Boffins on the best way to decorate a Xmas tree – including how big the star should be

The clever formula takes into consideration things like how many baubles you have and how tall your tree is

Who knew that you could use maths to make your Christmas tree Instagrammable?
Who knew that you could use maths to make your Christmas tree Instagrammable?

With Christmas looming, it’s time for us to wipe off the dust from our Christmas trees and get our best baubles out.

There are some people that manage to get their decs looking absolutely perfect, with others facing the issue of wonky foliage.

Some prefer simplistic classic decorations, others prefer more garish and bright, which begs the question – how do you make your Christmas tree look so good?

How much tinsel is too much tinsel? How many baubles should you put on your tree? Incredibly, mathematics can answer these questions.

Students at Sheffield University Maths Society have come up with some clever formulas to perfect your tree.

If you’re wondering about lengths of tinsel and the amount of baubles, there’s a handy algorithm to solve your problems.

The students calculated that a 152cm (5ft) Christmas tree would require 31 baubles, 776cm of tinsel and 478cm of lights with a 15cm star or angel on the top.

Length of tinsel = 13 x Pi/8 x (tree height in cm)

Number of baubles = √17/20 x (tree height in cm)

Height of star in cm = Tree height in cm ÷ 10.

They’ve even created a calculator if you don’t want to do the maths yourselves, which will work out everything for you.

According to the calculator, if you have a standard sized 6ft Christmas tree, you’ll need approximately 38 baubles, 929cm of tinsel and 572cm of lights.

To top it all off, your star should be 18cm in height to finish off the perfect ratio of tinsel, baubles and lights according to maths.

The sum is all down to trigonometry, or as they like to call it ‘treegonometry’.

What about bauble colours?

There are plenty of different approaches in terms of colours for baubles, it’s very much down to personal preference.

But if you want to add some mathematics to it, to get the right aesthetic balance you need to consider ‘four-colour conjecture’.

A second maths theory could help work out the amount of bauble colours



The four-colour problem was first considered in 1852 by Francis Guthrie, a South African mathematician.

He noticed that he needed just four colours for a map of the counties of England, and was eventually proved in 1976 by Kenneth Appel and Wolfgang Haken.

Luckily for us, the Christmas tree theory is much simpler than one to do with maps.

As reported by Irish Times, if we have four baubles of different colours, there is a way to arrange them so none of the same colours touch each other – something all perfectionist tree decorators can appreciate, we’re sure.

If all the baubles are the same size, they can also be arranged in a regular pattern like the squares of a chessboard.

So, if you choose to decorate your Christmas tree using maths or decide to just improvise, it would seem that certain measurements and amount of colour really does matter.

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George Holan

George Holan is chief editor at Plainsmen Post and has articles published in many notable publications in the last decade.

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