A pitch adjusted measurement refers to a measurement from a 2-dimensional plan that factor in a slope. When reading a set of plans, these materials need to factor in the extra lengths and square footages required to span or cover a sloped area.
A 10-foot by 10-foot shed with a single slope roof will have a total of 100 square feet of floor space, but the roof will have slightly more square footage because of its pitch. The steeper the pitch, the greater the amount of additional square footage. The rafters will also need to be longer to cover the span once they’re pitched at the angle of the roof.
The easiest way to calculate a pitch adjusted measurement is by using pitch conversion multipliers.
The table below shows the pitch multipliers for some common roof slopes. Using this table is quite simple, take the ‘flat’ or unadjusted dimensions, and multiply them by the multiplier that corresponds with the appropriate slope.
| Pitch | Multiplier |
|---|---|
| 1/12 Pitch | 1.0035 |
| 2/12 Pitch | 1.0138 |
| 3/12 Pitch | 1.0308 |
| 4/12 Pitch | 1.0541 |
| 5/12 Pitch | 1.0833 |
| 6/12 Pitch | 1.1180 |
| 7/12 Pitch | 1.1577 |
| 8/12 Pitch | 1.2019 |
| 9/12 Pitch | 1.2500 |
| 10/12 Pitch | 1.3017 |
| 11/12 Pitch | 1.3566 |
| 12/12 Pitch | 1.4142 |
Using the shed example, the roof needs to cover 100 square feet at a pitch of 4/12:
100 x 1.0541 = 105.41
The same applies for the rafters which need to span 10 feet:
10 x 1.0541 = 10.54
It’s really that simple!
How are pitch multipliers calculated?
One way that you can calculate those multipliers yourself is by using the using the Pythagorean theorem:
a2 + b2 = c2
With roofs, the hypotenuse (c) is the rafter length, and a and b are the rise and run of our slope. Using the 4/12 slope again we can plug those numbers into the Pythagorean theorem and solve for c:
42 + 122 = c2
Dividing the rafter length by the run of 12 allows us to know the ratio of rafter length in relation to the run total run:
12.649/12 = 1.0541
That number tells you that for each linear or square foot you’ll need 1.0541 times more material to cover the slope. By using these multipliers, you can quickly and easily determine the pitch adjusted measurements for any set of plans or drawings.
Using these multipliers is much easier than trying to use the Pythagorean theorem with the actual dimensions provided on your plans. In many cases your plans will only show the scale of the page a few dimension lines, and the slope of the roof which is in inches per foot. The run or span (b), of the pitched area might be easy to find, but the total rise (a) across that span might not be immediately obvious.
Additional Considerations.
One final point to note about rafter framing is that the rafters will typically need to be cut “plumb” to fit the ridge beam and fascia boards. Consider this example:
Once the end of the rafter is cut plumb to match the ridge, the useable board will be slightly shorter. That extra little amount depends on the size of the rafters you’re using and the steepness of the slope. On the other hand, it can be offset somewhat by the thickness of the ridge beam itself. Getting all these small factors exactly right may not make the biggest difference in the end but it is something to consider.
Computer programs like PrebuiltML and even some online rafter calculators can easily account for all these factors and save you the time of doing calculations on your own. But even with all the conveniences of architecture and construction software, it’s important to know how to deal with pitch and pitch adjusted measurements when working on smaller projects around the house. With the way that lumber prices are trending you can never be too accurate!