Blue Monday is the name given to a day in January (typically the third Monday of the month) said by a UK travel company, Sky Travel, to be the most depressing day of the year. The concept was first published in a 2005 press release from the company, which claimed to have calculated the date using an "equation". It takes into account weather conditions and thus only applies to the Northern Hemisphere.
Scientists have dismissed the idea as baseless pseudoscience.
This date was published in a press release under the name of Cliff Arnall, who was at the time a tutor at the Centre for Lifelong Learning, a Further Education centre attached to Cardiff University. Guardian columnist Ben Goldacre reported that the press release was delivered substantially pre-written to a number of academics via public relations agency Porter Novelli, along with an offer of money to those who offered to put their names to it. A statement later printed in the Guardian sought to distance leaders of Cardiff University from Arnall: "Cardiff University has asked us to point out that Cliff Arnall . . . was a former part-time tutor at the university but left in February."
Variations of the story have been repeatedly reused by other companies in press releases, with 2014 seeing Blue Monday invoked by legal firms and retailers of bottled water and alcoholic drinks. Some versions of the story purport to analyse trends in social media posts to calculate the date.
In 2018, Arnall told a reporter at the Independent newspaper that it was "never his intention to make the day sound negative", but rather "to inspire people to take action and make bold life decisions". It was also reported that he was working with Virgin Atlantic and Virgin Holidays, having "made it his mission to challenge some of the negative news associated with January and to debunk the melancholic mind-set of 'Blue Monday'".
The date is generally reported as falling on the third Monday in January, but also on the second or fourth Monday. The first such date declared was 24 January in 2005 as part of a Sky Travel press release.
The formula uses many factors, including: weather conditions, debt level (the difference between debt accumulated and ability to pay), time since Christmas, time since new year’s resolutions have been broken, low motivational levels, and the feeling of a need to take action. One relationship used by Arnall in 2006 was:
where Tt = travel time; D = delays; C = time spent on cultural activities; R = time spent relaxing; ZZ = time spent sleeping; St = time spent in a state of stress; P = time spent packing; Pr = time spent in preparation. Units of measurement are not defined; as all the factors involve time, dimensional analysis of the "formula" shows that it violates the fundamental property of dimensional homogeneity and is thus meaningless.
The 2005 press release and a 2009 press release used a different formula:
where W=weather, D=debt, d=monthly salary, T=time since Christmas, Q=time since the failure of new year's resolutions, M=low motivational levels, and Na=the feeling of a need to take action. Again, no units were defined; the lack of any explanation for what is meant by "weather" and "low motivational levels" means the dimensional homogeneity of the resulting formula cannot be assessed or verified, rendering it similarly meaningless.
Ben Goldacre has observed that the equations "fail even to make mathematical sense on their own terms", pointing out that under Arnall's original equation, packing for ten hours and preparing for 40 will always guarantee a good holiday, and that "you can have an infinitely good weekend by staying at home and cutting your travel time to zero". Dean Burnett, a neuroscientist who has worked in the psychology department of Cardiff University, has described the work as "farcical", with "nonsensical measurements".
In 2016, Arnall claimed to have attempted to "overturn" his "theory" by visiting the Canary Islands; his claim was publicised by the Canary Islands Tourism Board 
Arnall also says, in a press release commissioned by Wall's ice cream, that he has calculated the happiest day of the year – in 2005, 24 June, in 2006, 23 June, in 2008, 20 June and in 2010, 18 June. So far, this date has fallen close to Midsummer in the Northern Hemisphere (June 21 to 24).
- ^ Burnett, Dean (16 January 2012). "Blue Monday: a depressing day of pseudoscience and humiliation". The Guardian. London. Retrieved 20 January 2014.
- ^ a b c Goldacre, Ben (16 December 2006). "MS = media slut, but CW = corporate whore". The Guardian. London. Retrieved 21 January 2008.
- ^ Goldacre, Ben (18 November 2006). "How GxPxIxC = selling out to your corporate sponsor". The Guardian. London. Retrieved 20 January 2014.
- ^ a b "Snopes: Blues Druthers". Snopes. 14 January 2015. Retrieved 20 January 2015.
- ^ "Man who coined the term 'Blue Monday' apologises for making January more depressing" The Independent 5 January 2018
- ^ a b Burnett, Dean (19 January 2015). "Blue Monday: is it really the most depressing day of the year?". The Guardian. Retrieved 20 January 2015.
- ^ a b "Jan. 24 called worst day of the year". NBC News. 24 January 2005. Retrieved 13 March 2007.
- ^ "Campaign aims to help ease January blues British public urged to 'Beat Blue Monday'". www.mentalhealth.org.uk. 13 January 2009. Archived from the original on 21 February 2010. Retrieved 13 January 2009.
- ^ Burnett, Dean (21 January 2013). "Blue Monday: a depressing day of nonsense science (again)". The Guardian. London. Retrieved 20 January 2014.
- ^ Cliff Arnall Beats "the Blue Monday" Blues in the Canary Islands Press Release Canary Islands Tourism Board 17 January 2016
- ^ "It's the happiest day of the year, formula shows". CTV.ca. 23 June 2006. Archived from the original on 20 January 2011. Retrieved 13 July 2007.
- ^ "Cheer up for year's happiest day". BBC. 24 June 2005. Retrieved 13 March 2007.
- ^ "Smile, it's the happiest day of the year". China Daily. 23 June 2006. Retrieved 13 March 2007.
- ^ Smith, Rebecca (20 June 2008). "Today is the happiest day of the year according to Cliff Arnall's maths formula". The Daily Telegraph. London. Archived from the original on 22 June 2008. Retrieved 20 June 2008.
- ^ Grant, Alistair (18 June 2010). "Happiness is, today, claims maths equation". Irish Examiner. Cork. Retrieved 18 June 2010.
- BBC pages referencing Blue Monday: 2005; 2009; 2012
- Tulloch, Rosalind (20 January 2020). "Blue Monday is bad and you shouldn't feel bad about ignoring it". PosAbility Magazine. Retrieved 20 January 2020.