January 18, or Blue Monday as it was christened by scientists from the lesser known college of Sky Travel, is upon us again.

Dr Cliff Arnall, formerly of Cardiff University, was the man behind the dubious formula which was used to sell more holidays in a 2005 press release for the now-defunct travel firm.

So what is the science behind the equation, and how does it predict yearly apex of misery?

Here is the offending formula.

It may look impenetrable, but according to Dr Arnall it uses many factors including weather conditions, debt level, the time since Christmas, how long it has been since we failed our New Year's resolutions, motivational levels and feeling of a need to take action.

With these taken into account, Dr Arnall assigned this specific Monday (the third of the month) as the saddest day of the year.

It has become a media phenomenon, with endless coverage of how to beat the Monday blues, but is derided by the scientific community.

Ben Goldacre, academic and science writer, said the equations "fail even to make mathematical sense on their own terms".

He found a number of different credible sources which refuted Dr Arnall's claim, citing studies which low mood to be most prevalent at many different times of year, showing no clear pattern of seasonally affected unhappiness.

Dr Arnell also put his name to an equation for "the perfect long weekend" and, inevitably, "the happiest day of the year".

Surprisingly, even the NHS has been taken in by the PR master stroke, while giving some sensible advice to those affected by a post-festive low.

While it might not be strictly possible to designate sadness to a specific calendar position, there are some more credible measures of satisfaction and well-being.

The Office for National Statistics has a "wheel of measures" to judge the nation's well-being, and The Outer Hebrides was recently revealed as the happiest place to live in Scotland, while Dundee scored lowest happiness ratings.

Residents on the islands gave an average happiness score of 7.99, after more than 300,000 people across the UK were asked to rate their happiness on a scale of zero to ten.

Well-being rates across the UK vary slightly, but it appears we are a generally happy bunch here, with happiness ratings averaging at nearly 8/10 for those surveyed.

So it seems while satisfaction can be loosely measured, the equations to prove that January 18 is the most miserable day of the year are not worth crying over.