The spiral is a right triangle rolled up
Unroll the surface of a column onto a table and the spiral becomes a straight diagonal line. Each wrap travels the circumference sideways while rising by the spacing, so one wrap measures the square root of circumference squared plus spacing squared. A 36 inch girth at 3 inch spacing gives a wrap of 36.12 inches. The number of wraps is the height divided by the spacing: 96 inches of trunk at 3 inch spacing is 32 wraps. Multiply and you get 1,156 inches, which is 96.3 feet of lit string on one 8-foot trunk — and since that lands about four inches past what four 24 foot strings cover, it is five strings, not four.
Here is the part worth taking away, and it runs against what people expect. The spiral itself adds almost nothing. Thirty-two flat rings of 36 inches would be 96 feet exactly — the slope adds four inches over the whole trunk, about a third of one percent. Everyone braces for the diagonal to be the hidden cost and it is not. It only tips the string count here because 96 feet was already sitting exactly on a boundary.
The spacing is the whole calculation
What actually decides the answer is that wrapped length is very nearly girth divided by spacing, per unit of height. On the 36 inch trunk that is 12 feet of string for every foot of trunk at 3 inch spacing. At 6 inch spacing it is 6 feet per foot. At 1 inch it is 36. Halving the spacing doubles the lights, exactly, and this is where the under-buying happens: somebody looks at an 8 foot trunk, buys two 24 foot strings, and finds themselves out of lights three feet up.
The table on the calculator shows the same trunk at 1, 2, 3, 4, 6 and 12 inch spacing so the shape of that relationship is visible at a glance. It is the single most useful thing on the page, because the spacing is the one input people treat as a detail and it is the one that moves the answer by a factor of twelve.
Girth, not diameter, and measure it where you are wrapping
A tape around the trunk is the right measurement, and it is worth taking rather than converting from a diameter you eyeballed. Bark on a mature tree adds real inches, and a trunk with deep ridges takes more string than a smooth column of the same nominal size because the wrap follows the surface.
Trunks also flare. The section right at the ground is often noticeably fatter than the section four feet up, and the wraps near the base are correspondingly longer. Measuring around the middle of the section you intend to wrap averages that out well enough for buying purposes. If you are wrapping something that tapers hard — a young tree, a tapered porch column — measure top and bottom, run the calculation twice, and take the average of the two answers.
The gap you see is not the spacing you set
Spacing on this page is measured straight up the column, because that is how you lay it out: mark the height, divide, wrap. But the visible gap between two neighbouring wraps is measured square across them, and because the wraps are slightly sloped that gap is slightly less than the vertical spacing. At 3 inch spacing on a 36 inch girth the visible gap is 2.99 inches, which is a distinction with no practical consequence. On a narrow post it stops being negligible: 3 inch spacing on a 6 inch girth gives a visible gap of 2.68 inches, about a tenth tighter than you asked for, because the wrap is climbing steeply.
Going the other way, the calculator will run backwards. Tell it how many strings you already own and it solves for the spacing those strings actually stretch to, which is usually the more honest question in December. Six 24 foot strings on that 8 foot trunk work out to 2 inch spacing; two strings stretch to about 6.1 inches, which will read as a spiral with plenty of bark showing rather than a column of light.
A tree, as opposed to a trunk, tapers all the way to a point, and the arithmetic is a different one — that is on the tree light and garland calculator. Roofline and window outlining is on the christmas light string calculator, what the string count means electrically is on the chain and circuit calculator, and low-voltage runs out to a yard feature are on the landscape lighting calculator.
Questions people ask
How many lights do I need to wrap a tree trunk?
Take the girth in inches, divide by the spacing you want in inches, and multiply by the height in feet. That is the feet of lit string, to within about half a percent. A 36 inch trunk wrapped 3 inches apart for 8 feet is 36 divided by 3, times 8, which is 96 feet. The exact figure including the slope of the spiral is 96.3 feet, and since that is past what four 24 foot strings cover, it is five strings for one trunk.
Does the spiral shape add much length?
Almost none, which surprises most people. A wrap rises by the spacing while travelling the whole circumference around, so it is a very shallow diagonal. At 3 inch spacing on a 36 inch girth the wrap is 36.12 inches instead of 36 — a third of one percent over the whole trunk. The length comes from the number of wraps, not from their slope. It only starts to matter on something narrow, like a 4 inch post wrapped every 3 inches, where the wrap climbs steeply.
What spacing should I use?
That is a look, not a calculation, so the calculator shows the same column at 1, 2, 3, 4, 6 and 12 inch spacing rather than picking for you. Tight spacing on a trunk reads as a solid column of light and costs accordingly; wide spacing reads as a spiral and you can see the bark between the wraps. What is worth knowing before choosing is that the two ends of that table differ by a factor of twelve in how much string you buy.
Can I work out the spacing from the strings I already have?
Yes, and the calculator does it. Enter the strings you own per column and it solves for the spacing that uses all of them exactly. Six 24 foot strings on an 8 foot trunk of 36 inch girth comes to 2 inch spacing, and two strings stretch to about 6.1 inches. It is often the more useful direction in practice, since the boxes in the garage are a fixed quantity and the spacing is the thing that can flex.
Does this work for a tapered column or a young tree?
Approximately. The model is a cylinder of constant girth, so it is exact for a porch post and close enough for a mature trunk if you measure around the middle of the section you are wrapping. On something that tapers hard, measure at the bottom and at the top, run it twice and average the two answers. A whole tree, tapering to a point, is a different shape and a different formula, and that one is on the tree light and garland calculator.