![]() ![]() b = vertical rise or change in height - in our example above this is also given as Y.a = horizontal run - in our example above this is also give as X.Remember the basic formula for the lengths of sides of a right triangle (half of a roof) Key concept: If we know the length of any two sides of a right triangle we can calcluate the length of the missing side. Now that we used tan to find the run length, we’ll go back to our formula for the lengths of sides of a right triangle -your roof. Using basic rules of algebra we can rewrite the equation: multiply both sides by run (b) Or, looking up 32 in the TAN table found at ROOF SLOPE CALCULATIONS (or on your calculator) Tan 32° = rise (4 ft 9 in or all in inches: 48+9 = 57 inches) / run (unknown) TAN (Roof Angle or Slope) = Roof Rise / Roof Horizontal Run In your problem statement the tangent T of the 32 degree angle (the roof slope) is the ratio: Then we can use simple algebra and arithemetic to calculate the rafter length.Ī tangent is also defined as a ratio of two lengths: the length of the side of the triangle opposite the angle divided by the length of the adjacent side of the angle.įor a right triangle (such as a roofing triangle) in which the roof rise is the vertical line opposite the roof angle or slope, the tangent of the roof angle is the ratio of roof rise over the length of the sloped roof surface. We can use the Tangent function to give us the ratio of two sides of our roof triangle (one of which, the rafter length) is unknown. When we know the length of just one side (rise or b in your problem an din our sketch above)Īnd where we know the roof slope in degrees (32° ) You'd use 32° instead of our example of 38° roof slope and use the TAN function (or a TANGENTS TABLE like the one we provide in that article) to calculate the sloped side or upper side of your triangle - the rafter. In our sketch (above) and below in more detail we show you how to calculate the rafter length you want.Īt and also at ROOF SLOPE CALCULATIONS in a section titled "How to Convert Slope or Angle in Degrees into Distance Rise or Run" we go through the basic calculations using a 38° roof. THANK YOU for asking a helpful question: how to calculate rafter length if all we know is the roof rise and roof angle or slope. Here are the details of the rafter length calculation given above See CONVERT ROOF SLOPE or ANGLE in DEGREES to RISE or RUN Details of Rafter Calculations from Roof Slope Note: if your roof slope is expressed in the more widely used "rise" such as a rise of 7.5" meaning the roof slope rises 7.5" for every 12" (or foot) of horizontal run, and if you want to convert that to a roof angle in degrees (as we use roof angle on this page) then Knowing the length of any two sides of a right triangle lets us calculate the length of the missing side, because the relationship of the three sides of a right triangle can be written as the square of their lengths/ Knowing the tangent of the roof angle or slope + the length of either of the two sides (roof rise or roof run) lets us calculate the length of the missing side. Tangent of an angle is defined as the ratio of the length of the right triangle's side adjacent to the angle (a) to the length of the side opposite the angle (b). Here is a summary of how we use the TAN or tangent function to calculate the length of a rafter when all we know is the roof slope and the roof total rise. If the vertical change in height is 4 feet 9 inches as indicated, how long must the rafter be? - 2 Moderator reply: The angle of elevation of a roof top is 32°. ![]() How to Calculate Roof Rafter Length from Slope & Rise Question: if my roof slope is 32° and the rise is 4' 9", how long will the rafter be We also provide an ARTICLE INDEX for this topic, or you can try the page top or bottom SEARCH BOX as a quick way to find information you need. Page top sketch of various roof slopes is provided courtesy of Carson Dunlop Associates (found at page bottom, Click to Show or Hide), Toronto. This article series gives every possible way to figure out any or all roof dimensions and measurements expressing the roof area, width, length, slope, rise, run, and unit rise in inches per foot. These same calculations used for roof rafter length will let you compute the length of roof trusses or the length of ramp or stair support stringers. ![]() Roof total rise (at the ridge), roof horizontal run distance, rafter length, or roof slope in rise/run or slope or percent slope or even a tangent value. Roof rafter length or calculation is easy if we know any tworoof measurement numbers chosen from: We have no relationship with advertisers, products, or services discussed at this website. InspectAPedia tolerates no conflicts of interest. ![]()
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