Unlock the geometry of 45° corner projections. Understand why common rafters use 12" of run while hips & valleys use 16.97" (17"), and how to read the HIP-VAL scale on your speed square effortlessly.
Runs perpendicular from the top plate to the ridge. For a 6/12 roof, it rises 6 inches for every 12 inches of horizontal run.
Runs at a 45° diagonal angle across the corner. For the exact same 6" rise, the hip rafter must travel 17 inches horizontally.
Find the scale marked HIP-VAL on your square. If your main roof pitch is 6/12, rotate the square pivot until the edge aligns with 6 on the HIP-VAL scale (which equals 19.5° instead of 26.6°).
The hip rafter connects to the ridge at a 45-degree angle. Draw your plumb line, then bevel your circular saw table to 45 degrees to create the side cheek cuts that fit snugly against the ridge board.
Because the hip rafter sits over the corner of two exterior plates, the seat cut must be deep enough so the center of the hip aligns with the plane of the common rafters (or the hip must be planed/backed).
Enter your common roof pitch and building run to instantly calculate exact Hip/Valley plumb angles and true line length.