A gable roof spanning 28 ft with a 7 ft rise has a run of 14 ft, so the pitch is 6/12: an angle of 26.6° and a slope of 50%. With a 1 ft overhang each rafter measures 16.77 ft along the slope, and the roof surface is 1.118 times the footprint.
Result
Angle26.6°
Slope50 %
Pitch6/12
Rafter length16.77 ft
Cut the rafter at16 ft 9.75 in
Pitch factor (roof area ÷ plan area)1.118
How the number is worked out
A roof slope is a right triangle. The run is the flat side, the rise is the
upright side, and the rafter is the long side between them. The angle comes
from the arctangent of rise over run, the rafter from Pythagoras, and nothing
in between depends on a product, a brand or a supplier - which is why this
calculator needs no assumptions panel.
If you already know the angle, switch the input to it. The calculator then works
the other way and gives you the rise for your run.
Pitch, degrees and percent are the same thing
6/12, 26.6° and 50% describe one roof. The x/12 form is the American
convention, degrees are what a speed square and most European drawings use, and
percent is rise divided by run times a hundred. A 12/12 roof is 45° and 100%,
which is the easiest of the three to remember.
Why the cutting length rounds up
The rafter length is the only result you cut timber to, so it is shown twice:
the exact figure, and a cutting length rounded up to the next quarter inch. A
rafter a hair too long gets trimmed in place; one a hair too short goes on the
scrap pile.
Worked example
Gable roof, 28 ft span with a 7 ft rise
Angle
26.6°
Slope
50 %
Pitch
6/12
Rafter length
16.77 ft
Pitch factor (roof area ÷ plan area)
1.118
Calculated by materiacalc using the same engine that runs the tool above.
In this market
In the US a roof pitch is quoted as inches of rise per 12 inches of run, and shingle and underlayment instructions are written against that number. Every shingle bundle states a minimum pitch for standard installation; check it before settling on a low roof, because below it the warranty usually asks for extra underlayment or a different product.
Questions
How do I measure the run?
Horizontally, from the outside of the wall plate to the point directly under the ridge. On a gable roof that is half the building's width; on a lean-to it is the whole width.
Why is the rafter longer than the overhang on the plan suggests?
Because a plan measures the overhang flat, while the rafter follows the slope. The steeper the roof, the bigger the difference, and the calculator adds it for you.
What is the pitch factor for?
Multiply the roof's footprint, overhangs included, by it and you get the sloped surface - the area shingles, underlayment and sheathing are ordered by.