You may need to calculate a pitched roof if you are considering replacing your roof or having other repairs done. Although a basic understanding of algebra is helpful, it is not necessary. There is certainly no advanced mathematics used, which is helpful if math was not your favorite subject in school. By using a grade-school algebra principle, the slope, you can easily determine the pitch of your roof.
The pitch of a roof is the number of inches that the roof rises per every 12 inches that it runs. In other words, for every 12 inches that you pass, how much do you go up? You might remember learning about "rise over run" in school. The same principle applies here. Mark the 12-inch spot on your level with your pencil to make it easier to spot when you begin your measuring. Situate your ladder on the side of your house, where you can easily assess the angle of the roof. Your first step is to climb your ladder, level in hand, and place your level horizontally from a spot on the roof.
Ensure that the level is indeed perfectly horizontal, and then measure down from the top of the roof to the 12-inch mark you made prior to climbing the ladder. This number is your rise. The 12-inch mark is your run. Be sure to measure from the bottom of the shingle layers. Shingles have their own slope on top of the roof pitch—which should not be included in the pitch calculation. Note that if you have several layers of shingles or if your roof is uneven, you may need to calculate from a rafter rather than the roof itself. Do this by situating your ladder on the barge end, and use the same methodology as before.
Another way to calculate the roof pitch is to assess the entire rise over the entire run, then divide both numbers by 12 to make it fit standard pitch calculations. However, the former method is usually easier and often more accurate. There are also specialized tools that quickly calculate roof pitch without the need of a level or tape measure. These can be extremely helpful if you're having difficulty fumbling with several tools while on the ladder.
Now it's time to get mathematical. Be sure that you take your measurements in inches, regardless of where you take the measurements. For example, if you took the pitch from the roof itself or from a gable, both measurements should be in inches. The formula for roof pitch is "x/12." The x in the equation is the vertical measurement you got in Step 1. For example, if you measure 2 inches, then your pitch is 2/12, which is very low. However, a 12/12 pitch, which would be a 45-degree angle, is very steep.
It is not necessary to mathematically reduce your pitch's fraction, because 12 inches is the standard run. This means that if your pitch is 6/12, do not tell the contractor that it is 1/2.