Understanding Roof Pitch: Degrees, Percent and Ratio
Roof pitch is one of the most important parameters when planning a roof. It determines not only the building's appearance but also affects the choice of roofing material, snow load capacity and usable space in the attic. But how is roof pitch actually expressed?
In Germany, three notation systems are common: degrees, percent and ratio. The degree measurement describes the angle between the roof surface and the horizontal. A gable roof with a 45-degree pitch has a roof surface standing at exactly 45 degrees to the horizontal.
The percentage notation expresses the ratio of height to horizontal distance. At 45 degrees, the slope is exactly 100%, because the height equals the horizontal distance. At 35 degrees (a typical gable roof), it is approximately 70%. The conversion formula is: Percent = tan(angle) x 100.
The ratio (e.g., 1:1.4) indicates how many horizontal units are needed to rise one vertical unit. At 35 degrees, the ratio is approximately 1:1.4 -- over 1.4 m of horizontal distance, the roof rises by 1 m. This notation is frequently used in construction plans.
In practice, most roofers and architects work with degrees. Building code requirements also typically refer to degrees. The percentage notation is more common in civil engineering and slope calculations.
Calculating Rafter Length and Ridge Height
Rafter length (also called common rafter length or slant height) is the length of the timber beam that reaches from the eave to the ridge. It is crucial for material ordering and structural calculations of the roof frame.
The basic formula for rafter length derives directly from trigonometry. For a gable roof with symmetrical pitch: Rafter length = half building width / cos(pitch angle). For a 10 m wide building with 35-degree pitch: Rafter length = 5 / cos(35) = 5 / 0.819 = 6.10 m.
However, this is only the rafter length without overhang. In practice, the rafter extends beyond the exterior wall to protect the facade from rain. This roof overhang typically measures 30 to 80 cm. The corrected formula is: Rafter length with overhang = (half width + overhang) / cos(angle).
With a 50 cm overhang: (5 + 0.5) / cos(35) = 5.5 / 0.819 = 6.71 m. The rafter must therefore be at least 6.71 m long. In practice, you order slightly longer (e.g., 7 m) since wood is needed at both ends for connections.
Ridge height above the eave also comes from trigonometry: Ridge height = half width x tan(angle). At 10 m width and 35 degrees: 5 x tan(35) = 5 x 0.700 = 3.50 m. The ridge sits 3.50 m above the eave line.
For the absolute ridge height above ground, add the eave height (height of the exterior wall to the roof edge). With an eave height of 5 m, the absolute ridge height is: 5 + 3.50 = 8.50 m.
Roof Area for Gable, Lean-To and Hip Roofs
Roof area is the actual surface to be covered -- it is always larger than the building footprint because the sloped surface is longer than its horizontal projection.
For a gable roof, the total roof area is: Roof area = 2 x rafter length (with overhang) x (building length + 2 x overhang). For our example (10 x 12 m, 35 degrees, 50 cm overhang): Roof area = 2 x 6.71 x (12 + 1) = 2 x 6.71 x 13 = 174.5 sqm.
For a lean-to (pultdach) roof, there is only one sloped surface. The rafter spans the entire building width (not just half). Formula: Roof area = rafter length x (building length + 2 x overhang). The rafter length is: (building width + overhang) / cos(angle).
The hip roof is more complex. It consists of four sloped surfaces: two trapezoidal main faces (along the building length) and two triangular hip faces (at the ends). The ridge length is shorter than the building length because the hip faces shorten the ridge.
The ridge length of a hip roof is: building length minus building width. For a 10 x 12 m building: 12 - 10 = 2 m ridge length. The main faces are calculated as trapezoids, the hip faces as triangles.
For a flat roof, the calculation is simplest: the roof area nearly equals the footprint since the pitch is minimal (typically 2 to 3 degrees). Roof area = (width + 2 x overhang) x (length + 2 x overhang).
Roofing Material: Minimum Pitch per Material
Not every roofing material suits every pitch. The minimum pitch (also called standard roof pitch) is the pitch at which a material reliably remains waterproof.
Clay tiles and concrete tiles require at least 22 degrees. At lower pitches, rain can penetrate through the tile overlaps. In snowy regions, 25 degrees is often recommended.
Slate coverings require at least 25 degrees. Slate is a natural stone split into thin sheets. The covering relies on overlap, which is insufficient at lower pitches.
Asphalt shingles can be used from 15 degrees. They are flexible and nailed down, providing good rain resistance even at lower pitches.
Standing seam metal can be used from 7 degrees. The standing seams ensure reliable sealing even on flatter roofs. Trapezoidal metal works from as low as 5 degrees.
EPDM membranes and other synthetic sealants can be used from 2 degrees and are the standard solution for flat roofs.
Calculating Snow Load per DIN EN 1991
Snow load on the roof is a critical parameter for structural design. In Germany, calculation follows DIN EN 1991-1-3 with the national annex.
Germany is divided into five snow load zones: Zone 1 (lowest load, typical for northern Germany), Zone 1a, Zone 2 (central mountains), Zone 2a and Zone 3 (Alpine foothills, highest load). Assignment is based on the building's geographic location.
The characteristic ground snow load (sk) is calculated from the snow load zone and terrain elevation. For Zone 1: sk = 0.19 + 0.91 x ((h + 140) / 760)^2, where h is the elevation in meters above sea level.
The snow load on the roof is obtained by multiplying with the shape coefficient mu, which depends on pitch angle: At 0 to 30 degrees, mu = 0.8. At 30 to 60 degrees, mu decreases linearly: mu = 0.8 x (60 - alpha) / 30. Above 60 degrees, mu = 0 (snow slides off).
Roof Overhang and Eave: Construction Details
Roof overhang is the horizontal distance by which the roof extends beyond the exterior wall. It protects the facade and base area from driving rain and direct sunlight.
In Germany, roof overhangs between 30 and 80 cm are typical. On modern buildings with good facade sealing, the overhang can be smaller (20-30 cm). On historic buildings or in snowy regions, overhangs of 80-120 cm are not uncommon.
The eave is the lower edge of the roof where rainwater drips off. A gutter is typically mounted at the eave to collect and channel water. The eave length of a gable roof is: 2 x (building length + 2 x overhang).
The overhang construction directly affects rafter length: each centimeter of overhang extends the rafter by more than one centimeter since the rafter is angled. At 35 degrees, the factor is 1/cos(35) = 1.22. A 50 cm overhang therefore extends the rafter by 61 cm.