A loop is a traverse, and a traverse has to close
Surveyors have had a name for this problem for two hundred years. Walk a closed shape as a series of legs and turns, and when you get back to where you started you should be exactly where you started. Two things have to be true for that: the turns must add up to 360 degrees, and the leg lengths must be consistent with them. The first is easy to check and the second is not, which is why the calculator walks the polygon and reports where the last leg actually ends.
Six legs of 200, 150, 180, 200, 150 and 180 feet with 60 degree turns close exactly. That is not luck — with equal 60 degree turns the legs point along six directions 60 degrees apart, and the loop closes when opposite legs are equal, so leg one must match leg four, two must match five, three must match six. Change the fourth leg to 220 and the last point lands 20 feet from the start, which on the ground is two stakes in the same corner and an argument about which one is right.
Reading the closure figure
| Closure error | On a 1,060 ft loop | What it usually means |
|---|---|---|
| 0 ft | 1 in infinity | The numbers are consistent; the ground may still disagree |
| 2 ft | 1 in 530 | Rounding and pacing, spread it across the legs |
| 10 ft | 1 in 106 | One leg measured wrong, or a turn out by a couple of degrees |
| 25 ft or more | 1 in 42 or worse | A leg or a turn is wrong outright, not accumulated error |
The advice on a big error is always the same: check the longest leg first. A one percent error on a 200 ft leg moves the endpoint two feet; the same one percent on a 60 ft leg moves it seven inches. Long legs carry the blame in proportion to their length, and they are also the ones most likely to have been paced rather than wheeled.
The bounding box is the ground you actually need
Perimeter tells you what to buy; the bounding box tells you whether it fits. The six-leg example above has a perimeter of 1,060 feet but a bounding box of 365 by 285.8 feet — 104,313 square feet, or 2.4 acres of rectangle to contain a loop whose line would fit in a shopping bag. That gap between line length and ground occupied is the thing that catches people out when they look at a field and estimate by eye.
The ratio the page prints — line length divided by the square root of the box area — is a shape number with two fixed points worth remembering. A circle scores pi, about 3.14, and a square scores exactly 4. The six-leg example comes out at 3.28, so it is a fairly round loop using its rectangle well. Much above 4 and the loop is long and thin, which uses more line for the same ground and takes more pulleys to steer.
Pulleys, splices and the parts nobody counts
One pulley per change of direction is the arithmetic, and it is exact: six corners, six pulleys. What is not arithmetic is that every spool boundary in the line is a splice, and splices are where things fail. A 1,060 foot loop with ten percent spare and thirty feet of tie-off is 1,196 feet of line, which off 600 foot spools is two spools and one splice — plus whatever joins the two ends of the loop itself.
How any of it is rigged, driven, tensioned or stopped is not on this page. Line under tension along hundreds of feet of ground is a real hazard and it belongs to whoever supplied the equipment and to the club running the course. This page counts feet and pulleys and stops there.
Where this hands off
For a circular curve rather than a straight-leg polygon — radius, chord, middle ordinate, and the offsets to stake it from a tape — use the curve layout calculator. To prove a rectangle is square before you stake anything, site layout squaring does the diagonals. If what you are laying out is a fenced ring for a course rather than an open loop, the agility ring size calculator handles the footprint and the run-off band, and the field use hours calculator covers what a season of use does to the ground underneath.
Questions people ask
Which direction should I walk the loop in?
Either, as long as you are consistent. Every turn must be the same way round — all left or all right — because the arithmetic adds them up and expects 360 degrees. If you enter a mix of left and right turns without signs, the total will be wrong and the closure figure will be nonsense. If the loop genuinely has a reflex corner, enter that turn as a negative angle.
My turns add to 360 but the closure error is 30 feet. What now?
The angles are right and a length is wrong. Check the longest leg first, because an error there moves the endpoint furthest, then the next longest. If everything re-measures the same, the error is in the turns after all — two or three degrees on a couple of corners is invisible on the ground and will move a 1,000 ft loop by tens of feet. The per-leg adjustment figure is a fallback, not a fix.
Does one lap equal the perimeter?
Yes for the ground the lure travels, which is what the perimeter measures. The line itself is a continuous loop of the same length plus whatever the drive takes up and whatever you leave for tying off, which is why the line figure is larger than the perimeter. If your setup routes line back to a drive rather than running it round the loop, add that run into the tie-off field.
How many pulleys will I need?
One per change of direction, so as many as there are legs in a closed loop. That is the geometry and it is exact. What size, what rating and how each is anchored are questions for whoever supplied the equipment, and the stakes-per-pulley field is there so you can count anchors on your own basis rather than one this page invents.
Can I use this to lay out a course that is not a closed loop?
The perimeter, bounding box and line figures all work on an open path, and the closure section will simply tell you how far the end is from the start — which for an open path is the point rather than an error. What you lose is the 360 degree check, since an open path has no reason to satisfy it. Read the closure distance as the gap between the two ends and ignore the warning about it.