Framing the Roof (Stick by Stick)
Before the invention of prefabricated roof trusses, every house in the world was "stick-framed." Carpenters would measure, cut, and install every single roof rafter by hand directly on the job site. Even today, stick-framing is still required for complex custom homes, dormers, vaulted ceilings, and remodeling additions.
A roof rafter is a massive piece of dimensional lumber (usually a 2x8, 2x10, or 2x12) that runs diagonally from the peak of the roof (the ridge board) down to the exterior walls of the house.
Accurately calculating the true diagonal length of a rafter is the most challenging mathematical task in residential carpentry. If you cut a rafter too short, you have completely ruined a $1 piece of lumber.
The Geometry of a Rafter
A roof is a right triangle. To find the length of the rafter, you must use the Pythagorean theorem (A² + B² = C²).
The three sides of the roof triangle are:
- The Run (Base): This is exactly half the total width of the house. If a house is 24 feet wide, the Run is 12 feet.
- The Rise (Height): This is how far the roof goes straight up from the top of the wall to the peak of the roof.
- The Rafter (Hypotenuse): The true diagonal length of the wood.
Calculating Rafter Length
The Formula
Instead of doing complex trigonometry on the job site, modern carpenters use a "Pitch Multiplier" derived from the roof's slope (e.g., 6/12 pitch).
- Determine the Run of the roof in feet (Half the width of the building).
- Determine your Roof Pitch (e.g., 6/12) and find its corresponding multiplier:
- 4/12 Pitch = 1.054
- 6/12 Pitch = 1.118
- 8/12 Pitch = 1.202
- 10/12 Pitch = 1.302
- 12/12 Pitch = 1.414
- Multiply the Run by the Pitch Multiplier. This gives you the diagonal length from the peak down to the wall.
- Determine your Overhang (the Eave) in inches. This is the part of the roof that sticks out past the wall.
- Convert the Overhang to feet (divide by 12) and multiply it by the Pitch Multiplier.
- Add the two numbers together.
Simplified Equation:
Quick Example: 24 ft Wide Building with 6/12 Pitch
You are building a garage that is 24 feet wide. The roof will have a 6/12 pitch (Multiplier = 1.118). You want a 12-inch overhang to keep rain off the siding.
- Find the Run:
24 ft wide ÷ 2 = 12 ft Run - Convert Overhang to feet:
12 inches = 1 ft - Add Run and Overhang:
12 ft + 1 ft = 13 ft total horizontal run - Multiply by Pitch Multiplier:
13 ft × 1.118 = 14.53 feet
Your total rafter length is 14.53 feet. You must go to the lumber yard and purchase 16-foot 2x10s, because 14-foot boards will be a few inches too short!