Pyramid Hip Roof Calculator
About Pyramid Hip Roof Calculation
This calculator estimates a pyramid hip roof for a rectangular building: eaves dimensions, slope angles, roof area, total length and volume of rafters, battens and additional timber elements. It can also estimate the waterproofing area, number of rolls and insulation volume.
The calculation is based on a geometric model with four roof slopes, one top apex, four diagonal rafters and intermediate rafters on sides A and B. All main dimensions are entered in millimetres, while final lengths, areas and volumes are converted to metres, m² and m³.
Guidelines and recommendations
Pyramid hip roof geometry
Eaves dimensions. The calculator first increases the building length and width by the roof overhang on both sides. If the building length is A, the width is B, and the overhang is C, the final roof dimensions at the eaves are calculated as follows:
Ae = A + 2 × C
Be = B + 2 × C
Slope angle. For a rectangular building, two angles are shown because the slopes along the long and short sides have different horizontal runs. Each angle is calculated from the roof height H and half of the corresponding building side:
αA = arctan(H / (A / 2))
αB = arctan(H / (B / 2))
The meaning of the formula is simple: a higher H makes the roof steeper, while a larger span makes it flatter. The result is shown in degrees with an accuracy of 0.1°.
Roof area
Slope factors. The area is calculated over the inclined roof slopes, not over the horizontal projection. Two factors are used to convert half of the span into the actual sloping length:
kA = √((A / 2)2 + H2) / (A / 2)
kB = √((B / 2)2 + H2) / (B / 2)
Final area. After adding the overhangs, the calculator multiplies the horizontal roof projection by the average effect of the two slopes:
S = Ae × Be × (kA + kB) / 2
Since the dimensions are entered in millimetres, the area is divided by 1000000 to convert mm² to m². The final roof area is rounded upward to 0.1 m² so that the result does not underestimate the material quantity.
Rafters
Diagonal rafters. The model always includes 4 diagonal rafters from the roof corners to the top apex. Their length is determined from the spatial diagonal, so these elements are longer than ordinary intermediate rafters.
Intermediate rafters. Rafters on sides A and B are placed symmetrically. The calculator uses the specified spacing between rafters and adds elements as long as there is enough room on the slope for the next row, taking the board width into account.
Element length. For each rafter group, the length is calculated along the inclined roof slope. The lower angled cut of the board is also included, so the calculated length may be slightly greater than the pure geometric distance from the eaves to the apex.
Total volume. First, the lengths of all rafter elements are summed. Then the total is multiplied by the board width and thickness:
Vr = Lr × S1 × S2 / 1000000000
Here Lr is the total rafter length in mm, S1 is the board width in mm, and S2 is the board thickness in mm. Division by 1000000000 converts mm³ to m³.
Battens, counter battens, fascia board and wall plate
Battens. Batten rows are calculated separately for the slopes on side A and side B. The board width, spacing between boards and roof slope are taken into account. The final length is the sum of all batten rows over the four roof slopes.
Counter battens. The total counter batten length is taken as equal to the total rafter length. This corresponds to a common layout where the counter batten is installed along each rafter.
Fascia board. The fascia board length is calculated along the outer eaves perimeter, including the overhangs:
Lf = 2 × (Ae + Be)
Wall plate. The wall plate length is calculated along the building perimeter without overhangs. To avoid counting corner overlaps twice, four wall plate widths are subtracted from the perimeter:
Lw = 2 × A + 2 × B - 4 × M1
The volume of battens, counter battens, fascia board and wall plate is calculated in the same way: total length in mm is multiplied by the element width and thickness in mm, then divided by 1000000000 to convert to m³.
Waterproofing and insulation
Waterproofing. The base waterproofing area is taken as equal to the roof area. If the roll length, roll width and overlap are specified, the calculator adds area for sheet overlaps:
Sw = S + S × (Go × (Gl + Gw) / (Gl × Gw))
Here S is the roof area in m², Gl is the roll length in mm, Gw is the roll width in mm, and Go is the overlap in mm. The number of rolls is calculated by dividing the area including overlaps by the area of one roll and is shown to an accuracy of 0.1 roll, without rounding to a whole package.
Insulation. The insulation volume is calculated from the area of the roof slopes without the eaves overhang. The insulation thickness is entered in millimetres, so it is converted to metres:
Vi = Si × U / 1000
Here Si is the insulated roof area in m², and U is the insulation thickness in mm. The result is shown in m³ with an accuracy of 0.01 m³.
Practical guidelines
Rafter spacing. Values around 600 mm are often used because this spacing is convenient for board and roll insulation products. For heavy roofing, large spans or high snow loads, the spacing and rafter section should be checked by structural calculation.
Batten spacing. Common values depend on the roof covering. For sheet and tile materials, the spacing is set according to the covering manufacturer's requirements, while a continuous deck uses board or panel sheathing instead of spaced battens.
Material allowance. The calculator gives the geometric volume and area based on the specified dimensions. For purchasing, an allowance is usually added for cutting waste, timber sorting, joints, damage and installation details. For timber, an allowance of about 5-10% is often used.
Related European standards
EN 1990 Eurocode. Basis of structural design. This standard sets the general principles for reliability and design situations. It is important because a geometric roof calculation does not replace a structural capacity check.
EN 1991-1-3 Eurocode 1. Actions on structures. Snow loads. This standard is used to determine snow load on the roof. In a real design, the slope, pyramid hip roof shape and construction region affect the design load on the rafters.
EN 1991-1-4 Eurocode 1. Actions on structures. Wind actions. This standard is used to calculate wind pressure and suction. For a pyramid hip roof, building height, eaves shape, edge zones of the slopes and local pressure coefficients are important.
EN 1995-1-1 Eurocode 5. Design of timber structures. This standard is used to check timber rafters, deflection, stability and connections. The calculator estimates geometry and material quantities, while section selection should take this standard into account.
FAQs
Why are two slope angles shown for a pyramid hip roof?
If the building is rectangular, the slopes along the long and short sides have different horizontal runs. With the same roof height, this creates two different angles. That is why the pyramid hip roof calculator shows the angle for each pair of slopes separately.
Why is the roof area larger than the building area?
The roof area is calculated along the inclined slopes, not over the horizontal projection of the house. Eaves overhangs on both sides are also included. As a result, the final pyramid hip roof area is always larger than the area of the building rectangle.
Why are diagonal rafters longer than ordinary rafters?
A diagonal rafter runs from a roof corner to the top apex, so its horizontal projection is longer than that of an intermediate rafter. The roof height is then added to this projection, which gives a greater inclined length. This is why diagonal elements usually require a separate section check.
Why can the number of waterproofing rolls be fractional?
The calculator divides the calculated waterproofing area by the area of one roll and shows the mathematical result. It does not round the value to a whole roll, so the actual material requirement remains visible. For purchasing, the final quantity is usually rounded upward.
Can the result be used as a complete rafter system design?
The result shows the pyramid hip roof geometry and an approximate quantity of materials. For a working design, sections, connections, supports, snow actions and wind actions must be checked separately according to applicable European standards. This is especially important for large spans, heavy roofing and demanding service conditions.