"One in four" is not one roof
There are four common ways to state a pitch and at least three of them get confused with each other:
- Degrees: 35°.
- Rise to run, rise written first: 1:1.43.
- Run to rise, run written first: 1.43:1. Same roof, opposite notation.
- x in 12: 8.4 in 12, the American convention.
Written rise first, 1:4 is about 14 degrees. Written run first, 4:1 is about 76 degrees. Those are not similar roofs, and a drawing that says "1 in 4" without saying which convention it means is a genuine hazard.
So this tool never shows a pitch on its own. Put it in however you have it, and all four forms come back together. That is the entire design decision and it is the reason the page exists.
The slope factor, and the short tile order
A roof is bigger than the footprint it covers, by 1 / cos(pitch).
At 30° that is 1.155. At 35°, 1.22. At 45°, 1.414: the roof is 41 per cent bigger than the plan. Take a tile quantity off a plan area at that pitch and you are 41 per cent short, and you find out on the last day.
It is on the panel permanently, next to the pitch, because it is the number that costs money. Working the other way is just as useful: a slope area divided by the factor gives you the footprint, which is what you need for the scaffold.
Why your first hip rafter was short
Everybody does this once. You work out the common rafter, cut the hip to the same length, and it does not reach.
A common rafter runs straight across the run. A hip runs diagonally, so its horizontal distance is the diagonal of the two runs, not either one of them. The length is √(rise² + runA² + runB²), which over equal runs is √(rise² + 2·run²).
And there is a second half nobody mentions: the hip sits at a shallower angle than the common pitch. Over equal runs at 40°, the hip is at about 30°. So a hip cut to a common rafter bevel does not seat properly either, even if you got the length right.
The tool gives you both, the true hip length and the angle it actually sits at, for exactly this reason. Unequal runs work too, which is what makes it a valley calculation.
The run includes the overhang
The run is half the span plus the overhang, and the overhang is the bit that gets left out. Half of 8 metres is 4, but with a 300mm eaves projection the rafter is running 4.3 metres horizontally, and at 35° that is 350mm of extra rafter per side.
Both fields are on the tool and both feed the rafter length.
What these lengths are and are not
They are true lengths along the slope, to the face of the rafter. Pure geometry from the numbers you gave it.
They do not allow for half the ridge board thickness, the birdsmouth seating over the wall plate, or a plumb cut at the tail. Those are set out on the rafter itself from the working line, and no calculator can do them for you because they depend on the timber in your hand.
Next to it: roof area and tile counts, which uses the same slope factor, and printing a drawing to scale before you measure anything off it.
Common questions
What pitch is my roof?
Measure two things and the tool gives you the rest. The RUN is the horizontal distance from the outside of the wall to the centre of the ridge, which is half the span on a normal gable. The RISE is the vertical from the top of the wall plate to the underside of the ridge. Those two give the angle in degrees, the ratio, and the true rafter length, and any one of the three can be the one you already know. Measuring from inside the loft is usually easier and just as accurate, as long as you take the rise to the same point you took the run from.
What does a 1 in 4 roof pitch mean?
That depends who said it, which is exactly the problem. Written rise first, 1:4 is one up for four along: about 14 degrees. Written run first, 4:1 is four up for one along, about 76 degrees. Some drawings mean one form, some the other, and the American convention is different again. This tool shows all of them at once so nobody has to guess.
How do I convert roof pitch to degrees?
Degrees is the arctangent of rise divided by run. A 6 in 12 pitch is atan(6/12) = 26.6 degrees. A 1:2 rise to run is the same thing. Enter it however you have it: degrees, rise and run, or x in 12, and read it back in whichever form you need.
How do I work out rafter length?
Run divided by the cosine of the pitch, where the run is half the span plus the overhang. At 35 degrees over a 4m run that is 4 / cos(35) = 4.88m. The tool does it and includes the overhang, because it is the bit people forget until the eaves come up short.
Why is my hip rafter too short?
Because a hip does not run across the same distance a common rafter does. It runs diagonally, so its horizontal run is the diagonal of the two runs rather than either one. And it sits at a shallower angle than the common pitch, so a common-rafter bevel does not fit it either. This tool gives both the hip length and the angle it actually sits at.
What is the slope factor?
One divided by the cosine of the pitch: how much bigger the roof is than the footprint it covers. At 35 degrees it is 1.22, so the roof is 22 per cent bigger than the plan. At 45 degrees it is 1.41. It is the number that turns a plan area into an ordering area, and forgetting it is the classic short tile order.
Do the lengths include the cuts?
No. They are true lengths along the slope, to the face of the rafter. They do not allow for half the ridge board, the birdsmouth seating, or a plumb cut at the tail. Mark from the working line and set those out on the rafter itself.