Gable Roof Calculator
About Gable Roof Calculation
The calculator determines the geometry of a gable roof and the main material quantities for the rafter system. The calculation includes two roof slopes, eaves and gable overhangs, rafters, collar ties, posts, battens, wall plates, waterproofing membrane, counter-battens, insulation, fascia boards, and barge boards.
The calculation is based on a geometric model of a symmetrical gable roof. All input dimensions are entered in millimeters, areas are shown in m2, timber and insulation volumes are shown in m3, and material lengths may be shown in mm or m depending on the result line.
Guidelines and recommendations
Roof geometry model
Roof pitch angle is determined from half of the building width and the roof height. The calculator treats the roof cross-section as a right triangle, where the horizontal leg equals half of the building width and the vertical leg equals the roof height.
α = arctan(H / (X / 2))
Slope length is calculated from the pitch angle and the eaves overhang. If the building width is X, the roof height is H, and the eaves overhang is C, the calculated slope length includes half of the span and the overhang.
Lsk = (X / 2 + C) / cos α
Roof width along the building length is increased by two gable overhangs. If the building length is B and the gable overhang is C2, the calculated roof width is taken as follows.
W = B + 2 * C2
Roof area is calculated for two identical slopes. Since the input dimensions are given in mm, the result is converted to m2 by dividing by 1000000.
A = 2 * Lsk * W / 1000000
Rafters and spacing
Number of rafters is calculated from the working roof width, the offset of the outer rafters, the rafter board thickness, and the spacing between rafters. The offset is applied on both sides, so the working zone equals the total roof width minus two offsets.
Wwork = W - 2 * O
Nside = floor((Wwork - S2) / (R + S2)) + 2
Ntotal = 2 * Nside
Length of one rafter is taken as greater than the geometric slope length. The calculation adds a correction for the rafter board width, depending on the pitch angle.
Lrafter = Lsk + S1 * tan α
Rafter volume is calculated as the product of quantity, length, board width, and board thickness. Division by 1000000000 converts mm3 to m3.
V = Ntotal * Lrafter * S1 * S2 / 1000000000
For timber rafters, spacing of 600-900 mm is often used. Common section sizes depend on span, snow zone, roofing material, and support scheme, so the geometric quantity calculation does not replace a load-bearing capacity check.
Collar ties and posts
Collar tie is calculated as a horizontal member placed at the specified height above the roof base. The collar tie height is limited to the range from 0 to H, so a value higher than the roof height does not increase the calculated geometric height.
Collar tie length decreases as the member is placed higher above the base. The higher the collar tie is located, the shorter its calculated length becomes within the triangular roof section.
Ltie = (X + 2 * C) * (H + K - Z) / (H + C * 2H / X)
Number of collar ties is taken as equal to the number of rafter pairs on one side of the calculation. The collar tie volume is calculated from length, quantity, width, and thickness, with conversion from mm3 to m3.
Posts are calculated according to their position relative to the roof center. If the offset from the center is 0, one post is taken for each rafter pair. If the offset is greater than 0, two symmetrical posts are taken for each rafter pair.
Npost = Nside * 1
Npost = Nside * 2
The post height is determined from the slope line at the installation point. The calculator finds the vertical distance from the base to the inner line of the rafter layout and multiplies it by the number of posts and the post section to obtain the volume.
Battens, counter-battens, and edge boards
Battens are calculated as rows across the slope. The length of one row equals the calculated roof width W, and the number of rows is determined from the slope length, batten board width, and spacing between boards.
Nrow = ceil(Lsk / (O3 + O1) + 1) * 2
Total batten length equals the length of one row multiplied by the number of rows for the two slopes. Batten volume is calculated from total length, board width, and board thickness.
Vbatten = W * Nrow * O1 * O2 / 1000000000
Counter-battens are calculated along the rafters. The length of one element equals the slope length, and the total length equals the slope length multiplied by the number of rafters.
Lcounter = Ntotal * Lsk / 1000
Fascia board is calculated along the two eaves sides. Its total length equals two calculated roof widths.
Lfascia = 2 * W / 1000
Barge board is calculated along the four sloping edges of the gable ends. Its total length equals four slope lengths.
Lbarge = 4 * Lsk / 1000
Wall plate, waterproofing membrane, and insulation
Wall plate is calculated along the two longitudinal walls of the building. In the calculation, its length equals twice the building length, and its volume is determined from the length, width, and thickness of the timber.
Lmauerlat = 2 * B / 1000
Waterproofing membrane is calculated from the area of the two slopes with an allowance for overlaps between sheets. The added area depends on roll length, overlap, slope length, and roll width.
Ahydro = A + (Lroll * Hoverlap * Lsk / Wroll) / 1000000
Number of rolls is obtained by dividing the calculated waterproofing area by the area of one roll. The area of one roll is calculated as roll length multiplied by roll width.
Nroll = Ahydro / (Lroll * Wroll / 1000000)
Insulation is calculated from the area of two slopes without the eaves overhang. For this, the calculator uses the rafter line length from the ridge to the wall, the building length, and the insulation thickness.
Vins = 2 * L0 * B * Tins / 1000000000
Rounding and units
Linear dimensions for the main geometric results are rounded to whole millimeters. The pitch angle is shown to 0.1 degree, areas are usually shown to 0.1 m2, and timber and insulation volumes are shown to 0.01 m3.
Element quantities are determined as whole values by rounding up or by adding edge elements. This approach is used so the calculation does not underestimate the number of batten rows, rafters, and other repeated components.
Related European documents
EN 1990 Eurocode. Basis of structural design. This document sets the general principles for reliability, design situations, and combinations of actions for building structures.
EN 1991-1-1 Eurocode 1. Actions on structures. Densities, self-weight, imposed loads for buildings. The document is related to determining loads from material self-weight and imposed actions.
EN 1991-1-3 Eurocode 1. Snow loads. This document is used when determining snow load on a roof, taking into account roof shape, slope pitch, and local climate data.
EN 1991-1-4 Eurocode 1. Wind actions. This document is used to assess wind pressure and suction on roof surfaces, edges, and areas near gable ends.
EN 1995-1-1 Eurocode 5. Design of timber structures. The document is related to the design of timber rafters, posts, collar ties, connections, and the verification of timber load-bearing capacity.
FAQs
Why is the roof area larger than the building area?
The area of a gable roof is calculated along the sloping roof surfaces, not along the horizontal projection of the building. The result is affected by the pitch angle, eaves overhang, and gable overhang, so the roofing material area is always larger than the plan area of the building.
Why does the number of rafters change in steps rather than smoothly?
Rafters are counted as whole elements. When the working roof width or rafter spacing crosses the next calculation interval, the calculator adds or removes one rafter pair at once, so the result changes step by step.
How does roof height affect rafter length?
As height H increases, the pitch angle becomes steeper and the calculated rafter length increases. At the same time, the slope area, barge board length, rafter volume, and some related material quantities also increase.
Why is insulation calculated without the eaves overhang?
Insulation is usually installed within the heated envelope, not across the full length of the roof overhang. Therefore, the calculator uses the slope length from the ridge to the wall without adding the eaves overhang.
What rafter spacing is suitable for a preliminary calculation?
For a preliminary calculation, spacing of 600-900 mm is often used. It is practical to choose the value according to the insulation width, roofing material type, and required load-bearing capacity of the rafter system.