Most carpenters refer to a rafter length table to find rafter lengths, but calculating rafter lengths requires only basic maths. A gable roof can be thought of as two right triangles placed back to back. For calculating rafter lengths, we only need to be concerned with one of these triangles.

The distance from the outside wall of the building to the centre of the building is the adjacent or base side of the triangle. The height of the ridge, relative to the top of the wall plates, is the opposite side of the triangle. Since we know these figures, we can calculate the hypotenuse, which is the rafter length.

If you don't know the ridge height, but know the pitch of the roof, you can calculate the ridge height. Simply multiply the base length by the pitch. For example, a roof 3 m (120 inches) wide with a pitch of 4/12 = 3 x 4/12 = 1 m (or 120 x 4/12= 40 inches). The rafter length for this roof would be the square root of (3^2 + 1^2) = 3.16 m (or the root of (120^2 + 40^2) =126 1/2 inches). We then need to subtract half the ridge thickness, so for a 3.75 cm (1 1/2-inch) thick ridge, our final figure would be just over 3.14 m (125 3/4 inches).

- Skill level:
- Easy

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### Things you need

- Calculator with square root function

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## Instructions

- 1
Determine the distance from the edge of the building to the midline of the building for gable roofs (building width x 0.5). For shed roofs, use the width of the building. This is the base, or adjacent side of your triangle.

- 2
Determine the ridge height. Use the distance from step one times the pitch of the roof in cm of rise per cm of run (or inches of rise per inches of run). This is the vertical, or opposite side of your triangle.

- 3
Take the square of the adjacent side, and add it to the square of the opposite side.

- 4
Take the square root of the result in step three and subtract half your ridge thickness; this is your rafter length. If you want a rafter tail, add the tail amount to the calculated rafter length.

#### Tips and warnings

- Expressing all of your dimensions in the same unit will make the calculations easier.