A swag is a catenary and everyone buys it short
Hang anything flexible between two points and it settles into a specific curve — the one a chain makes, which is why it is called a catenary. The length of that curve is set entirely by the span and the drop, and it is always longer than the straight line between the anchors. Six feet between anchors with a 14 inch drop wants 6.57 feet of garland, 9.5 percent more than the straight line. Buy six feet, and to make it span the gap you have to pull it tight, and then it does not drop at all.
The relationship is not linear, which is why intuition is unreliable in both directions. On a 6 ft span, a 3 inch drop adds about a third of an inch to the length. A 6 inch drop adds an inch and a third. A 12 inch drop adds five inches, and a 24 inch drop adds a foot and a half. The extra length grows with the square of the drop, so shallow swags are essentially free and deep ones are not.
Running it the other way is usually the real question
Most people are not choosing a drop, they are holding four nine-foot garlands and wondering how far apart the nails can go. The calculator solves that direction too. Nine feet of garland over a six foot span produces a drop of just over 36 inches, which is a very deep swoop; over a seven foot span it drops about 30 inches; over eight feet, about 22 inches. The same garland looks like a completely different decoration depending on where the anchors go, and moving the nails is free while buying more garland is not.
There is a limit at the bottom of that: if the garland is shorter than the span it simply will not reach, and the page says so rather than producing a nonsense drop.
The tails are where the shortfall actually happens
The curve is only part of what gets used. At every anchor there is garland wrapped around the nail, wired to the rail, tucked behind the bracket, or falling past the anchor as a cascade. Six inches at each end of each swag on a three-swag mantel is three feet — a third of a nine-foot piece, gone into places nobody looks at. This is the most common reason a run that was calculated correctly still comes up short, and it is a field on this page for that reason.
Piece joins are the other overlooked cost. Three swags of 7.57 feet each is 22.7 feet, which is three nine-foot pieces, and since a swag is 7.57 feet and a piece is 9, each swag can come out of one piece with 1.43 feet wasted per piece. Try to be efficient and cut across pieces and you get joins in the middle of a swag, which have to be wired and hidden. On a mantel the honest choice is usually to accept the waste.
Where the model stops being true
A catenary is what a uniform, perfectly flexible thing does. A rope garland or a light string behaves close enough. A wired pine garland does not — it holds whatever shape you bend it into, usually a shallower arc than gravity would give, and it will take slightly less than the calculation says. A garland with three heavy ornaments hung at intervals is not uniform and will hang lower at those points. And this assumes both anchors are level with one another, which rules out a staircase rail, where the swag hangs from points at different heights and the geometry is a different problem.
The page also compares its answer against the parabolic approximation that most references quote, because at ordinary decorating depths the two agree to a fraction of an inch and it is worth seeing that rather than wondering. They part company once the drop passes about a quarter of the span, which is a very deep swag by mantel standards but an ordinary one on a porch rail.
Garland wound around a tree is a spiral rather than a hanging curve and the length is on the tree light and garland calculator; around a column, the column and trunk wrap calculator. If the swags carry lights, the christmas light string calculator turns the run into whole strings.
Questions people ask
How much garland do I need for a swag?
More than the span, and how much more depends on the drop. Over a 6 ft span, a swag dropping 14 inches in the middle needs 6.57 ft of garland — 9.5 percent more than the straight-line distance. Add whatever you use tying off at each end, typically 6 inches a side, and a single swag of that shape comes to 7.57 ft in practice.
How far apart should the nails go for a 9 foot garland?
Depends on the drop you want, and the calculator will solve it directly. Nine feet over a 6 ft span gives a drop of just over 36 inches, which is a very deep swoop. Over 7 ft it drops about 30 inches. Over 8 ft, about 22 inches. If you want a specific look, moving the anchors is the free adjustment; buying more garland is not.
Why is a swag longer than the distance between the anchors?
Because it hangs. A flexible thing suspended between two points takes the curve a chain takes, and any curve between two points is longer than the straight line joining them. The extra grows with the square of the drop: on a 6 ft span, a 3 inch drop adds about a third of an inch, but a 24 inch drop adds about 18 inches. Shallow swags cost almost nothing extra and deep ones cost a lot.
How many garland pieces for a mantel?
Work out the length per swag including the tails, multiply by the number of swags, and divide by the piece length, rounding up. Three swags on a 6 ft span with a 14 inch drop and 6 inches of tail per anchor is 22.7 ft, which is three 9 ft pieces. Cutting to eliminate waste means joins in the middle of a swag, and every join has to be wired and hidden, so most people take the waste instead.
Does this work for garland on a staircase?
No. This assumes the two anchor points are at the same height, which is what a mantel, a porch rail or a fence gives you. A staircase rail anchors each swag at two different heights, the low end takes more of the weight and the curve is not symmetric, so the length is greater than this page reports. Measure a single swag on the stairs with a length of string and use that as your unit instead.