Members of Sheffield University’s maths society, known as SUM, were asked to come up with calculation by department store Debenhams, which will use it in decorating stores nationwide.
Four separate sums make up the complete calculation, which also provides instruction on the ideal length of tinsel and lights as well as the height of the star or fairy which is placed on top.
The calculations suggest that the tree-topper should be precisely a tenth of the size of the tree, while the number of lights is calculated by multiplying the mathematical constant Pi by the height of the tree in centimetres.
In an example provided by members of the maths society yesterday, a 6ft (180cm) Christmas tree would need 37 baubles, 919cms of tinsel and 565 cms of lights.
An 18cm-high angel or star would be required to “achieve the perfect look”.
Students Nicole Wrightham and Alex Craig, both 20, created the formulas after the university was approached by Debenhams’ personal shopper team.
Miss Wrightham said: “The formulas took us about two hours to complete. We hope the formulas will play a part in making Christmas that little bit easier for everyone.”
“The formula allows customers to be savvy when buying the Christmas decorations, as they can calculate exactly how much they need to create a beautifully decorated tree.
Debenhams Christmas decorations buyer Sarah Theobold said the chain, which has 240 stores in 28 countries around the work, sold hundreds of thousands of different Christmas decorations every year.
She said: “The formula is so versatile it will work for a tree large enough for the Royal Family at Balmoral but also on trees small enough for the most modest of homes.
“Customers are often making the error of buying too large or small an angel; however this simple formula means you’ll have the tree to star ratio correct.”
All four of the calculations for the perfect Christmas tree can be seen on Sheffield University’s website at www.sheffield.ac.uk/news