A hip rafter extends diagonally downward from the ridge at the top of the roof to the top plate at the building corner. The top plate is the horizontal 5 x 10 cm (2 x 4 inch) or 5 x 15 cm (2 x 6 inch) joist that ties together the upper ends of the building studs. Neither the plan-view of the building (looking down from above) nor any elevation view (looking toward the building at an exterior wall) shows the actual length of the hip rafter (since it lies in neither the plan nor elevation plane), nor indicates the angles of the necessary cuts at either end of the hip rafter. But you can calculate length and angles using measurements taken from the plan and elevation views, then use this information to cut the hip-rafter to the correct length and angles.

- Skill level:
- Easy

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### Things you need

- Architectural drawings of plan and elevation of the building
- Carpenter's square and/or a large protractor
- Timber to make hip rafter
- Rotary saw
- Paper and pencil

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## Instructions

- 1
Draw a vertical line "b"downward from the ridge to the elevation of the top plate on the elevation view of your architectural drawing.

- 2
Draw a diagonal line "a" from the top plate at a building corner over to the end of the ridge on the plan view of your architectural drawing.

- 3
Measure "a" and "b". You can then multiply "a" by itself (which is the square of "a"), multiply "b" by itself (the square of "b") and add "a" squared and "c" squared together to find the value of "c" squared. The formula looks likes this: "a" squared plus "b" squared equals "c" squared, and is called The Pythagorean Theorem. You can then find the value of "c" (the square root of "c" squared) on a calculator, which is the length of your hip-roof. But using the Internet, there is an easier way.

- 4
Find the value of "c" by looking it up on any number of online maths websites, such as the square roots page on the A Zillion Monkeys website (see Resources). Plug in the value for the sum of "a" squared plus "b" squared and it will output "c." This is the length of your hip rafter measured at the top of the rafter, which is its maximum length.

- 5
Cut the hip-rafter to the correct length with a rotary saw, being careful to cut both ends precisely at right-angles.

## Finding the length

- 1
Find the angles for the cuts at either end of your hip rafter by looking them up on an online math page such as Hamilton's website (see Resources) Input "a" and "b" and this Web page will output both angles. One angle will be closer to a right-angled than the other; this is the angle at the top of the rafter where it joins the ridge. The other angle is the angle where the hip rafter joins the top-plate.

- 2
Mark off the two lines describing these angles onto your hip-rafter with a carpenter's square. Cut the hip-rafter to the correct angles with a rotary saw.

- 3
Make two side-cuts, one on either side of the top-end of the hip-rafter, which allow the hip rafter to fit into the angled space formed by the intersection of the rafters running upward at right-angles to one another to join the ridge. This sounds more complicated than it is. There are online calculators that will determine these angles for you, such as Blocklayer (see Resources), but in practice if you lay the hip-rafter in its approximate final position on the roof, you can come close enough simply by eyeballing them, marking them off with your carpenter's square, then making both cuts with a rotary saw.

- 4
Make two similar side-cuts at the lower-end of the hip-rafter unless your building is going to have an eave. If so, leave the hip-rafter long and cut it to the right length after it is in place.

## The angles of the cuts

#### Tips and warnings

- If your hip-rafter will be part of an eave, take that into account when calculating the hip-rafter's length. First calculate the length without the eave, then add the additional length needed for the eave. You can calculate this additional length online or you can leave the hip-rafter long, make the angle and side-angled cuts at the top, put it in place, and mark off the final length with a carpenter's square.
- Note that the additional length (called the "tail") to be added to a hip-rafter forming an eave is not the same length as the other rafter tails; it will be somewhat more because the other tails are at right-angles to the top-plate and the tail of the hip-rafter is at a diagonal. In mathematical terms it is a hypotenuse of the triangle formed by top-plate, the nearest rafter and line drawn from the end of the tail of that rafter to the foot of the tail of the hip-rafter. Leave the hip-rafter long, then put your carpenter's square at the foot of the rafter tail, extend it over past the long end of the hip-rafter, draw a line where the carpenter's square meets the hip-rafter, and cut along that line.