Arc length, and why the poly order is bigger than the floor
A semicircular hoop of span S has an arc length of pi times S divided by 2, because the arc is half the circumference of a circle whose diameter is the span. A 20 ft span gives 31.42 ft of arc. Multiply by the tunnel length and that is the bare roof skin: 48 ft of tunnel needs 1,508 square feet of film before any allowance for reaching the ground rail, burying an edge in a trench, or wrapping a hip board.
Film is also sold by width, and the width you need is the arc plus the overhang allowance, not the span. Ordering by span is the mistake that leaves you a third short. The calculator gives both the width across the hoops and the total area so you can match a roll size rather than working backwards from square footage.
End walls are half-discs. The area of a semicircle of diameter S is pi times S squared divided by 8, so a 20 ft span end wall is 157 square feet before doors and vents are cut out. Two of those is another 314 square feet, which is a fifth of the roof and is usually covered in a different material anyway.
Profiles, and the honest limits of the gothic figure
| Profile | Arc length | Trade-off |
|---|---|---|
| Semicircular | pi x span / 2, about 1.571 x span | Simplest to bend, least headroom at the edges, sheds snow poorly at the peak |
| Gothic peak | Roughly 1.6 to 1.9 x span | Steeper peak sheds snow better; arc varies by design so measure a hoop |
| Semicircle on straight sidewalls | pi x span / 2 plus twice the sidewall | Recovers usable width at the edges; more wind load on the flat sides |
The gothic figure is the weakest number on this page and is presented as an approximation deliberately. Gothic profiles are not one shape, and the arc depends on how the peak was formed. If the hoops exist, run a tape along one from ground to ground and use that. If they do not, the manufacturer publishes the developed length for their bend.
Beds and paths across a curved span
The layout arithmetic assumes a path on both sides of every bed, with adjacent beds sharing a path, so n beds require n plus one paths. A 20 ft span with 4 ft beds and 2 ft paths takes three beds using 18 ft, leaving 2 ft to spread across the paths or the outer beds. Bed width should be set by reach rather than by a round number: 4 ft is about the practical limit for reaching the middle from both sides, and a bed against a wall you can only reach from one side wants to be half that.
What the arithmetic cannot see is headroom. In a semicircular tunnel the hoop meets the ground at the sidewall, so the outermost foot or two of floor has almost no vertical space above it. Tomatoes at the edge of a round hoop house hit the poly; lettuce does not. Straight sidewalls of even two or three feet change that completely, which is the main reason people accept the extra wind load they bring.
Heat loss, and what the number leaves out
Conduction loss through a covering is area times a U-value times the temperature difference. A 20 by 48 round tunnel has about 1,822 square feet of exposed surface counting both ends, and at a single-poly U-value near 1.2 and a 30 degree difference that is around 65,000 BTU per hour. Double inflated poly roughly halves it, which is why the air layer is worth the blower.
That figure is a floor and not a load. Air leakage in a hoop house is substantial and often comparable to the conduction loss: doors, end wall joints, roll-up sides, and every batten and channel where film is fastened all leak. Perimeter loss into the ground is not counted here either. Solar gain works the other way and is the reason a tunnel can be hot at noon and freezing at dawn, which no steady-state calculation captures. Use the number to compare a single-poly design against a double-poly one, or one span against another, and take the actual heater sizing to someone who does it in your climate.
Snow, wind and the permit question
Tunnels fail from snow, and they fail at night in the middle of winter when nobody is watching. Whether a given frame carries a given load depends on the rib spacing, the purlin, the bracing, the ground snow load where you are and whether the house is heated. None of that comes from a covering area. The frame specification belongs with the manufacturer, and for anything large or unusual, with an engineer who knows the local load figures.
Whether a hoop house needs a permit is a local question and the answers vary. Some jurisdictions treat an unheated seasonal structure differently from a heated year-round one, some exempt agricultural structures below a size threshold, and setbacks may apply either way. Ask the building department before you buy hoops, and ask the extension office what has actually gone down in local winters, which is usually the more informative conversation.
For filling the beds once the frame is up, the raised garden bed soil calculator handles volume and the vegetable garden starter guide covers spacing and timing. A tunnel is also a catchment surface, and the rainwater harvesting calculator works out what the footprint yields. For heat loss on a conventional insulated building rather than a film-covered one, the heat loss calculator is the right tool.
Questions people ask
How much plastic do I need to cover a hoop house?
The arc length of a semicircular hoop is pi times the span divided by two, so a 20 ft span needs 31.4 ft of film across the hoops, and a 48 ft long tunnel needs about 1,508 square feet of roof skin before any allowance. Add 10 to 20 percent for reaching a ground rail, burying an edge, or wrapping a hip board, and add the two end walls separately at pi times span squared over eight each, which is 157 square feet apiece at a 20 ft span. Order by width as well as area: the roll has to be at least the arc plus the overhang, and ordering film the width of the span is the single most common mistake in a first build.
How wide should the beds and paths be inside a tunnel?
Bed width is set by reach, not by the span. Four feet is about the limit for reaching the centre comfortably from both sides, and a bed you can only work from one side wants to be around half that. Paths of 18 inches to 2 feet suit a person on foot, and a wheelbarrow or a cart needs 2.5 to 3 feet, so decide what has to travel down the path before fixing the width. The other constraint is headroom rather than floor width. In a round tunnel the hoop meets the ground at the edge, so the outermost foot or two has very little vertical space and is only useful for low crops. Straight sidewalls of two or three feet recover that space and are usually worth the extra material.
How much heat does a hoop house lose on a cold night?
Conduction loss is the exposed surface area times the covering U-value times the inside-to-outside temperature difference. A 20 by 48 ft round tunnel has roughly 1,822 square feet of surface counting both ends, so at a single-poly U-value near 1.2 and a 30 degree difference that is about 65,000 BTU per hour. Double inflated poly at around 0.7 cuts it to roughly 38,000. Treat those as a floor. Air leakage in a film-covered structure is large, frequently in the same range as the conduction loss, and it comes from doors, end wall joints, roll-up sides and every fastening point. Ground and perimeter losses are extra. Size an actual heater with someone who does it in your climate rather than from a steady-state number.
Is a gothic arch better than a round hoop?
For snow, generally yes, and that is usually the reason people choose it. A peaked profile sheds snow that a semicircular top allows to sit and accumulate, and accumulated snow is what collapses tunnels. The costs are a longer arc, so more covering material for the same span, and a shape that is harder to bend accurately at home. The arc length is also less predictable: gothic profiles vary by manufacturer and by how the peak was formed, running roughly 1.6 to 1.9 times the span, which is why the estimate on this page is flagged as approximate. If the hoops exist, measure one with a tape from ground to ground. That measurement beats any formula.
Do I need a permit for a hoop house?
Possibly, and it varies enough between jurisdictions that assuming either way is a mistake. Some places treat an unheated seasonal structure with no permanent foundation differently from a heated year-round greenhouse, some exempt agricultural structures under a size threshold, and some do not distinguish at all. Setback requirements from property lines may apply regardless of whether a permit does, and a homeowners association or deed restriction can add its own limits. Separately, ground snow load and wind exposure figures for your location determine what frame specification is adequate, and those come from the building department too. Call before buying hoops. The conversation is short and the alternative is expensive.