Hip Roof Calculator
About Hip Roof Calculation
The calculator determines the geometry of a hip roof from the house dimensions, roof height, overhang, and parameters of the timber elements. It determines the calculated roof dimensions, slope angles, roof surface area, rafter length, batten length, timber volumes, waterproofing quantity, and insulation volume.
The calculation is suitable for preliminary material estimation, comparison of roof pitch options, and preparation of input data for further structural checking. All dimensions are entered in centimeters, while final material lengths are shown in meters, areas in square meters, and volumes in cubic meters.
Guidelines and recommendations
Basic roof geometry
Calculated roof outline. The calculator first increases the house dimensions by the overhang on both sides. If the house length is A cm, the width is B cm, and the overhang is C cm, the roof dimensions in plan are taken as follows:
Br = B + 2C
Ar = A + 2C
These dimensions are used to calculate the slope area, create the drawings, and determine the fascia board length.
Ridge length. By default, the ridge length is taken as the difference between the longer and shorter roof sides. This gives a classic hip roof geometry in which the main slopes are coordinated with each other. If a custom ridge length is specified, the calculator uses it only if the value is smaller than the short side and does not create an excessively steep geometry.
Slope half-spans. To calculate the pitch, the roof is divided into horizontal sections from the eaves to the ridge. These sections may differ along the length and width, so the calculator determines the angle separately for the main direction and for the width direction.
Angles and roof area
Slope angle. The angle is calculated from the roof height H and the horizontal half-span L. The trigonometry of a right triangle is used:
α = arctan(H / L)
The value L is taken in centimeters. If the house length and width are different, the calculator may show two different angles because the slopes rise to the ridge over different horizontal distances.
Slope factor. The area is calculated not from the horizontal projection, but from the actual inclined surface of the slopes. For this, the horizontal length is multiplied by the slope factor:
K = sqrt(L2 + H2) / L
If the factor is 1.00, the surface is horizontal. The steeper the slope, the larger the factor and the larger the actual roof area compared with the plan area.
Roof area. The calculator separately accounts for the central area around the ridge and the hip sections. The overhang C is included in the calculation, so the final area refers to the entire roof surface, not only to the area above the house walls.
Rafters and battens
Rafters. The calculator builds the rafter system layout and sums the element lengths from the drawing. It accounts for four hip rafters, the central ridge section if present, and the common and jack rafters on the slopes.
Rafter spacing. The rafter spacing is used as the calculated distance between adjacent elements. A spacing of about 60 cm is often used, especially when the structure needs to match slab or roll insulation. The actual spacing may be adjusted according to loads, timber section, and support layout.
Rafter volume. After summing the length, the calculator multiplies it by the width and thickness of the rafter board:
Vraf = Lraf × S1 × S2 / 1000000
Here Lraf, S1, and S2 are specified in centimeters. Division by 1000000 converts the result to m3.
Battens. The batten length is determined from the batten lines on the slopes, taking into account the specified board width and the distance between boards. The volume is then calculated:
Vbat = Lbat × O1 × O2 / 1000000
The distance O3 affects the number of batten rows. For a solid deck under flexible roofing, a different material selection principle is used, while for spaced battens the spacing is usually coordinated with the type of roof covering.
Additional materials
Fascia board. Its total length is calculated along the perimeter of the calculated roof outline including overhangs:
Lfas = 2 × (Br + Ar)
The fascia board volume is determined by multiplying this length by the board width and thickness, with conversion from cm3 to m3.
Wall plate. The wall plate length is calculated along the house perimeter, but four beam widths are subtracted from the sum. This approximates the joining of elements at the corners:
Lwp = 2A + 2B - 4M1
The wall plate volume is calculated in the same way as the volume of other timber elements: length is multiplied by width and thickness.
Waterproofing. First, the roof area is taken, then an allowance for overlaps between sheets is added. The calculation uses the roll length, roll width, and specified overlap:
Sw = Sr + Sr / (D × W) × (D × N + W × N)
Here Sr is the roof area, D is the roll length, W is the roll width, and N is the overlap. After that, the number of rolls is determined by dividing the calculated waterproofing area by the area of one roll.
Counter-battens. The total counter-batten length is taken as equal to the total rafter length. This corresponds to a common layout in which the counter-batten strips run along the rafter legs. The volume is calculated from the strip length, width, and thickness.
Insulation. The insulation volume is calculated from the slope area between the rafters and the specified layer thickness. The thickness is entered in centimeters, so division by 100 is used to convert the result to cubic meters:
Vins = Sins × T / 100
Practical guidelines and European standards
Roof pitch. A commonly used range for pitched roofs is approximately 20-45 degrees. Lower pitches depend more strongly on the roof covering type and overlap requirements, while higher pitches increase the roof area and wind load.
Roof overhang. Common overhang values for a private house are approximately in the range of 30-70 cm. A larger overhang protects the walls from precipitation more effectively, but increases the roof area, fascia board length, and stiffness requirements for the eaves detail.
Regulatory check. In European practice, the verification of load-bearing capacity and loads is usually linked to Eurocode 1 EN 1991-1-3 for snow loads, Eurocode 1 EN 1991-1-4 for wind loads, and Eurocode 5 EN 1995-1-1 for timber structures. These documents are used to check rafter sections, fasteners, and the overall stability of the roof system.
FAQs
Why is the hip roof area larger than the house area?
The roof area is calculated along the inclined surface, not from the horizontal projection. In addition, overhangs on all sides are included in the calculation. Therefore, the final slope area is always larger than the rectangle measured along the external walls.
Why can the calculator show two slope angles?
A hip roof may have different horizontal half-spans along the length and width of the house. With the same roof height, different half-spans give different angles. This is normal for a rectangular building if the geometry is not fully symmetrical.
How does a custom ridge length affect the calculation?
The ridge length changes the shape of the side and hip slopes. The longer the ridge, the shorter the hip sections and the differently the rafters are distributed. The calculator uses the specified ridge length only within valid geometry so that the roof layout remains correct.
Why is the waterproofing quantity larger than the roof area?
Waterproofing is installed with overlaps, so the working material consumption is larger than the clean slope area. The calculator adds an allowance for sheet overlaps along the roll length and width. The resulting area is then divided by the area of one roll.
Can this calculation be used as the final material specification?
The calculation gives a technically clear preliminary specification for geometry and volumes. For purchasing, an allowance is usually added for cutting, timber grade, joints, fasteners, and the specifics of the selected roof covering. Load checks according to applicable European standards are also required for load-bearing elements.