About this calculator
This calculator takes off a whole single-slope (mono-pitch, lean-to, shed) roof: the rafter length along the slope including the overhangs, the number of rafters at your spacing, the total timber run and volume, the eaves and high-edge lengths, and the roof's surface area next to its plan projection.
The one thing to take away is that roof area is not floor area. A sloping
surface is longer than its shadow on the ground by a factor of 1 / cos(pitch),
and the overhangs add area that the building's own footprint does not have. The
calculator reports the footprint, the projected roof area and the true surface
area side by side so the difference is visible — it is the difference people
forget when ordering covering, membrane and battens.
This calculator does not design the structure. The rafter section is your input: it sizes the timber volume and nothing else. Whether a 50 × 200 rafter can span 6 m at 600 mm centres under your snow and wind loads is a question for span tables or an engineer working to Eurocode 5 and its national annex — this page does not answer it and does not recommend a section.
Formula
Pitch can be entered as an angle or as a rise per run (two lengths, so 4 in 12
or 250 per 1000 both work); rise/run is converted once with pitch = atan(rise / run) and everything below uses the angle. The slope arithmetic is the same the
rafter calculator uses:
run = building width (wall to wall)
rise = run × tan(pitch)
projected width = eaves overhang + run + high-side overhang
rafter length = projected width / cos(pitch) (along the top edge)
slope length = run / cos(pitch) (wall to wall only)
roof length = building length + 2 × gable overhang (= eaves length = high-edge length)
roof surface area = rafter length × roof length
projected roof area = projected width × roof length
footprint area = building length × building width
area factor = 1 / cos(pitch) (= surface / projection)
rafter count = ceil(roof length / rafter spacing) + 1
total rafter run = rafter count × rafter length
timber volume = rafter count × rafter length × rafter width × rafter depth
Rafter length is measured along the top edge, from tail to tail, in one division so it is rounded once. The rafter count places one rafter at each end of the roof (the barge or fly rafters at the gable overhangs) and one per spacing interval between them, rounded up — the last bay comes out shorter than the spacing, never longer.
Worked example
Defaults: 10 × 6 m building, pitch 15°, eaves overhang 500 mm, high-side overhang 300 mm, gable overhang 300 mm, rafters 50 × 200 at 600 mm.
rise = 6000 × tan 15° = 6000 × 0.26795 = 1607.7 mm
projected width = 500 + 6000 + 300 = 6800 mm
rafter length = 6800 / cos 15° = 6800 × 1.03528 = 7039.9 mm
roof length = 10000 + 2 × 300 = 10 600 mm
surface area = 7.0399 × 10.6 = 74.62 m²
projected area = 6.8 × 10.6 = 72.08 m² (surface is 3.5 % more)
footprint = 10 × 6 = 60.00 m² (surface is 24 % more)
rafters = ceil(10 600 / 600) + 1 = 18 + 1 = 19
total rafter run = 19 × 7.0399 = 133.8 m
timber = 19 × 7.040 × 0.05 × 0.2 = 1.338 m³
At 15° the slope adds only 3.5 % over its projection; it is the overhangs that make this roof a quarter larger than the floor beneath it. At 45° the factor is √2 = 1.414 — a 45° roof has 41 % more surface than its shadow.
FAQ
Why is the roof area larger than the building area?
Two reasons, and the calculator separates them. The slope: a surface tilted at
angle θ has 1 / cos θ times the area of its plan projection (3.5 % at 15°,
15 % at 30°, 41 % at 45°). The overhangs: every edge that projects past the
wall adds roof that the footprint does not contain. Order covering by the
surface area, not by the floor plan.
Which pitch input should I use? Whichever your drawing gives. An angle is what a drawing usually shows; rise per run is how imperial pitches (4 in 12) and some metric ones (1 : 4) are quoted. Both are converted to the same angle, so the results are identical.
Does the rafter count include the ones at the gable ends? Yes — one at each end of the roof length (which includes the gable overhangs), plus one per spacing interval, rounded up. If your design carries the gable overhang on a ladder rather than a full rafter, the outermost rafter is still a piece of timber of that length; count it.
Can I use this for a flat roof with a fall? Yes, down to 1°. Below about 18° (4 in 12) the calculator warns that the covering must be rated for the slope — that threshold is a general rule of thumb, not a standard; the real minimum pitch is the covering manufacturer's.
Does it check the rafter size? No. The section is your input and only sizes the timber. Spans, loads and deflection are governed by Eurocode 5 with the national annex for your country, or by published span tables — this calculator does not attempt them.
Why are the section lengths in whole millimetres? Rafter length, slope length and rise are cut dimensions, so they are shown in millimetres regardless of size; the totals (eaves length, total rafter run) are summary quantities and scale to metres.
Assumptions and limits
No standard is cited. Roof area, rafter length and rafter count are trigonometry and counting; no standard governs them and none has been invented. The 18.4° (4 in 12) low-slope warning is a general guideline, not a code requirement.
Geometry only, no structural design. The rafter section is a user input used solely for the timber volume. This page does not check spans, loads, bearing, bracing, or connections, and does not recommend a section.
The rafter is straight and continuous from tail to tail; birdsmouth cuts, purlins, ridge or wall-plate thickness and any splice are not modelled. Rafter length is the top-edge line length, the same convention the rafter calculator uses; it is not the centreline and it is not a purchase length rounded to a stock size.
No waste allowance is applied to the timber; the count already includes the end rafters and rounds the last bay up.
Overhangs are horizontal projections (measured in plan, not along the slope), and the gable overhang is the same at both ends.