Single-Slope Roof
About Single-Slope Roof Calculation
The Single-Slope Roof Calculator performs rafter and roof pitch calculations for a single-pitch roof and determines the required quantities of the main timber elements and roll materials. The calculation uses the building dimensions, roof overhangs, roof pitch, rafter and batten layout, and selected additional elements. It is suitable for estimating lean-to roofs and other single-pitch structures and provides calculation data for the rafter system, battens, and materials used with rigid or flexible roofing.
All input linear dimensions are specified in millimetres. Areas are calculated in m2, timber and insulation volumes in m3, and total lengths of individual materials in metres. The geometric formulas do not include safety or waste factors. Material quantities are determined from the actual calculated geometry, taking into account the element layout rules, overlaps, and other conditions described below.
Guidelines and Recommendations
Single-Slope Roof Geometry
Roof pitch. The roof pitch angle α is determined from the roof rise H and the horizontal building width X. The overhangs do not change the angle because they continue along the same roof slope.
α = arctan(H / X)
Slope length. Two overhangs C are first added to the building width. The resulting horizontal projection is converted into the inclined slope length using the calculated roof angle.
Lroof = (X + 2C) / cos(α)
Slope width. The roof dimension perpendicular to the direction of the slope equals the building length B plus two side overhangs C2.
Wroof = B + 2C2
Roof area. The area of the single roof slope is the product of its inclined length and full width. Division by 1000000 converts mm2 to m2.
Aroof = Lroof × Wroof / 1000000
Rafter Length and Layout
Rafter length. The calculated rafter length is slightly greater than the geometric roof slope length. A correction for the angled cut is added to the slope length; it depends on the rafter width S1 and the roof pitch.
Lrafter = Lroof + S1 × tan(α)
Edge rafter offset. The rafters are distributed along the building length B. The specified offset D is measured from the outside face of the wall to the outside face of the edge rafter on each side. To prevent the two edge rafters from overlapping, the offset used in the calculation is limited to the range from 0 to (B - S2) / 2, where S2 is the rafter thickness.
Manual rafter spacing. The spacing P is the distance between corresponding points of adjacent rafters, for example between their outside faces. The available length between the two edge rafters is calculated as:
Lavailable = B - 2D - S2
The number of spaces is rounded up:
n = ceil(Lavailable / P)
With manual distribution, the specified main spacing is retained between the internal rafters. The remaining length is divided equally between the first and last spaces. If there are at least two spaces, the edge spacing is calculated as:
Pedge = (Lavailable - (n - 2) × P) / 2
For this reason, the distances at the two edges may differ from the entered spacing, but they are equal to each other. This method avoids leaving one unusually narrow space on only one side.
Equal distribution. When equal rafter distribution is selected, the entered limit is used as the maximum permitted spacing Pmax. The calculator first determines the minimum whole number of spaces required to stay within this limit, then divides the available length equally between them.
n = ceil(Lavailable / Pmax)
Pequal = Lavailable / n
The resulting actual rafter spacing is identical along the full building length and does not exceed the specified maximum value.
Outer rafters. When outer rafters are added, the calculator places additional rafters at the two outer side edges of the roof, within the side overhangs C2. If an additional position practically coincides with an already calculated rafter position within less than 0.5 mm, a second rafter is not added at the same location.
Rafter volume. The total timber volume of the rafters is calculated from the actual number of rafter members, their cross-section, and the calculated rafter length.
Vrafter = Nrafter × S1 × S2 × Lrafter / 1000000000
Batten Calculation
Batten spacing. The value O3 is used as the spacing between corresponding points of adjacent batten rows. The first row is positioned at the beginning of the slope, and subsequent rows are laid out along its inclined length.
First batten spacing. If a separate first spacing Ofirst is specified, the second batten row is positioned at this distance from the first. All subsequent rows use the main spacing O3. This arrangement is used, for example, with roofing materials where the spacing between the first and second rows differs from the regular batten spacing.
For some metal roof tile systems with a main spacing of about 350 mm, a first spacing of approximately 280-300 mm is commonly used. The exact value depends on the profile and the measurement method, so it should be taken from the installation instructions for the selected roofing product.
Last batten row. After all regular rows have been positioned, the calculator checks the remaining distance to the end of the roof slope. If the free section after the last board is greater than the larger of 120 mm or the batten board width O1, an additional row is placed at the opposite edge.
R > max(120, O1)
This additional row is positioned directly at the calculated end of the roof slope. Therefore, the final interval may differ from the main batten spacing.
Number and length of battens. The length of each batten row equals the full roof width Wroof. The total calculated batten length shown in the results is rounded up to the next whole metre.
Lbatten = ceil(Wroof × Nbatten / 1000)
The batten volume is calculated without rounding the total length to whole metres, using the actual number of rows and the batten cross-section.
Vbatten = Wroof × O1 × O2 × Nbatten / 1000000000
Additional Timber Elements
Fascia board. The total fascia length is calculated for the two transverse edges of the single-slope roof and equals twice the full roof width.
Lfascia = 2Wroof / 1000
Barge board. The board is calculated along the two inclined side edges, so its total length equals twice the roof slope length.
Lbarge = 2Lroof / 1000
Wall plate. The calculation assumes two wall plate runs along the building length B. Roof overhangs are not added to this length.
Lwallplate = 2B / 1000
Counter-battens. One counter-batten is assumed to have the full roof slope length Lroof. The number of counter-battens corresponds to the actual calculated number of rafters, including outer rafters when they are added.
Lcounterbatten = Nrafter × Lroof / 1000
Total timber volume. For each timber element, the volume is determined by multiplying its total length, width, and thickness and converting mm3 to m3. The total always includes the rafters and battens. Fascia boards, barge boards, wall plates, and counter-battens are added only when the corresponding elements are included in the calculation.
V = L × b × h / 1000000000
Roofing Membrane
Side overlap. The specified overlap Goverlap is subtracted from the full roll width GW. The result is the effective coverage width of one membrane strip.
Geffective = GW - Goverlap
The number of strips is determined from the inclined roof slope length and is always rounded up to a whole number:
Nstrip = ceil(Lroof / Geffective)
For a valid calculation, the specified overlap must be smaller than the full roll width.
Base material length. Each membrane strip extends across the full roof width. Therefore, before roll joints are taken into account, the total material length is:
Lbase = Nstrip × Wroof
Joints along the roll length. If the total strip length exceeds the length of one roll GL, the calculator determines the number of joints between consecutive roll sections. An additional 1000 mm of material is allowed for each such joint.
Njoint = max(0, ceil(Lbase / GL) - 1)
Lmembrane = Lbase + 1000 × Njoint
The calculated roofing membrane area is determined using the full roll width, while the required number of rolls is based on roll length. The number of rolls is shown as a calculated fractional value without rounding up to whole packages.
Amembrane = Lmembrane × GW / 1000000
Nroll = Lmembrane / GL
Insulation
Insulation volume. The insulated section uses the inclined length between the walls without the roof overhangs. This length is calculated from the building width X and the roof pitch.
Linsulated = X / cos(α)
The insulation volume is determined from this length, the building length B, and the specified insulation thickness U. The calculation assumes continuous filling of the calculated area without subtracting the volume occupied by the rafters.
Vinsulation = Linsulated × B × U / 1000000000
Practical Guidelines
- Single-slope and lean-to roofs often use roof pitches of approximately
5-30°. The permitted value depends on the roofing material, overlap requirements, and manufacturer instructions. - Common timber rafter spacing is approximately
400-800 mm. The appropriate value depends on the span, rafter cross-section, design loads, and dimensions of the insulation boards. - Roof overhangs of approximately
300-600 mmare commonly used. Increasing the overhang changes the roof area and the lengths of elements located along the roof edges. - For roofing underlay membranes, overlaps of approximately
100-200 mmare commonly used. The required value depends on the roof pitch, membrane type, and manufacturer instructions. - When purchasing timber and roll materials, an additional allowance is commonly added for cutting, sorting, joints, and site waste.
Related European Standards
- EN 1991-1-3, Eurocode 1: Actions on Structures - Part 1-3: General Actions - Snow Loads. Snow actions appropriate to the construction location and roof shape are considered when selecting rafter spacing and cross-section.
- EN 1991-1-4, Eurocode 1: Actions on Structures - Part 1-4: General Actions - Wind Actions. Wind actions are considered when selecting timber member dimensions and connections, particularly for roof overhangs and edge zones of a single-slope roof.
- EN 1995-1-1, Eurocode 5: Design of Timber Structures - Part 1-1: General - Common Rules and Rules for Buildings. This standard is used when selecting and verifying the cross-sections of timber rafters, battens, and other structural timber elements.
- EN 13859-1, Flexible Sheets for Waterproofing - Definitions and Characteristics of Underlays - Part 1: Underlays for Discontinuous Roofing. This standard relates to the characteristics of roofing underlay membranes used beneath roof coverings.
FAQs
What is the difference between manual rafter spacing and equal distribution?
With manual spacing, the specified rafter pitch is retained between the internal rafters, while the remaining length is divided between the two edge spaces. With equal distribution, the entered value is treated as the maximum permitted spacing and all spaces are then made equal. The actual equally distributed rafter spacing is therefore usually slightly smaller than the specified maximum.
Why is the rafter length slightly greater than the roof slope length?
The geometric roof slope length is measured along the roof surface, while the rafter calculation also includes a correction for the angled cut. This correction equals S1 × tan(α) and increases as the roof pitch and rafter width increase.
Why can the last batten spacing differ from the specified value?
The main batten rows are positioned at the specified spacing, after which the remaining distance at the opposite end of the roof slope is checked. If the free section is greater than 120 mm and also greater than the batten board width, the calculator adds an edge row at the end of the slope. The final interval is therefore determined by the remaining geometry in this situation.
How does roofing membrane overlap affect the required material quantity?
The side overlap reduces the effective coverage width of each membrane strip, so increasing the overlap may require additional strips. The calculation also adds 1000 mm of material for each joint required when moving from one roll section to the next along the roll length.
Why does adding outer rafters increase the amount of counter-batten material?
Counter-battens are calculated according to the actual number of rafter lines. When additional rafters are placed along the outer roof edges, separate full-length counter-battens are also included for those rafters. As a result, the number of rafters, timber volume, and total counter-batten length all increase.