Wrapping awkwardly shaped Christmas presents is always a headache, but here's the formula for perfect gift wrap.

You've carefully chosen the presents. You have scissors, tape and even some rolls of suitably jolly paper at the ready. For all but the most accomplished of festive elves, however, your gift is still likely to end up chaotically cocooned in a patchwork of wrapping and tangle of tape.

This is probably why wrapping Christmas presents is rarely a job that many people relish. This year, however, you might prefer to add a ruler and calculator to your festive wrapping supplies. It is time to employ the power of mathematics this Christmas.

Perhaps the easiest item on your wrapping list this year will be those cube-shaped boxes. But many of us still struggle to cut the right amount of paper to cover even this simplest of gift-shapes. We might end up with swathes of extra paper folded messily in at the ends or find we come up short and need to apply some surgical skills to fashion an insert to ensure total coverage.

There is, however, a neat formula developed by Sara Santos, a mathematician at King's College London in the UK, that can help not only reduce waste but also match some patterns together at the join. First measure your box's height and multiply that by 1.5. Then measure the diagonal of your box's largest side from corner to corner – adding the two figures together. This gives you the dimensions of a square of wrapping paper you will need to cut.

So, for example, if you're wrapping a cube that measures 4.5cm (1.7in) diagonally and 3cm (1.2in) tall, you need to cut a 9cm x 9cm (3.5in x 3.5in) square of paper. But here comes the clever bit…

When you place your gift onto the paper, rotate it so it sits diagonally in the centre of the paper. Then carefully bring the four corners of the paper into the centre, tucking in the tabs at each corner of your box under the larger flaps as you fold them in. You should be able to secure the paper with just three small pieces of tape, and if you're using stripey paper, the pattern may even match up at the joins.

This method can sometimes be used for cuboids too. "However, if your paper is square, it's not always true that the diagonal wrap is better," says Holly Krieger, professor of mathematics at the University of Cambridge. For example, if you have a box that measures 2cm x 4cm x 8cm (0.8in x 1.6in x 3in), using the diagonal method requires a 14 x 14cm (5.5in x 5.5in) square of paper, but it's possible to wrap the same gift in a more conventional way using a 12cm (4.7in) square of paper, she explains.

The diagonal positioning trick is most useful if you have a spare square of paper that doesn't quite fit around a cube in the traditional way. Turning it diagonally may allow it to cover the present. Similarly, rectangles of paper that don't quite cover cuboid-shaped presents like a shoebox can be coaxed around........

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