitch, so again for every foot of horizontal run, there’s a rise of 6”. Relative to the main rafters however, the hip and valley rafters rise at an angle up the incline of the roof. Their rise in inches is exactly same but the horizontal distance to get to that point is longer.
To simplify this, envision a section of the roof with a valley or a hip as a right triangle. When doing so, hips and valleys will always be the hypotenuse or the longest edge of that triangle. Their horizontal distance will always be longer than that of the main rafters. If the rise is the same but the run (and therefore the span) is different, then hips and valleys will have a different pitch.
If your plans don’t show the pitch of hips and valleys you’ll have to calculate it on your own with the information that you do have. Calculating the pitch of the hips and valleys is relatively simple when both intersecting roofs are the same pitch.
The general rule of thumb is that for every 12 inches in run for your rafters, hips and valleys have about 17 inches in run. So, for this roof, the rafters have a pitch of 6/12, and the hips and valleys have a pitch of 6/17. But 6/17 isn’t expressed in a way that’s useful in construction so it needs to be converted to a value per foot. To do this, simply multiply the pitch by 12:
Here’s a quick reference table of rafter pitch to hip and valley pitch. Though again, this chart is only relevant for the hips and valleys of roofs of the same pitch.
|Rafter Pitch||Hip/Valley Pitch|
|1.0 / 12||0.7 / 12|
|2.0 / 12||1.4 / 12|
|3.0 / 12||2.1 / 12|
|3.5 / 12||2.5 / 12|
|4.0 / 12||2.8 / 12|
|4.5 / 12||3.2 / 12|
|5.0 / 12||3.5 / 12|
|5.5 / 12||3.9 / 12|
|6.0 / 12||4.2 / 12|
|7.0 / 12||4.9 / 12|
|8.0 / 12||5.7 / 12|
|9.0 / 12||6.4 / 12|
|10.0 / 12||7.1 / 12|
|11.0 / 12||7.8 / 12|
|12.0 / 12||8.5 / 12|
For calculating the pitch for hips and valleys between two roofs of different pitch, don’t over complicate things. There are many online resources that explain the trigonometry you’ll need to use, and some even have calculators to help. But the complexity of modern construction brings with it the conveniences of software assistance! You can always leverage takeoff software like PrebuiltML to automate the process and take care of pitch calculations and length adjustments for you. Click here to check out our Knowledge Base for more information on roof calculations and pitch in PrebuiltML.