Hip Roof Calculator
About Hip Roof Calculation
This calculator determines the geometry of a hip roof from the building dimensions, roof height, and eaves overhang. The calculation shows the roof plan dimensions, slope angles, inclined roof area, estimated total length of rafters and battens, plus the volumes of selected timber elements and insulation materials.
The tool is used for a preliminary material estimate for a hip roof on a rectangular building. All input dimensions are entered in millimetres, material lengths are shown in metres, areas in square metres, and volumes in cubic metres.
Guidelines and recommendations
Roof plan geometry
Calculation outline. First, the calculator increases the building length and width by the overhang on both sides. If the building sides are A and B, and the overhang is C, the roof plan dimensions are calculated as follows:
Ar = A + 2C
Br = B + 2C
These dimensions are used to draw the scheme, calculate the roof area, determine the fascia board length, and define the full roof outline.
Ridge. By default, the ridge length is taken as the difference between the longer and shorter roof side. This produces a standard hip roof geometry with coordinated roof slopes. If a custom ridge length is entered, the calculator uses it only under two conditions: the value must be less than the shorter roof side, and the ratio H / (Lshort - Lr) must not exceed 5. If this condition is not met, the custom ridge value is not applied.
Roof pitch angle and roof area
Roof pitch angle. The angle is calculated from the roof height H and the horizontal distance from the eaves to the ridge L. A right triangle is used:
α = arctan(H / L)
For a hip roof, the two directions can have different angle values because the horizontal spans along the building length and width may be different.
Slope coefficient. The area is calculated not from the horizontal projection, but from the real inclined surface. For this, the horizontal part of the roof slope is multiplied by a coefficient:
K = sqrt(L2 + H2) / L
The coefficient K shows how many times larger the inclined surface is than its horizontal projection. The higher the roof is for the same span width, the greater the coefficient and the final material area.
Roof area. The calculator divides the roof into main trapezoidal and triangular parts, taking into account the ridge length, half-spans of the hip slopes, and the overhang. The final area is rounded up to 0.1 m2 so that the result is not underestimated during preliminary material ordering.
Rafters and battens
Rafter system. The lengths of rafter elements are determined from the constructed roof geometry. The calculator takes into account common rafters, hip rafters, jack rafters, the rafter spacing in millimetres, and the actual inclined lengths of the elements.
Total rafter length. All calculated rafter elements are summed. The total length is shown in metres:
Lraf = sum(Li) / 1000
Rafter volume. The timber volume is calculated from the total length, section width, and section thickness:
Vraf = Lraf.mm × S1 × S2 / 1000000000
In this formula, all dimensions are substituted in millimetres, so division by 1000000000 converts the result to cubic metres.
Battens. The batten length is determined over the roof slopes with allowance for the spacing between boards. The smaller the spacing between boards, the more batten rows are needed and the greater the total material length. The batten volume is calculated in the same way as the rafter volume:
Vbat = Lbat.mm × O1 × O2 / 1000000000
Additional materials
Fascia board. The fascia board length is taken along the perimeter of the calculated roof outline, including the overhangs:
Lfas = 2(Ar + Br)
The fascia board volume is calculated from its length, width, and thickness, with conversion from cubic millimetres to cubic metres.
Wall plate. The wall plate length is calculated along the building perimeter without overhangs. Four timber widths are subtracted from the sum of the sides so that the length is not overestimated at the corner joints:
Lwp = 2A + 2B - 4Wwp
The wall plate volume is calculated by the formula Vwp = Lwp × Wwp × Twp / 1000000000.
Waterproofing membrane. The waterproofing area starts with the roof area and is increased by an approximate allowance for overlaps. With roll length Lroll, roll width Wroll, and overlap N, the calculation is:
Swm = Sr + Sr / (Lroll × Wroll) × (Lroll × N + Wroll × N)
The number of rolls is determined by dividing the final waterproofing area by the area of one roll:
Qroll = Swm / (Lroll × Wroll / 1000000)
Counter-battens. The counter-batten length is taken as equal to the total rafter length. This corresponds to placing counter-battens along the rafter legs. The volume is calculated from the length, width, and thickness of the batten.
Insulation. The insulation area is determined from the internal geometry of the slopes, without adding the roof overhang. The insulation volume is calculated by multiplying this area by the layer thickness:
Vins = Sins × Tins / 100000
Here the area is given in square metres, the thickness in millimetres, and the result is shown in cubic metres.
Practical reference values
Rafter spacing. For timber pitched roofs, a rafter spacing of about 600 mm is often used. This spacing is convenient for many insulation boards and sheet materials, but the final value depends on the span, section size, load, and support layout.
Roof overhang. Common overhang values are often in the range of 300-700 mm. Increasing the overhang increases the roof area, fascia board length, and material consumption around the perimeter.
Waterproofing overlap. For roll membranes, an overlap of about 100-150 mm is often used. A larger overlap increases the calculated waterproofing area and the number of rolls.
Related European standards. For design verification of a timber roof, Eurocode 5 EN 1995-1-1 is commonly used for timber structures, Eurocode 1 EN 1991-1-3 for snow loads, and Eurocode 1 EN 1991-1-4 for wind actions. These documents are not replaced by a material estimate, but they provide the basis for checking sections, loads, deflections, and element stability.
FAQs
Why can a hip roof have two different roof pitch angles?
The roof height is the same, but the horizontal distances from the eaves to the ridge may differ along the length and width. Therefore, the calculator determines the angle separately for each direction. This is normal for a rectangular building with a hip roof.
Why is the roof area larger than the building area in plan?
The roof has a slope and overhangs, so its real surface is larger than the horizontal projection of the building. The calculator adds the overhang on both sides and multiplies the slope parts by the slope coefficient. The higher the roof and the larger the overhang, the greater the final area of roofing material.
How does the calculator choose the ridge length?
If a custom ridge length is not entered, the difference between the longer and shorter roof side is used. If the length is entered manually, it is applied only when it is less than the shorter side and does not create excessively steep geometry. This keeps the calculation geometrically consistent.
Why are the rafter and batten volumes calculated through millimetres?
The timber sections are entered in millimetres, and the internal element lengths are also summed in millimetres. Therefore, the volume is first obtained in cubic millimetres, then divided by 1000000000 and shown in cubic metres.
Can the result be used as an exact material specification?
The calculation gives a technically clear preliminary schedule based on the entered geometry and selected element sizes. For purchasing, an allowance is usually added for cutting, material sorting, junction details, and the actual installation layout. Section sizes and element spacing should be checked against loads and project requirements.