The Physics of Santa Claus

A colleague of mine recently mentioned something to me about an article that circulates every year during the holiday season, entitled “The Physics of Santa Claus”. This was news to me, so I ran a few Google searches to find out what she was talking about.

It seemed that some enterprising person had taken the time to go through and explain just what is involved in Santa’s Christmas Eve trip around the world delivering presents. How many households does he have to visit? How much do all those presents really weigh? How fast do the reindeer need to fly in order to get it all done in a finite amount of time? There is much speculation as to the origins of this piece; the general consensus seems to be that it began life published in SPY magazine in the early 1990s. Whatever the true story, it’s still an entertaining read in 2008.

I’ve taken some time to update the original with more current data – for instance, it seems the world’s population has grown a bit in the last 20 years. According to the Population Reference Bureau, the world population in 2008 was approximately 6,705 billion; 28% of these are children (defined as being under 15):

In fact, making some assumptions about the percentage of these children that celebrate Christmas and the number of children per household, it turns out that Santa needs to visit close to 200 million homes in one night.

We assume he distributes gifts from 5 pm to midnight, or for 7 hours. Due to the Earth's rotation, there is an overall time difference of 24 hours between different time zones, so we can therefore say that Santa has 31 hours to finish his work (assuming he logically travels east to west). Visiting 200 million homes in 31 hours means that Santa has to visit approximately 1586 homes per second:

This gives him about 1/1600th of a second to do everything at each home, such as parking his sleigh, looking for the right gifts, climbing down the sleigh and chimney, binge on snacks, fill the stockings, come up again and rush to his next stop!

For the complete details of his annual trip, visit the Applications Center where I’ve posted the Maple document in which I’ve recreated the Santa calculations. Happy Holidays!!

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