Seven thousand miles of travel plus the minute or two he's puttering around in your living room. It's a daunting task to complete, even with the aid of magic.
But, of course, that’s not the proposition. Instead we are told that Santa Claus does this for every house, that he makes a journey from one house to the next, finessing the same routine, each time returning to a sleigh overloaded with gifts specific to each destination. The daunting scale of this is immediately apparent; thinking only about our own blocks or our own cities, the task seems improbable. Expanded beyond that, it seems impossible.
What's not clear is exactly how broad that expansion is. What sort of scale are we talking about here? Is Santa purportedly visiting hundreds of thousands of homes between dusk and dawn that evening? Millions? Tens of millions?
The answer is somewhat north of that. But the way in which one figures out that answer is a story in and of itself.
Who is included?
The most immediate question one must ask when trying to determine how many kids Santa visits each Christmas is “What counts as a kid?” There is certainly an upper age limit on the Santa-child gift pipeline, but it’s not really clear how that’s determined. Is belief in Santa a prerequisite for receiving gifts? Does he just stop worrying about kids when they hit 10? 18?
Then there’s the other boundary: faith. Santa Claus is derived, however vaguely, from Saint Nicholas, an actual saint in the Catholic canon. Christmas, as the president will remind you, is a holiday predicated on the Christian faith. Should we assume, American commercialism notwithstanding, that Santa necessarily limits his generosity to those who embrace the religiosity of the day?
For the sake of estimating the scale of Santa’s workload, yes. There are certainly thousands of children in the United States alone who don’t adhere to Christian traditions but who expect Santa to nonetheless dutifully deliver. Of course, there are also thousands of kids whose behavior between December 25ths has failed to meet Santa’s standards, a group that’s almost certainly impossible to catalogue. Therefore, we’ll just call those two groups a wash.
And, for reasons that will become clear in the next section, we’ll consider anyone age 14 or younger a kid.
There are no doubt many dubious things that the Central Intelligence Agency is engaged in, but in the realm of centralized intelligence, it does have its moments. For example, the CIA publishes the “World Factbook,” a collection of demographic and cultural data detailing nearly every country in the world.
The collection includes two important sets of data for our purposes: national population by age and the composition of the country’s religious identity. In other words, we can learn from the CIA what percentage of every country is Christian and what percentage is age 14 and younger — one of the age groupings that the “World Factbook” provides.
This is not as easy as it might seem, for several reasons.
The first is that the CIA's descriptions of a country's religious composition might necessarily be vague, simply noting a mix of Muslim and Christian, for example. In other places, Christianity is blended with other belief systems. In Eswatini (formerly Swaziland), for example, 40 percent of Christians adhere to "a blend of Christianity and indigenous ancestral worship." Does that include room for Santa Claus? The CIA is unhelpfully vague on this point.
What’s more, a number of other denominations don’t celebrate Christmas or don’t celebrate Christmas on Dec. 25. Eastern Orthodox Christians celebrate in January, as do a number of other eastern European sects. Jehovah’s Witnesses don’t celebrate Christmas at all. Some groups, like Seventh Day Adventists, popular in the Caribbean, leave the door open a crack for people to celebrate if they choose. For our calculations, then, we excluded members of the Eastern Orthodox faith and Jehovah’s Witnesses and added Adventists to a “maybe” category — along with a percentage of anyone identified under the vague heading of “other” by the United States’ foremost spy agency.
Population wasn’t always simple, either. In some places, population data were missing. The website for the annual census conducted on Tokelau, an island a bit northeast of Australia, probably doesn’t get many visitors. But for us to determine that the island is home to 475 overwhelmingly Christian kids younger than 15, we visited that website.
The data were riddled with odd twists, pleasant and not. There’s Christmas Island, for example, also near Australia. It’s home to about 300 kids, about a fifth of whom are Christian — a neat tally to add to the total.
On the grimmer end of the spectrum was the entry for Syria, appended with a note: “The Christian population may be considerably smaller as a result of Christians fleeing the country during the ongoing civil war.”
Plugging these data into a spreadsheet and comparing them yielded a count for the number of kids Santa might be expected to visit: 536,785,866, plus an additional 13.6 million who fell into the "maybe" category.
If we’re trying to figure out the feasibility of Santa visiting all of these children, though, there’s a complicating factor: Where do they live? Take Russia, for example. It would be easy for Santa if the kids all lived north of the Arctic Circle. Unfortunately for him, though, they don’t.
We know that because of another government agency, NASA. The U.S. space agency produces a detailed set of data using imagery to estimate the world’s population by latitude and longitude. Running that data through an admittedly excessive set of calculations and comparing it with our per-country estimates of children, we were able to generate a rough map of where the children Santa has to visit live.
You'll notice some oddities there. One is that the NASA data are a bit rough, making some expected high-density areas seem fairly empty. Another is that certain areas of the map are unexpectedly blank — until you remember our criteria. Turkey, for example, looks empty, but that's because the CIA informs us that the country is predominantly Muslim.
The United States’ combination of large population and high density of Christians establishes us as the country with the largest number of children Santa might be expected to visit, nearly 42 million in total. (Here we’re including the “maybe” category.) Brazil comes in second, with more than 40 million. It’s only slightly ahead of Nigeria. China and India have a lot of children — but relatively few practicing Christians. The Philippines, however, is the fifth-most-populous country on Santa’s itinerary.
No country makes Santa’s job easier than Monaco, where the 3,100 kids he needs to visit are all relatively closely packed, 1,562 kids per square kilometer. The density of children relative to the country’s total area is lowest in Greenland, where there are 0.005 kids per square kilometer — though the region where people live is much smaller.
This nonetheless raises another important consideration in our calculations: Many children live with other children. In other words, it's not the case that Santa has to visit 537 million separate houses. In a lot of places, he can check two or three kids off his list at once.
There are data for this, too. The United Nations compiles information on the number of people per household in countries, including, in some cases, the number of people younger than 15. We used that to estimate how many of the children were likely to be sharing households (defaulting to one kid per house where the data were missing). That gave us our other important number: Santa needs to visit an estimated 395,830,485 households on Christmas Eve — with another 8.7 million in the “maybe” category.
Putting it into perspective
These are obviously very big numbers, and we'll explore what they mean for Santa's journey in a moment. First, though, let's consider the other aspect to his efforts: That he's bringing everyone presents at the same time.
So let’s say, for the sake of argument, that Santa Claus has decided to bring every child on his list precisely one present, a Rubik’s cube. Light (less than a quarter of a pound) and relatively small (a 2.2-inch cube), it’s the perfect present to give in bulk.
How bulky would 537 million Rubik’s cubes be? Quite. They would weigh about 59,000 tons, about as much as the Titanic. They would occupy about as much space as half the Hindenburg (thanks to WolframAlpha for that reference point). Or, if you’d like a less fraught analogy, the equivalent cargo space of more than 1,200 tractor-trailers.
Santa’s sleigh would be cumbersome.
That’s one present for each kid. But, remember, that’s not all that Santa’s doing. He’s not just popping down chimneys, leaving a Rubik’s cube under the tree and leaving. He’s also tasked with eating the cookies left for him and taking a sip of milk — just enough to let the kids know that he has been there.
If Santa were to eat one Oreo at each of the 396 million households he visits, he would be eating about 21 billion calories — the equivalent of the recommended daily caloric intake for an adult for nearly 29,000 years. He would have eaten 871 million pounds of fat alone, a weight approximately equivalent to 800 eight-reindeer teams. Add in that ounce of milk, and his caloric intake soars to 25.7 billion calories, the same amount of energy a car burns in a year and a half.
None of this gets to the central question, though: Is any of this feasible? The short answer is no, but the longer answer is more fun.
In computer science, there's something called the "traveling salesman problem." In short, it's the question of how someone — say, a salesman — can most efficiently visit each house on his itinerary. Should he visit House A before House B and then House C? Or does he save time by switching B and C? This isn't an abstract question. For companies like UPS, identifying the fastest routes for deliveries means saving enormous amounts of time and gasoline.
In a three-house example, this seems easy to figure out. There are only six possible iterations (ABC, ACB, BAC, BCA, CAB, CBA), and estimating each duration is feasible. But as you add houses, the possibilities increase exponentially. A brute-force calculation of the traveling salesman problem for a number of houses, n, yields n! possibilities. The exclamation point there isn’t the end of a sentence but, instead, denotes a factorial, the value obtained by multiplying the number by every number that precedes it. So 3! is 3 times 2 times 1, or six — the number of permutations for our example traveling salesman.
Santa has to visit nearly 396 million houses. Therefore, the number of possible routes he can take is 395,830,485! — or 8.9 times 10 to the 3.2 billionth power.
How big is that number? A few years ago, a guy named Scott Czepiel used a story illustrated what 52! — the number of possible orderings of a deck of cards — looked like. In short, if you:
- walked around the equator, taking a step every billion years, and
- removed a drop of water from the Pacific Ocean each time you went around and
- when the ocean was entirely empty, laid a sheet of paper on the ground, each time adding another piece on the stack,
by the time the stack of paper reaches the Sun, less than 1/3000th of the 52! seconds has passed.
Again, the number of possibilities Santa is presented with is 395,830,485!.
Fine. Let's assume Santa's North Pole home has the computational power to recalculate the optimal route every year. What are the contours of this journey?
First, let’s establish how much time Santa has to achieve his goal. We are assuming he works only in the dark, for obvious reasons. It makes sense for him to start as far east as possible and head west, allowing him to remain under the cover of darkness as Earth rotates in relation to the sun.
On Dec. 24, the sun sets in the Gilbert Islands (just west of the international date line) at 6:29 p.m. That’s a bit later than elsewhere, given the islands’ location in the Southern Hemisphere and proximity to the equator. (In Northern Russia, for example, it sets a bit after 1 p.m.) But it’s useful when considering when the sun rises on Howland Island, to the east of the Gilbert Islands but on the other side of the date line. On Dec. 25, the sun rises there at 5:44 a.m. — giving Santa 35 hours and 15 minutes of darkness to complete his task.
As the map above shows, the first few hours of Santa’s journey will be relatively easy. From the date line to 126 degrees east longitude, heading west, Santa needs to cover only (“only”) about 7.3 million kids. That gets him about halfway across Australia and into the Philippines. In short order, things escalate, with 35 million kids in the next 7 degrees of longitude.
The real problem comes once he hits eastern Africa. There, thanks in large part to the extent to which land extends along that meridian, there are a lot of kids he needs to reach. Hopefully he saved time crossing the Pacific to burn here.
This is a key factor: He also needs to go north and south to deliver to kids across the globe. The east-west travel is his boundary on time, as the sun trails behind him, but it’s not the only factor in play. (To indicate how far he has to go, we’ve indicated the full north-to-south range by longitude on the map above.)
While Brazil and the United States are the most populous countries, by the time he gets to our Eastern Seaboard, the hardest part of his night is over. There are a lot of countries in Africa and Europe, many of which have lots of children and, cumulatively, make up a lot of places to get to.
Since we’re not ourselves solving the traveling salesman problem here (and since we don’t have every kid’s address) we can’t say with certainty how long this will take. But we can estimate it.
Let’s say that each house is an average of one mile from the next, a figure that’s obviously too small in eastern Russia — but obviously too large in New York City. That means that Santa has to travel 395,830,485 miles over the course of the night to hit each household. (This is excluding his trip to and from the North Pole which he could probably do during the day since he would mostly be flying over the empty Pacific.)
Covering 396 million miles in 35.25 hours means traveling at 11.2 million mph, even without incorporating the time spent at each house. He would have 321 microseconds to get from one house to the next, on average, a duration that is about half as long as the period of time a baseball spends in contact with the bat. It’s not speed-of-light fast, but it’s 1-percent-of-speed-of-light fast, which is still very fast.
If we include the tasks he has to perform at each house (down chimney, drop Rubik’s cube, swig milk, leave) we quickly see how impossible it becomes. All of that can’t take even one second in total — he has only 321 microseconds for each stop and travel to the next one! If he spends 200 microseconds dropping off the gifts, he’s left with 121 microseconds to travel the mile to the next house, about as fast as a neutron.
And, yet, somehow he does it! Somehow, each year, he does the necessary calculations, evaluates the worthiness of each child, loads his sleigh with numerous gifts (most larger than a Rubik’s cube) and blitzes around the globe without a break for more than 30 hours stopping at house after house after house. Somehow, he does all of this, so that your kid can get her board game.
Maybe he burns off all those calories he’s eating. Consider leaving him two Oreos this year.