Pyramid Hip Roof Calculator

About Pyramid Hip Roof Calculation

This calculator determines the geometry of a pyramid hip roof, including roof slope area, pitch angles, total length and volume of timber elements, and an approximate amount of underlay membrane and insulation. It is intended for preliminary structural layout, comparison of roof pitch options, and preparation of a material estimate.

The calculation uses a geometric model with four roof slopes, diagonal rafters running from the corners to the roof apex, and intermediate rafters on sides A and B. All input dimensions are entered in centimetres, while final areas, volumes, and total lengths are converted to m², m³, and metres.

Guidelines and recommendations

Roof geometry

Eaves dimensions. The roof length and width are calculated from the building dimensions and the overhang on both sides. If the building length is A, the width is B, and the overhang is C, the final eaves dimensions are calculated as follows:

Be = B + 2 × C

Ae = A + 2 × C

Pitch angle. For a pyramid hip roof on a rectangular building, the calculator shows two angles because the slopes related to the building length and width have different horizontal runs. The angle is calculated from the roof height H and half of the corresponding building side:

αA = arctan(H / (B / 2))

αB = arctan(H / (A / 2))

The meaning of this formula is simple: the greater the height H for the same half-span, the steeper the roof slope. The result is shown in degrees.

Roof area. The area is calculated as the sum of the four inclined roof slopes. To do this, the calculator uses the horizontal roof projection including the overhangs and two slope factors for sides A and B:

kA = √((A / 2)2 + H2) / (A / 2)

kB = √((B / 2)2 + H2) / (B / 2)

S = Ae × Be × (kA + kB) / 2

The factors k_A and k_B convert the horizontal projection into the actual inclined area of the slopes. The final area is rounded up to 0.1 m².

Rafter system

Diagonal rafters. The calculator uses 4 diagonal rafters. Their length is determined by the distance from the eaves corner to the roof apex, taking the height H into account, so diagonal elements are longer than ordinary intermediate rafters.

Intermediate rafters. On sides A and B, rafters are placed symmetrically relative to the roof axes. The number of rafter rows is selected according to the rafter spacing: the calculator adds rafters as long as the remaining part of the slope allows another element to be placed with the specified spacing.

Rafter length. For each rafter type, the length is calculated along the inclined line of the slope. The lower angled cut of the board is also included, so the calculated element length is slightly greater than the pure geometric length of the slope.

Total length and volume. The total rafter length is the sum of all calculated elements. The volume is calculated from the board cross-section:

V = L × S1 × S2 / 1000000

Here L is the total length in centimetres, and S₁ and S₂ are the rafter board width and thickness in centimetres. Division by 1000000 converts cm³ to m³.

Battens, counter-battens, and boards

Battens. Batten rows are calculated separately for the slopes on side A and side B. The calculator takes into account the board width, spacing between boards, and roof slope, then sums the lengths of all rows.

Counter-battens. The total counter-batten length is taken as equal to the total rafter length. This matches a common arrangement where a counter-batten is installed along each rafter.

Fascia board. The fascia board length is calculated from the eaves perimeter including the overhang:

Lf = 2 × (Ae + Be)

Wall plate. The wall plate length is calculated along the building perimeter. To avoid counting the corner sections twice, four wall plate widths are subtracted from the perimeter:

Lw = 2 × A + 2 × B - 4 × M1

The volume of the fascia board, wall plate, battens, and counter-battens is calculated in the same way: the total length is multiplied by the width and thickness of the element, then the result is converted from cm³ to m³.

Underlay membrane and insulation

Underlay membrane. The base membrane area is taken as equal to the roof area. If the roll length, roll width, and overlap are specified, the calculator adds extra material for overlapping sheets:

Sm = S + S × (Go × (Gl + Gw) / (Gl × Gw))

Here S is the roof area, G_l is the roll length, G_w is the roll width, and G_o is the overlap. The number of rolls is calculated by dividing the area including overlaps by the area of one roll.

Insulation. The insulation volume is calculated from the slope area without the eaves overhang and from the specified layer thickness:

Vi = Si × U / 100

Here S_i is the calculated area of the insulated part of the roof in m², and U is the insulation thickness in centimetres. Division by 100 converts the thickness from centimetres to metres.

Regulatory references

Eurocode EN 1990. This standard sets out the general principles for structural design and the approach to calculation reliability. For a working structure, the calculator results should be checked against the building's structural scheme, materials, and service conditions.

Eurocode EN 1991-1-3. This standard is used for snow loads. In an actual project, rafter spacing, board section, and permissible roof pitch depend on the snow load zone, roof shape, and snow accumulation factors.

Eurocode EN 1991-1-4. This standard is used for wind actions. For a pyramid hip roof, the building height, wind load zone, eaves shape, and increased suction zones near edges are important.

Eurocode EN 1995-1-1. This standard applies to the design of timber structures. It is needed to check strength, deflection, stability, and connections in the rafter system.

FAQs

Why are two pitch angles shown for a pyramid hip roof?

For a rectangular building, the slopes related to the long and short sides have different horizontal runs. With the same roof height, this gives two different pitch angles. Therefore, the calculator separately shows the angle for the slope on side A and the angle for the slope on side B.

Why is the roof area larger than the building area?

The roof area is calculated along the inclined slopes, not by the horizontal projection of the building. The eaves overhang is also included. Therefore, the final area of a pyramid hip roof is always larger than the area of the building rectangle.

Why are board width and thickness needed in the calculation?

These dimensions are needed to calculate the timber volume. The calculator first determines the total length of the elements, then multiplies it by the board cross-section. This gives an approximate volume of rafters, battens, counter-battens, fascia board, or wall plate in m³.

Why can the rafter length be slightly greater than the slope length?

In the rafter table, the length includes the lower angled cut. Such an element is longer than a simple line from the eaves to the roof apex. This helps estimate the actual blank length for cutting more closely.

Should extra material be added beyond the calculated result?

For practical purchasing, it is common to add extra material for trimming, timber sorting, joints, damage, and installation details. For timber, a reserve of about 5-10% is often used, while for roofing membranes the reserve depends on the laying pattern and overlaps.