Single-Slope Roof
About Single-Slope Roof Calculation
The Single-Slope Roof calculator performs a geometric calculation of a mono-pitch roof and estimates the main materials for a simple rafter layout. It calculates the slope angle, roof slope length and area, number of rafters, battens, waterproofing membrane, counter-battens, wall plate, fascia board, barge board, and insulation volume.
The calculation is used for preliminary layout of a single-slope roof and for estimating material quantities from the specified dimensions. All input linear dimensions are entered in millimetres, areas are shown in m2, volumes in m3, and total lengths in metres or millimetres depending on the result.
Guidelines and Recommendations
Roof slope geometry
Slope angle. The roof angle is determined from a right triangle: the roof rise H is divided by the horizontal building width X. Overhangs are not included in the angle calculation because they extend the already defined roof slope line.
α = arctan(H / X)
Roof slope length. The full inclined length is calculated from the building width and two eaves-side overhangs. The horizontal projection X + 2 * C is converted into an inclined length using cos(α).
Lroof = (X + 2 * C) / cos(α)
Roof slope width. The full roof width is calculated from the building length B and two side overhangs C2.
Wroof = B + 2 * C2
Roof slope area. The area is calculated as the inclined roof slope length multiplied by the full roof width. Division by 1000000 converts mm2 to m2.
Aroof = Lroof * Wroof / 1000000
Rafters
Rafter length. The rafter length is taken as greater than the roof slope length because an allowance is added for the lower bevel cut. This allowance depends on the rafter depth S1 and the roof slope angle.
Lrafter = Lroof + S1 * tan(α)
Number of rafters. First, two edge positions are defined: the first rafter is placed with an offset from one side edge, and the last one with the same offset from the opposite edge, taking the rafter thickness into account. Intermediate rafters are added with a calculated pitch equal to the sum of the clear spacing between rafters and the rafter thickness.
P = R + S2
Here R is the clear spacing between rafters in mm, and S2 is the rafter thickness in mm. If the remaining gap before the last rafter is less than 150 mm, the calculator redistributes the last section between two adjacent gaps so that there is no excessively narrow bay at the edge.
Rafter volume. The volume is calculated from the number of rafters, the cross-section of one rafter, and the calculated rafter length. Division by 1000000000 converts mm3 to m3.
Vrafter = Nrafter * S1 * S2 * Lrafter / 1000000000
Battens
Length of one row. One batten row runs across the roof slope, so the length of one row is equal to the full roof width Wroof.
Number of rows. Rows are distributed along the inclined roof slope length. The calculated cell is equal to the batten board width plus the spacing between boards, and the final number is rounded upward.
Nbatten = ceil(Lroof / (O1 + O3) + 1)
Here O1 is the batten board width in mm, and O3 is the spacing between boards in mm. Rounding upward is needed because any partial remainder along the roof slope requires installing one full additional row.
Total batten length. The total length is equal to the full roof width multiplied by the number of rows. The result is converted from millimetres to metres and rounded upward to a whole metre.
Lbatten = ceil(Wroof * Nbatten / 1000)
Batten volume. The volume is calculated from the total length of all rows and the batten board cross-section.
Vbatten = Wroof * O1 * O2 * Nbatten / 1000000000
Additional timber elements
Fascia board. The total fascia board length is calculated along the two horizontal edges of the roof slope. The calculation uses the full roof width including side overhangs.
Lfascia = Wroof * 2 / 1000
Barge board. The total barge board length is calculated along the two inclined side edges of the roof slope. This is why the inclined roof slope length is used.
Lbarge = Lroof * 2 / 1000
Wall plate. The wall plate length is taken along two sides of the building length without adding roof overhangs. The volume of the wall plate, fascia board, and barge board is calculated from the total element length, its width, and its thickness.
Lwallplate = B * 2 / 1000
Waterproofing membrane, counter-battens, and insulation
Waterproofing membrane area. The roof slope area is used as the base. To it, the calculated overlap area of the roll material is added: roll length is multiplied by the overlap value and by the calculated number of strips across the roll width.
Amembrane = Aroof + GL * Goverlap * (Lroof / GW) / 1000000
Here GL is the roll length in mm, GW is the roll width in mm, and Goverlap is the overlap in mm. The number of rolls is calculated by dividing the calculated waterproofing membrane area by the area of one roll.
Nroll = Amembrane / (GL * GW / 1000000)
Counter-battens. The length of one counter-batten is taken as equal to the roof slope length. The total length is calculated from the number of rafters because counter-battens run along the roof slope on the rafter lines.
Lcounterbatten = Nrafter * Lroof / 1000
Insulation. The insulation volume is calculated from the clear inclined length between the walls, the building length, and the insulation thickness. Overhangs are not included in this volume because they are usually outside the insulated envelope.
Vinsulation = (X / cos(α)) * B * U / 1000000000
Practical reference values
- For single-slope roofs, a slope of approximately
5°to30°is often used, but the minimum slope depends on the roofing material and the manufacturer’s requirements. - Rafter spacing is often selected in the range of
400-800mm. The final value depends on loads, span, timber section, and insulation width. - Roof overhangs are often taken at about
300-600mm. A larger overhang protects the facade better, but increases the requirements for edge stiffness and fastening details. - Roll waterproofing membrane overlap is often taken at about
100-200mm. For low slopes and difficult conditions, a larger overlap is usually used according to the material manufacturer’s instructions. - For purchasing timber, membranes, and insulation, it is common to add an allowance for cutting, sorting, and local waste.
Related European standards
EN 1991-1-3, Eurocode 1. Actions on structures. Snow loads. This document is used to determine snow loads on roofs. The geometric results of the calculator, including the roof slope angle and rafter layout, should be checked with regard to the snow region and roof shape.
EN 1991-1-4, Eurocode 1. Actions on structures. Wind actions. This standard is used to assess wind pressure, roof uplift, and loads on overhangs. This is especially important for single-slope roofs, where wind direction can significantly change the design effects.
EN 1995-1-1, Eurocode 5. Design of timber structures. This document is used to check timber elements for strength, stiffness, stability, and service conditions. The calculator determines geometry and material volumes, but it does not replace the structural design of rafters, wall plates, and connections.
EN 13859-1, Flexible sheets for waterproofing. Underlays for discontinuous roofing. This standard relates to the properties of roofing underlay membranes. It is important when selecting the waterproofing membrane, but it does not define rafter spacing or roof slope geometry.
FAQs
Why is the rafter length greater than the roof slope length?
The rafter length is increased by an allowance for the lower bevel cut. The greater the slope angle and the rafter depth, the more noticeable this addition to the cutting length becomes.
Why is the number of rafters not always equal to simply dividing the roof width by the spacing?
The calculator considers not only the spacing between rafters, but also the rafter thickness, two side offsets, and the position of the last element. If the remaining gap at the edge is less than 150 mm, the last section is redistributed so that the rafter layout is more even.
Why is the total batten length rounded upward?
Battens consist of full rows, and any partial remainder along the roof slope requires an additional row. Therefore, the number of rows and the total material length are rounded upward.
Why can the number of waterproofing membrane rolls be fractional?
The calculator shows the calculated requirement by area, not a finished roll cutting layout. For purchasing, a fractional value is usually rounded upward and an allowance is added for overlaps, cutting, and possible material damage.
Can this calculation be used to select the rafter section?
No, the single-slope roof calculation on this page determines geometry and approximate material quantities. The rafter section must be checked separately for snow, wind, and permanent loads, span, timber grade, and service conditions.