Greenhouse Frame Calculator
About Greenhouse Frame Calculation
Greenhouse Frame Calculator determines the dimensions, quantities and lengths of the members of an arched greenhouse frame and the total material length. The calculation covers greenhouses with circular or elliptical arches, with or without door openings.
The results include the greenhouse geometry, dimensioned drawings with numbered parts, and a frame-member schedule. They help prepare a structure for fabrication, estimate the required lengths of tubing and assess the approximate covering area, for example for polycarbonate.
Guidelines and recommendations
Greenhouse geometry and arch shape
Basic dimensions. The geometry is based on the greenhouse length A, width B, overall height H1 and straight-wall height H2. All input dimensions are in millimetres. The cross-section is assumed to remain constant along the entire greenhouse length.
Arch rise. The straight-wall height is subtracted from the overall height. The difference gives the rise of the curved roof section.
h = H1 - H2
Circular arch. The upper part is an arc of a circle passing through the greenhouse crown and the tops of the straight walls. The circle radius is calculated from width B and arch rise h.
R = B2 / (8h) + h / 2
The central angle of the arc is determined from the ratio between the rise and half the greenhouse width. The angle is used in radians to calculate arc length and circular-segment area.
θ = 4 × arctan(2h / B)
For a circular arch, the curved-section rise must not exceed half the greenhouse width: h ≤ B / 2. This limits the considered arc to the upper portion of a circle with a central angle no greater than 180°.
Elliptical arch. The upper section is modelled as half an ellipse with a horizontal semi-axis B / 2 and a vertical semi-axis h. Arc length and the area beneath the curve are obtained numerically: half the ellipse is divided into 1000 equal horizontal intervals and the lengths of short segments and trapezoidal areas are added. The result is doubled to account for symmetry.
Area, volume and perimeter
Base area. The greenhouse base is taken to be rectangular. Its area is the length A multiplied by the width B. The result is divided by 1,000,000 to convert square millimetres into square metres.
Sbase = A × B / 1 000 000
Base perimeter. This is the sum of the four sides of the rectangle. The result is converted from millimetres into metres by dividing by 1000.
P = 2 × (A + B) / 1000
Transverse frame length. Two straight side sections of height H2 are added to the curved roof length. For the circular shape, the upper arc length is the radius multiplied by the central angle. For the elliptical shape, the numerically summed length is used.
Larch = R × θ
Lframe = Larch + 2 × H2
Area of one end wall. The cross-section consists of a rectangle of width B and height H2 plus the curved upper part. For a circular arch, the upper segment area is determined from the radius and central angle.
Ssegment = R2 × (θ - sin(θ)) / 2
Send = B × H2 + Ssegment
For an elliptical arch, the upper area is obtained by numerical summation. In both cases, the end-wall area is measured within the outside contour. Door openings are not deducted from this area.
Greenhouse volume. Because the cross-section remains constant along the length, the internal volume is calculated by multiplying the area of one end wall by length A. When working in millimetres, divide the result by 1,000,000,000 to obtain cubic metres.
V = Send × A / 1 000 000 000
Roof and side-wall area. The full transverse contour length, including the straight walls and the arch, is multiplied by the greenhouse length. This gives the longitudinal surface area.
Slong = Lframe × A / 1 000 000
Total surface area. The two end-wall areas are added to the roof and side-wall area. The base area is excluded. The result is the geometric area of the greenhouse's external surface.
Stotal = Slong + 2 × Send / 1 000 000
Calculation of transverse frames and longitudinal members
Transverse frames. The greenhouse length is divided into the specified number of equal longitudinal bays. Frames are installed at the bay boundaries, including both ends. Therefore the number of frames is always one greater than the number of bays along the length.
For example, with a greenhouse length of 6000 mm and 5 bays, the frame spacing is 1200 mm and the total number of transverse frames is 6. The length of each frame follows the geometry of the selected arch.
Longitudinal members. The transverse greenhouse contour is divided into the specified number of horizontal sections. Longitudinal members run along the full greenhouse length at the boundaries of these sections. Their number is one greater than the number of sections, and each member is as long as the greenhouse length A.
For example, 6 horizontal sections of the side surface require 7 longitudinal members. The total length of this group equals the number of members multiplied by the greenhouse length.
Frame development drawing. For clearer presentation, the curved transverse contour is laid out as a straight line. This drawing shows the positions of transverse frames and longitudinal members, the distances between them and their part numbers in the schedule.
Calculation of end-wall members
Bottom rail. One horizontal member of length B is counted for each end wall. Two such members are included in the overall schedule, regardless of the number of door openings.
End wall without an opening. The structural height is divided into the specified number of horizontal sections. Internal horizontal rails are placed at equal vertical intervals, and their lengths depend on the greenhouse width at each level.
The end wall is also divided across its width into equal vertical sections. Internal uprights are positioned between the two outer edges, and each upright extends from the base to the arch contour. With 3 vertical sections, there are 2 internal uprights.
End wall with a door opening. The opening is centred on the end wall. Its width D2 and height D1 are specified in millimetres. The calculation includes two vertical opening uprights and a horizontal rail above the opening.
The top rail length is determined by the cross-section width at the opening height. It may therefore exceed the opening width because it extends to the outer contour of the end wall.
Opening height limit. The upper opening corners must lie within the arch contour. The maximum permitted height is determined by the arch height at a distance of D2 / 2 from the centreline. If the entered height exceeds this limit, it is automatically reduced to the calculated maximum.
If the available arch height at the opening edges is less than 1000 mm, the opening width is automatically set to half the greenhouse width and its height is recalculated from the arch contour.
Horizontal sections around an opening. The end wall is divided separately above and below the opening's top rail. The number of levels in each part is set proportionally to the opening height and overall greenhouse height, rounded to a whole number of sections. Where multiple sections are used, at least one remains above and one below the rail.
Above the opening, horizontal members span the available cross-section width. Below the opening, rails are split into left and right pieces beside the doorway. Their lengths are measured from the outer contour to the opening edge.
Vertical sections around an opening. Above the top rail, uprights are installed at equal intervals along its length. Increasing the number of vertical sections can add side uprights on both sides of the opening. Their height is limited by the door-opening height or the outer contour height at that position.
Number of door openings. With no openings, both end walls are calculated as identical closed structures. With one opening, the front and rear are calculated separately. With two openings, the same opening arrangement is applied at both ends. The schedule includes the combined number of members for both end walls.
Material quantities and result precision
Frame schedule. The geometric length of each member is determined in millimetres. Members of equal length within the relevant group are combined. Curved transverse frames and straight longitudinal members are counted separately even if their lengths match.
Part numbering. Each group of identical members is assigned a number. It appears on the drawings and in the material list. Each entry shows the quantity and individual member length.
Rounding. Each member length is rounded to 1 mm. The total for each item is its rounded length multiplied by the quantity. The summed material length is converted into metres and displayed to 0.001 m. Areas and volume are displayed to 0.01 m2 and 0.01 m3, respectively.
Total material length. The overall frame length is the sum of all transverse frames, longitudinal members and end-wall components. No material-use correction factor is applied: the calculation factor is 1.00 and the cutting allowance is 0%. When buying profiles, an additional allowance is usually made for supplied stock lengths and the intended cutting layout.
Practical guidance and European standards
Transverse frame spacing. The spacing between neighbouring frames is the greenhouse length divided by the number of longitudinal bays. Smaller spacing reduces the unsupported distance for the covering but increases the number of frame members and total material length. Choose the spacing with regard to greenhouse size, covering type and profile properties.
Polycarbonate covering. The geometric surface area is a starting point for estimating covering requirements. Actual sheet use depends on standard sheet sizes, laying direction, joint positions and cutting waste. For arched structures, the selected polycarbonate's minimum permitted bending radius must also be considered.
Standards guidance. For greenhouse design in Europe, EN 13031-1, "Greenhouses - Design and construction - Part 1: Commercial production greenhouses", is used. It sets requirements for mechanical strength, stability, serviceability and durability of commercial greenhouses, taking account of the characteristics of these structures.
Climatic actions are assessed using EN 1991-1-3, "Eurocode 1: Actions on structures - Part 1-3: Snow loads", and EN 1991-1-4, "Eurocode 1: Actions on structures - Part 1-4: Wind actions". Design loads and application rules are specified by the applicable national annexes and requirements of the country where the greenhouse is built.
FAQs
Why do circular and elliptical arches require different amounts of material for the same greenhouse dimensions?
At equal width and height, a circular arch forms part of a circle whereas an elliptical arch forms half an ellipse. These curves have different geometry and length, so the transverse frame lengths, external surface area and internal volume change. When selecting a shape, consider both material consumption and usable headroom near the side walls.
Why are there more transverse frames than longitudinal bays?
A bay is the space between two adjacent frames. Therefore, 5 longitudinal bays require 6 transverse frames, including the first and last. This also includes the members at both greenhouse ends.
How does changing the door-opening size affect frame material consumption?
Changing the opening width or height recalculates the upright lengths, top rail and internal end-wall members. The cross-section width at rail level depends on the chosen arch shape. Changing the door dimensions can therefore either increase or decrease the total length of end-wall members.
Why does greenhouse surface area differ from the amount of covering material needed?
Surface area is calculated from the geometry of the roof, side walls and end walls. With polycarbonate, consumption also depends on sheet sizes, layout, joints and offcuts. The geometric area is therefore the starting value for a separate covering-cutting plan.
How can the frame schedule be used to prepare a greenhouse for fabrication?
The schedule groups equal members by length and quantity, and the part numbers match those on the drawings. This helps determine material requirements and prepare a cutting list. When purchasing materials, also allow for standard stock lengths, joining methods and possible cutting waste.