Roof Pitch & Rafter Length Calculator
Turn a building span and roof pitch into rafter length, ridge rise, pitch angle and the area multiplier that decides how much roofing you actually order.
Full width, gable end to gable end.
4/12 is common on post-frame; 1/12 to 3/12 on steel.
Horizontal projection past the sidewall. 0 for a flush eave.
The area multiplier is the number to remember: a 1.054× factor means the roof surface is 5.4% larger than the footprint it covers. Ordering sheeting off the floor area is the classic way to come up short.
What this calculator does
Roof pitch is the input that quietly decides three other numbers: how long the rafters are, how high the ridge sits, and — the expensive one — how much bigger the roof is than the building underneath it.
Give it a span and a pitch and it returns all of them, including the area multiplier that most material shortfalls trace back to.
The geometry
A gable roof is two right triangles back to back. Half the span is the run, the pitch sets the rise, and the rafter is the hypotenuse:
run = span ÷ 2
rise = run × (pitch ÷ 12)
rafter = √(run² + rise²)A 40-foot building at 4/12: the run is 20 feet, the rise is 6.67 feet, and the rafter travels 21.08 feet from wall to ridge.
That 21.08 against 20 is the whole point. The roof surface is 5.4% larger than the footprint suggests, and that percentage flows straight into sheeting, insulation, purlins and labour.
The area multiplier is the number worth memorising
multiplier = √(pitch² + 144) ÷ 12| Pitch | Multiplier | Extra roof area |
|---|---|---|
| 1/12 | 1.003 | 0.3% |
| 3/12 | 1.031 | 3% |
| 4/12 | 1.054 | 5% |
| 6/12 | 1.118 | 12% |
| 9/12 | 1.250 | 25% |
| 12/12 | 1.414 | 41% |
Multiply the footprint by this and you have the true roof area. Below about 3/12 the correction is nearly negligible, which is part of why steel buildings are built shallow. Past 6/12 it is a material cost you should be choosing deliberately.
The metal panel calculator turns that area into a sheet count, and the same multiplier logic drives shingles in the roofing calculator — the geometry does not care what the covering is made of.
Overhang costs more than its horizontal length
A one-foot overhang does not add one foot of rafter. It adds one foot measured along the slope, so the rafter grows by the overhang times the multiplier.
Small on a shallow roof, real on a steep one: a two-foot overhang at 12/12 adds 2.83 feet to every rafter. The calculator reports the cut length with the overhang included, which is the figure you actually order lumber to.
Measuring an existing roof
You do not need to get on it. From inside the attic or under the rafters:
- Hold a level horizontally against a rafter’s underside.
- Mark 12 inches along the level.
- Measure straight down from the mark to the rafter.
That vertical distance is the rise. A six-inch drop is 6/12. Most US buildings land between 3/12 and 8/12; anything above 8/12 needs staging to work on safely, which is worth knowing before you price labour.
Choosing a pitch on a new build
Three considerations, in rough order of weight:
- Panel warranty. Many metal roofing products state a minimum slope, often around 3/12 for exposed-fastener panels and lower for standing seam. Below it, coverage can be void. Check before designing.
- Snow. Steeper sheds better, and in snow country that is a real durability argument, though the load itself is an engineering question for your site.
- Cost. More pitch means more roof, more rafter length, more purlins and harder work. At 12/12 you are buying 41% more roof than your floor.
What this will not tell you
The size of anything. Rafter depth, purlin gauge, spacing, connections and how snow and wind load your specific building are structural engineering, done for your site and stamped by a licensed engineer.
This page does trigonometry, which is genuinely useful for takeoffs and completely different from design. For the frame counts on a post-frame structure, the post-frame calculator applies the same rafter geometry to purlin rows and roof area.
How this is calculated
run = span ÷ 2 rise = run × (pitch ÷ 12) rafter = √(run² + rise²) area multiplier = √(pitch² + 144) ÷ 12 angle = arctan(pitch ÷ 12)
Frequently asked questions
- What does "4/12 pitch" actually mean?
- The roof rises 4 inches for every 12 inches it travels horizontally. It is a ratio, not an angle, and the 12 is always the run. A 4/12 roof is about 18.4 degrees. US construction talks in rise-over-12 because it is easy to lay out with a framing square, while the degree figure is mostly useful for cutting.
- Why is the roof area bigger than the building footprint?
- Because the roof is the sloped face of a triangle and the footprint is its base. The ratio between them is the area multiplier — 1.054 at 4/12, 1.118 at 6/12, 1.414 at 12/12. Ordering roof sheeting off the floor area is the most common material shortfall on a building.
- How do I measure pitch without climbing on the roof?
- From inside, hold a level horizontally against a rafter, mark 12 inches along it, and measure straight down to the rafter at that mark. That drop in inches is the rise over a 12-inch run. A six-inch drop is 6/12.
- Does this give me the rafter size I need?
- No. It gives the length a rafter travels — the geometry. What depth and grade of member can carry that span under your snow and wind loads is structural engineering, determined for your site and put on a stamped drawing. Length and size are different questions.
- What pitch should a metal building have?
- Steel buildings commonly run shallow, often 1/12 to 3/12, because the panels shed water at low slopes and a flatter roof uses less material. Post-frame and residential-style buildings usually run 4/12 or steeper. Snow country pushes steeper; check what your panel manufacturer warrants at low slope, since many void coverage below a stated minimum.