How this calculator works
A light strand spirals up the cone, and each turn covers a horizontal distance equal to the average circumference while rising by the spacing. The length of one turn is therefore the hypotenuse of those two distances, and the total is that length times the number of turns. The average diameter of a cone is half the base diameter, which is used here as a reasonable approximation for a Christmas tree. The foliage area is the lateral surface of a cone, pi times the radius times the slant height, which drives the bauble count. Real trees are bumpy and irregular, so treat the strand length as a starting point and keep a meter in reserve.
Formula
radius = diameter / 2. average circumference = pi x radius. strand length = (height / spacing) x sqrt(circumference^2 + spacing^2). To reverse, spacing = height x circumference / sqrt(strand^2 - height^2). foliage area = pi x radius x sqrt(radius^2 + height^2). baubles = ceil(density per square metre x area), with 1 square metre = 10.764 square feet.
Worked example
A tree 2 metres tall with a 1.2 metre base has a radius of 0.6 metres and an average circumference of 1.885 metres. At a natural spacing of 30.5 centimetres it needs 2 / 0.305 = 6.56 turns, and each turn is sqrt(1.885^2 + 0.305^2) = 1.910 metres long, so the strand is 12.52 metres. The foliage area is pi x 0.6 x sqrt(0.36 + 4) = 3.936 square metres. At 5 baubles per square foot, or 53.82 per square metre, that is 212 baubles.
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Frequently asked questions
How many lights does a tree need?
Guides often suggest about 100 lights per foot of tree for a dense look, fewer for an open one. This page works from spacing instead, because the length also depends on how wide the tree is at the base and how tightly you wrap.
Why does the model use half the base diameter?
The circumference of a cone shrinks linearly from base to tip, so its average is half the base circumference. Summing every turn exactly gives nearly the same answer, and the simpler average keeps the arithmetic readable.
Should I buy more strand than the figure?
Yes. Branches, gaps and the return lead all use extra length, and a strand that ends short is useless. Add 10 to 20 percent, or buy the next standard length up.
How many baubles are typical?
Three to five per square foot of foliage gives a full but not crowded tree. Dense displays use around ten per square foot, while sparse modern trees use one or two.