Treegonometry is the key to a perfect Christmas tree

For a Christmas tree to make your neighbours green with envy, maths students at the University of Sheffield have the perfect festive formula to help you decorate.


Created by members of the University’s maths society, called SUMS, the formula ensures the ratio of lights, tinsel and baubles is just right to turn a home into a winter wonderland.

Once the ideal Christmas tree has been found, use the calculator to make sure your tree-topping star or angel is the right height and you have the correct number of decorations for the perfect look.

The formula is as follows:


For example, a 180cm (6ft) Christmas tree would need 37 baubles, around 919 cms of tinsel and 565 cms of lights and an 18cm star or angel is required to achieve the perfect look.


Sam Hayes, President of SUMS said: “I’m often asked what the point of maths is; the Christmas tree formula - which was actually created by two former students and members of SUMS a couple of years ago - is something which everyone can relate to and shows how maths can be used in everyday life.

“It’s a bit of fun and if gets people engaging with maths while enjoying the festive season then it’s a good thing.”

Christmas tree facts

  • The world's tallest Christmas tree would, at 2,600ft tall, need more than 16,000 baubles, over 4,000 meters of tinsel, almost 2,500 meters of lights, and an 80 meter tall star.
  • This year's Trafalgar Square tree is about 20 meters tall, meaning it would need 412 baubles, over 100 meters of tinsel, 62 meters of lights and a two meter tall star.

Additional information

The University of Sheffield
With nearly 26,000 students from 125 countries, the University of Sheffield is one of the UK’s leading and largest universities. A member of the Russell Group, it has a reputation for world-class teaching and research excellence across a wide range of disciplines. The University of Sheffield was named University of the Year in the Times Higher Education Awards 2011 for its exceptional performance in research, teaching, access and business performance. In addition, the University has won four Queen’s Anniversary Prizes (1998, 2000, 2002, and 2007).

These prestigious awards recognise outstanding contributions by universities and colleges to the United Kingdom’s intellectual, economic, cultural and social life. Sheffield also boasts five Nobel Prize winners among former staff and students and many of its alumni have gone on to hold positions of great responsibility and influence around the world. The University’s research partners and clients include Boeing, Rolls-Royce, Unilever, Boots, AstraZeneca, GSK, ICI, Slazenger, and many more household names, as well as UK and overseas government agencies and charitable foundations.

The University has well-established partnerships with a number of universities and major corporations, both in the UK and abroad. Its partnership with Leeds and York Universities in the White Rose Consortium has a combined research power greater than that of either Oxford or Cambridge.


For further information please contact:

Clare Parkin
Media Relations Officer
The University of Sheffield
0114 2229851