Gable Roof Calculator
About Gable Roof Calculation
The Gable Roof Calculator performs rafter and roofing material calculation for a symmetrical gable roof. It determines roof slope dimensions, slope angle, roof area, and the quantity and volume of rafters, ties, posts, and battens. It can also calculate the wall plates, counter battens, fascia and barge boards, waterproofing membrane, insulation, and total lumber volume.
Main linear dimensions are entered in millimeters. Areas are shown in m2, material volumes in m3, and lengths in mm or m depending on the result.
Guidelines and recommendations
Gable roof geometry
Slope angle. The roof cross-section is treated as two identical right triangles. For a house width X and roof height H, the angle α of each roof slope is determined from the ratio of the height to half the house width.
α = arctan(H / (X / 2))
Slope length. The eave overhang C is added to half the house width in horizontal projection, and the resulting distance is converted to the inclined length using the angle α.
Lsk = (X / 2 + C) / cos α
Slope width. In the longitudinal direction, the calculation uses the house length B plus two gable overhangs C2.
W = B + 2 * C2
Roof area. The area of one slope equals its inclined length multiplied by the width W. For a gable roof, this value is doubled and converted from mm2 to m2.
A = 2 * Lsk * W / 1000000
Rafter layout and quantity
Working length for distribution. The main rafter pairs are positioned within the house length B. The setback O is measured from the outer edge of the house to the outer edge of the end rafter and is applied on both sides. In the calculation, O is limited to the range from 0 to (B - S2) / 2, where S2 is the rafter thickness.
D = B - 2 * O - S2
Manual rafter spacing. When the spacing is set manually, the specified spacing R is maintained between the internal rafter pairs. The number of intervals is determined by rounding upward, while the remaining length is distributed symmetrically between the first and last intervals. For this reason, the two outer intervals may be slightly smaller than the specified spacing.
n = ceil(D / R)
Redge = (D - (n - 2) * R) / 2
Here, ceil means rounding upward to the next integer. If the working length forms only one interval, the end rafters are placed at the boundaries of the calculated working zone.
Even distribution. With automatic distribution, a maximum permitted rafter spacing Rmax is specified. The calculator first selects the minimum whole number of intervals that does not exceed this limit and then makes all intervals equal.
n = ceil(D / Rmax)
Ractual = D / n
The actual rafter spacing therefore never exceeds the specified maximum. The displayed spacing is rounded to the nearest whole millimeter.
Outer rafters. When outer rafters are added, the calculator places additional pairs at the outer edges of the gable overhangs. If a position already coincides with an existing rafter within 0.5 mm, no duplicate element is added. Outer rafters are included in the rafter quantity and volume and in the counter-batten calculation, but the number of ties and posts is based only on the main rafter pairs.
Rafter length. A correction for the lower angled cut is added to the geometric slope length. The correction depends on the rafter width S1 and the roof angle.
Lr = Lsk + S1 * tan α
Rafter volume. Each rafter pair contains two rafter legs. The volume is calculated from the total quantity, length, and cross-section S1 × S2, with mm3 converted to m3.
Vr = Nr * Lr * S1 * S2 / 1000000000
For preliminary design of a timber gable roof, rafter spacing of about 600–900 mm is often used. The actual spacing should be coordinated with the timber section, insulation width, roofing material, span, snow load, and wind load.
Ties and posts
Ties. One tie is assigned to each main rafter pair. The specified height Z is limited to the range from 0 to H, after which the horizontal member length is determined from the roof triangle geometry, taking the eave overhang and rafter width into account.
K = S1 * sqrt(1 + (2H / X)2)
Ltie = (X + 2C) * (H + K - Z) / (H + 2CH / X)
The higher the tie is positioned, the shorter its calculated length becomes. Its volume is determined by multiplying the length by the number of ties and the specified cross-section.
Posts. When the offset from the roof center is 0 mm, the calculator uses one central post for each main rafter pair. When the offset is greater than 0, two symmetrical posts are used for each pair. The offset is limited to half the house width.
The post length is determined geometrically from the roof slope line at the installation position. The post width is also taken into account: for a rectangular member, the calculator uses the height at which both side edges fit beneath the inclined line of the rafter system.
Battens
Row layout. The first batten row is placed at the beginning of the slope. If a separate first spacing is not used, subsequent rows are positioned using the main batten spacing O3. If the first spacing option is enabled, the distance from the first to the second row is specified separately, and the main spacing O3 is used from the second row onward.
Last row. After placing the rows, the calculator checks the remaining free section at the end of the slope. If the distance from the far edge of the last row to the end of the slope exceeds the greater of 120 mm or the batten width O1, one additional row is placed directly at the end.
Rfree > max(120, O1)
The calculated number of rows is doubled for the two roof slopes. Each row has a length W. The total batten length is converted to meters and rounded upward to a whole meter, while the batten volume is calculated from the exact length without this rounding.
Vbatten = W * Nrow * O1 * O2 / 1000000000
First batten spacing. For some metal roof tile systems and modular profiled roofing materials, the first spacing is smaller than the main spacing. With a main spacing of 350 mm, manufacturers often specify approximately 280–300 mm for the first spacing, but the exact distance and measurement method should be taken from the installation instructions for the selected roofing material.
Additional lumber
Counter battens. One counter batten of length Lsk is placed along each calculated rafter leg, including outer rafters. The total length equals the number of rafters multiplied by the slope length.
Lcounter = Nr * Lsk / 1000
Fascia board. Two eave sides of the roof are included, so the total length equals twice the roof width W.
Lfascia = 2 * W / 1000
Barge board. Four inclined gable edges of the two roof slopes are included, so the total length equals four slope lengths.
Lbarge = 4 * Lsk / 1000
Wall plate. The calculation is based on the two longitudinal walls of the house and excludes the gable overhangs.
Lmauerlat = 2 * B / 1000
Member volume. For each lumber type, the actual calculated length and the specified rectangular cross-section are used. When all dimensions are in millimeters, volume is calculated using the general relationship below.
V = L * b * h / 1000000000
Total lumber volume. The final value includes rafters and battens, plus any enabled ties, posts, fascia boards, barge boards, wall plates, and counter battens.
Waterproofing membrane
Effective sheet width. The specified overlap Hoverlap is subtracted from the full roll width Wroll. The resulting value is the effective width provided by each successive sheet.
Weff = Wroll - Hoverlap
Number of sheets. The lengths of both roof slopes are added together, divided by the effective sheet width, and rounded upward. A final partial-width sheet is counted as a full sheet.
Nstrip = ceil(2 * Lsk / Weff)
Each sheet has a length W, so the base total length of waterproofing membrane is calculated first.
Lbase = Nstrip * W
Roll joints. The number of joints is determined from the base length before any additional allowance is added. A fixed 1000 mm of material is then added once for each such joint.
Njoint = max(0, ceil(Lbase / Lroll) - 1)
Lhydro = Lbase + 1000 * Njoint
Area and roll quantity. The membrane area is calculated using the full roll width, while the calculated number of rolls is obtained by dividing the required membrane length by the length of one roll. The roll quantity is displayed to two decimal places; for purchasing, it is normally rounded upward to a whole roll.
Ahydro = Lhydro * Wroll / 1000000
Nroll = Lhydro / Lroll
Insulation
Calculated volume. The insulation calculation uses the inclined length from the ridge to the outer edge of the wall without the eave overhang, the house length B without the gable overhangs, and the specified insulation thickness T. The calculation covers both roof slopes.
L0 = (X / 2) / cos α
Vins = 2 * L0 * B * T / 1000000000
The resulting volume represents a continuous insulation layer of the specified thickness over the calculated roof area.
Rounding of results
Linear dimensions. Main roof, rafter, tie, post, and individual member dimensions are displayed to the nearest whole millimeter. The slope angle is displayed to 0.1°, while roof and waterproofing membrane areas are displayed to 0.1 m2.
Volumes and lengths. Lumber and insulation volumes are displayed to 0.01 m3. Most total lengths in meters are displayed to 0.01 m, waterproofing membrane length to 0.1 m, while the total batten length is rounded upward to a whole meter.
Related European standards
EN 1990 Eurocode. Basis of structural design. Defines general principles for structural reliability, design situations, and combinations of actions.
EN 1991-1-1 Eurocode 1. Actions on structures. Densities, self-weight, imposed loads for buildings. Used when determining loads from the self-weight of materials and imposed actions.
EN 1991-1-3 Eurocode 1. Snow loads. Relevant to determining snow actions on roofs with consideration of roof shape, slope angle, and climatic conditions.
EN 1991-1-4 Eurocode 1. Wind actions. Used when assessing wind pressure and suction on roof surfaces and edge zones.
EN 1995-1-1 Eurocode 5. Design of timber structures. Contains rules for the design of timber members and connections and for checking the load-bearing capacity of rafter structures.
FAQs
Why is the automatically calculated rafter spacing smaller than the specified maximum?
The maximum spacing is treated as a limit, not as a required distance. The calculator rounds the number of intervals upward and then divides the working length between the end rafters by that whole number, so the rafters are distributed evenly with spacing no greater than the specified maximum.
Why are the outer rafter intervals different when manual spacing is used?
In manual mode, the specified main spacing is maintained between the internal rafters. The remaining length is divided equally between both ends, so the first and last intervals may be smaller than the main spacing while the rafter layout remains symmetrical.
How does the calculator account for the first batten spacing?
The separate value is applied only between the first and second batten rows. All subsequent rows use the main batten spacing, and an additional final row is added near the end of the slope when the remaining free section exceeds the greater of 120 mm or the batten width.
Why is the waterproofing membrane area greater than the gable roof area?
The waterproofing calculation is not based only on the geometric roof area. It also accounts for the reduction in effective sheet width caused by overlaps, upward rounding of the number of sheets, and an additional 1000 mm allowance for each roll joint.
Why does the number of rafters change in steps after small changes to the roof dimensions?
The number of intervals between rafters must always be a whole number and is determined by rounding upward. When the roof length or permitted spacing crosses the threshold for another interval, an additional rafter pair is required, so the total quantity changes by a complete pair.