How the pitch is worked out
Pitch is the angle whose tangent is the rise divided by the run. A 1,500 mm rise over a 3,000 mm run is 0.5, which is 26.6 degrees.
The same relationship gives rise per 12 of run, which is the rise divided by the run multiplied by 12. That is 6 in 12 for the same roof.
The percentage slope is the rise divided by the run times 100, so the same roof is 50 per cent. Three ways of saying one angle.
Worked example
A roof rising 1,500 mm over a 3,000 mm run has a pitch of 26.6 degrees, a rise of 6 in 12 and a 50 per cent slope.
The rafter is the hypotenuse, 3,354 mm, plus the overhang at the same angle. A 300 mm overhang makes the rafter 3,654 mm.
Why pitch matters
Pitch decides which covering will keep the water out. Plain tiles need a steeper roof than interlocking tiles, and some sheet materials have a minimum pitch of 10 degrees or less.
It also decides the headroom in a loft conversion. A 26 degree roof has little usable space, while 45 degrees gives a proper room in the middle.
Structural loads change with pitch too, because a steeper roof catches more wind and carries snow differently.
Limits of this calculator
It works on a straight, constant pitch. A curved roof, a mansard or a gambrel has several pitches and needs each one calculated.
It does not check the pitch against the minimum for a particular covering, which is the manufacturer's figure.
It gives the rafter length on the slope, not the cutting list. Birdsmouths, ridge cuts and wall plate positions are separate.
For the tiles that go on the roof, use the roof tile calculator.
Inputs for the roof pitch calculator
Rise
Vertical height the roof gains over the run, in millimetres.
Run
Horizontal distance from the wall plate to the ridge, in millimetres.
Eaves overhang
How far the rafter runs past the wall. Enter zero for a bare rafter.
CALCULATOR QUESTIONS
Roof pitch calculator questions
What is a 30 degree roof in rise over run?
About 6.9 in 12, or a 58 per cent slope.
What is the minimum pitch for tiles?
It depends on the tile. Interlocking concrete tiles often go down to 15 degrees, plain clay tiles need about 35.
How do I measure the run?
Horizontally from the outside of the wall plate to the centre of the ridge, not along the slope.
Does the overhang change the pitch?
No, but it changes the rafter length, because the overhang continues at the same angle.