Single-Slope Roof

About Single-Slope Roof Calculation

This calculator performs the geometric calculation of a single-slope roof and determines the main roof plane dimensions, slope angle, number of rafters, batten parameters, waterproofing membrane, counter battens, wall plate, fascia board and barge board, as well as the volume of timber and insulation.

The calculation is suitable for a preliminary material estimate and for checking the general layout of a simple single-slope roof. All calculations use dimensions entered in centimeters, while areas, volumes and total lengths are displayed in square meters, cubic meters or meters.

Reference values and recommendations

Single-slope roof geometry

Slope angle. First, the roof slope angle is determined from the roof rise H and the horizontal building width X. A right triangle is used, where H is the vertical leg and X is the horizontal projection of the roof slope.

alpha = arctan(H / X)

The angle alpha is displayed in degrees. Overhangs are not included in the angle calculation because they continue the already defined slope line.

Roof slope length. The full roof slope length is calculated along the inclined line, including the overhang on both sides. Therefore, twice the overhang is added to the building width.

Lroof = (X + 2 * C) / cos(alpha)

Here C is the roof overhang in centimeters. The result Lroof is displayed in centimeters.

Roof slope width. The roof width is calculated as the building length plus the overhangs on the two side edges.

Wroof = B + 2 * C

Roof area. The area is calculated from the inclined roof slope length and the full roof width. Division by 10000 converts square centimeters to square meters.

Aroof = Lroof * Wroof / 10000

Rafters

Rafter length. The rafter length uses the roof slope length and an additional allowance for the lower angled cut. This allowance depends on the rafter width and the roof slope angle.

Lrafter = Lroof + S1 * tan(alpha)

Here S1 is the rafter width in centimeters. Therefore, the calculated rafter length is slightly greater than the roof slope length.

Number of rafters. The calculator accounts for the full roof width, the offset of the outer rafters from the side edges, the rafter thickness and the clear spacing between rafters. The calculation interval is the sum of the clear spacing and the rafter thickness.

Nrafter = ceil((Wroof - 2 * O) / (R + S2) + 1)

Here O is the rafter offset, R is the clear spacing between rafters, and S2 is the rafter thickness. The function ceil means rounding up to a whole number of elements.

Rafter volume. The volume is calculated as the number of rafters multiplied by the cross-section of one rafter and its calculated length. Division by 1000000 converts cubic centimeters to cubic meters.

Vrafter = Nrafter * S1 * S2 * Lrafter / 1000000

Battens

Length of one row. One batten row runs across the roof width, so its length is equal to the full roof slope width Wroof.

Number of rows. Batten rows are distributed along the inclined roof slope length. The calculation interval is equal to the batten board width plus the spacing between boards.

Nbatten = ceil(Lroof / (O3 + O1) + 1)

Here O1 is the batten board width and O3 is the spacing between boards. Rounding up adds a full row if the calculated length is not divided by the interval without a remainder.

Total batten length. The total length is calculated as the width of one row multiplied by the number of rows. The result is then converted from centimeters to meters and rounded up to a whole meter.

Lbatten = ceil(Wroof * Nbatten / 100)

Batten volume. The volume is calculated from the total length of all rows and the board cross-section.

Vbatten = Wroof * O1 * O2 * Nbatten / 1000000

Fascia board, barge board and wall plate

Fascia board. The total fascia board length is calculated along the two horizontal edges of the roof slope.

Lfascia = Wroof * 2 / 100

The fascia board volume is calculated from the total length, board width and board thickness.

Barge board. The total barge board length is calculated along the two inclined side edges of the roof slope.

Lbarge = Lroof * 2 / 100

The barge board volume is calculated from this length and the selected board cross-section.

Wall plate. In this calculation, the wall plate length is taken along two sides of the building width, without adding roof overhangs.

Lwallplate = B * 2 / 100

The wall plate volume is calculated from the total length, timber width and timber thickness.

Waterproofing membrane and counter battens

Waterproofing membrane area. First, the roof slope area is taken, then an allowance for the longitudinal overlaps of the roll material is added. The allowance depends on the roll length, the specified overlap, the roof slope length and the roll width.

Amembrane = Aroof + Glength * Goverlap * (Lroof / Gwidth) / 10000

Here Glength is the roll length, Gwidth is the roll width, and Goverlap is the overlap. All these values are entered in centimeters.

Number of rolls. The calculated number of rolls is obtained by dividing the waterproofing membrane area by the area of one roll. The result may be fractional because the calculator shows the calculated material requirement, not a cutting layout.

Nroll = Amembrane / (Glength * Gwidth / 10000)

Counter battens. The length of one counter batten is equal to the roof slope length. The total length is calculated by the number of rafters because the counter battens run along the slope on the rafter lines.

Lcounterbatten = Nrafter * Lroof / 100

The counter batten volume is calculated from the total length, batten width and batten thickness.

Insulation

Insulation volume. Insulation is calculated using the clear roof slope area without roof overhangs. For this, the inclined length between the walls, the building length and the insulation thickness are used.

Vinsulation = (X / cos(alpha)) * B * U / 1000000

Here U is the insulation thickness in centimeters. This approach does not add insulation to the overhang zone because the overhang is usually outside the insulated envelope.

Practical reference values

• For single-slope roofs, a slope of approximately 5° to 30° is often used, but the minimum permitted slope depends on the specific roofing material and the manufacturer's requirements.
• In private construction, rafter spacing is often selected in the range of 40-80 cm. The final value depends on loads, timber cross-section, span and insulation width.
• A roof overhang is often taken at about 30-60 cm. A larger overhang protects the facade better, but increases the requirements for stiffness and fastening details.
• The overlap of roll waterproofing membrane is often taken at about 10-20 cm. For low slopes and difficult conditions, a more reliable overlap arrangement is usually required.
• For purchasing timber and roll materials, a practical allowance is usually added for cutting, sorting and local waste.

Related European standards

EN 1991-1-3 Eurocode 1: Actions on structures - Snow loads. This document is used to determine snow loads on the roof. The calculator does not calculate snow load, but the resulting angle, roof slope length and rafter layout should be checked with this document in mind.

EN 1991-1-4 Eurocode 1: Actions on structures - Wind actions. This document is used to assess wind actions, including roof uplift and loads on overhangs. A geometric calculation does not replace this check.

EN 1995-1-1 Eurocode 5: Design of timber structures. This document is used for the design of timber structures. The selection of rafter, wall plate, connection and fastener dimensions should account for strength, stiffness, moisture conditions and load duration.

EN 13859-1 Flexible sheets for waterproofing - Underlays for discontinuous roofing. This document relates to the properties of underlay waterproofing layers for discontinuous roofing. It is important when selecting a membrane, but it does not define the roof slope geometry.

FAQs

Why is the rafter length greater than the roof slope length?

The rafter length is additionally increased by an allowance for the lower angled cut. This allowance depends on the rafter width and the roof slope angle.

How is the number of rafters calculated?

The calculation accounts for the full roof width, two side offsets, the rafter thickness and the clear spacing between rafters. After division, the result is rounded up because a fractional rafter cannot be installed.

Why can the number of waterproofing membrane rolls be fractional?

The calculator shows the calculated material requirement by area, not a finished roll cutting layout. When purchasing, the number of rolls is usually rounded up and an allowance is added for overlaps, cutting and damage.

Can this calculation be used to select the rafter cross-section?

No, this calculator determines the geometry and approximate quantity of materials for a single-slope roof. The rafter cross-section must be checked separately according to loads, span, timber grade and the working conditions of the structure.