Yves here. It may seem a bit Scrooge-like to treat a light-hearted piece more seriously than it was intended, but I thought this could serve as an object lesson for economic and financial modeling. On the one hand, the author is to be commended for taking the problem apart in a systematic manner and making what look like reasonable assumptions for some of the key elements in the equation, like “How many homes does Santa have to visit?” But then there are other places where he makes assumptions to simplify the problem that seem to lead to a considerable understatement of the fuel needs, namely, omitting the extra fuel consumption required for takeoffs. One would think even a simple adjustment, like “Multiply the result by 1.x” would be a better approximation. And I suspect Serious Mathematicians might differ with his assumptions about how efficient a path Santa could devise for making his deliveries.

**By Michael McDonald, Michael, an assistant professor of finance and a frequent consultant to companies regarding capital structure decisions and investments. Originally published at OilPrice**

Every year around the world, hundreds of millions of children wait anxiously for Santa Claus to arrive and bring presents and good cheer. But what if Santa never came? What if this year the reindeer all fall ill, perhaps due to Crazy Reindeer disease (the analog to Mad Cow) and Santa is forced to cancel Christmas? The result would be devastating.

Fortunately, for any children reading, official word from the North Pole is that Santa’s sleigh has some new upgrades this year that allow it to run on good old fashioned jet fuel if the reindeer fail. And with the current glut of oil around the world, fuel prices are so affordable that even if the reindeer are feeling up to their usual task, Old Saint Nick might just give them the night off and choose to fly with fuel nonetheless.

**So how much oil does Santa need for his rounds on the night of the 24th?**

Well the answer is complicated by a number of factors most importantly, we just don’t know a lot of about Santa’s rounds, the shape of the sleigh, the air speed of the craft, or the weight of all those presents. But, we can take some educated guesses.

One 42 gallon barrel of oil is typically used to make a variety of different products. About 51 percent of the average barrel ends up being used for gasoline, while 12 percent ends up being used for jet fuel. Let’s assume then that Santa’s going to use standard jet fuel, and that 12 percent ratio holds – so for each gallon of jet fuel, we need around 8 gallons of oil. Recognizing that the byproducts of a processed barrel of oil are greater than the original 42 gallons, this 2:1 ratio is still a good place to start as a rough rule of thumb.

Next we need to get a rough idea of Santa’s fuel economy. How many miles does he go on a gallon of jet fuel? It’s not clear how much Santa’s sleigh weighs, or what it is shaped like, but we can probably envision it as something like a cross between a Suburban, a C-5 Galaxy fright aircraft, and an F-22 Raptor fighter jet. The sleigh looks blocky like a Suburban, carries about the same level of cargo as much as C-5 might, yet has the speed of a fighter jet. The fighter jet and c-5 achieve a fuel economy around the range of 0.1 miles per gallon to 0.5 miles per gallon. A 747 for instance burns around 5 gallons of fuel per mile.

But of course, those aircraft are all much larger than Santa’s sleigh. (Imagine poor Rudolph trying to pull a Dreamliner!) A Lear Jet uses around 1 gallon of fuel per 2.75 miles (based on a speed of 465 knots or 535 miles per hour). A Piper Cub uses about 1 gallon per 15 miles. Santa’s fuel economy is going to fall off the faster he goes, and to get to all the children of the world in one night, he is going to need to go a lot more than the Piper cub’s 65 knots per hour. Just to take off, Santa is going to need to hit about 180 miles an hour, and probably more than that given the sleigh designer’s seem to have a weak grasp on Bernoulli’s principle. Thus the Suburban is probably a good size comparison for Santa’s sleigh, and one might estimate the sleigh gets about 5 miles to 1 gallon of jet fuel (8 gallons of oil).

Now how far does Santa need to go? There are around 7.3 billion people in the world, which works out to around 1.5 billion households around the planet based on around 5 people per household. Now not everyone celebrates Christmas of course, but many Christians and non-Christians alike do. By some estimates, perhaps 45% of the world’s population celebrates Christmas. That means that Santa needs to visit about 675 million households. With about 7 households per square mile, and assuming that households celebrating Christmas are clustered (which seems logical given religious clustering), that means that Santa has to cover around 94 million square miles of households.

The most efficient mechanism for Santa to cover these households is a very complex mathematical problem. But assuming Santa wants to fly diagonally over each square mile (for a distance of 1.41 miles based on the Pythagorean Theorem), and households are on average distributed proportionally across this each 1 mile block, then Santa will have to fly over 2.41 miles of ground to cover each square mile as efficiently as possible. (You can use a variety of mathematical algorithms to model the most efficient flight path depending on population dispersion – this is just a reasonable approximation based on the assumptions outlined above).

As a result, Santa needs to travel around 226 million miles to deliver all of the presents to the world’s children. This assumes minimal idle time on each rooftop (he’s got to scarf down those cookies quickly), and abstracts away from the extra fuel needed for each takeoff.

Given our 5 miles per gallon of jet fuel efficiency calculated above, that means Santa needs around 45 million gallons of jet fuel for his annual voyage. With jet fuel going for around $1.20 a gallon right now on the spot market, and prices looking historically low, this puts the total fuel cost of Santa’s journey at a bit less than $54 million for one night. On second thought, maybe it’s time to break out the hay for those 8 reindeer.

Paul TioxonIf this is not proof of a de facto WAR ON CHRISTMAS, I don’t what is!!

What next, freedom killing regulations mandating all Santa Sleighs be electric with batteries too heavy to allow him to deliver on time! Has the world lost it’s damn mind!! And where will all of that electricity come from when he delivers in the middle of the night with NO sunshine to recharge his electric vehicle?

craazymanI’m a serius mathematician and the author fergot apartment buildings. That divides everything by 7.

Also, why would Santa want to fly diagonally across each square mile. That’s the farthest way to fly across. Much quicker just to go down one of the sides. Since 1 is less than the square root of 2.

Also, some people don’t deserve presents. Why does everybody get presents? That overstates the fuel needed.

Also, the world slopes downhill from the north pole. if Santa starts in Canada and goes to the equator, it’s all downhill. He may just need bursts of fuel to take off, then he can glide down hill.

Also, some people don’t celebrate Christmas but get presents anyway. That may boost the fuel needed a little.

You need to divide by 7 and multiply by 1.55. That should get an exact answer.

griffenEveryone deserves a present and a hug (also a warm meal). I am still waiting on that long promised pony, however; funny it never did appear like in those ever-present Lexusss commercials.

ambritSince many households leave out eggnog and cookies for Santa, a more realistic modeling of his sleighs’ flight plan would be “The Drunkards Walk.”

Apartment buildings do not represent the entire populations’ dwellings. Let us, say, cut the apartment ‘effect’ in half, and we come up with, divide by 3.5 and then multiply by 1.55.

Did you use the word “exact” in describing a social system? How curious.

NotTimothyGeithnerI’m pretty positive Santa has mastered an Alcubierre drive and possibly teleportation. I’m more concerned by a nuclear reactor landing on the roof.

Also, Santa drives a hatchback. I saw him at a dairy queen. I applaud his decision not to force animals into a cruel death march.

Sean BrodrickOh, I so totally disagree with this article. Santa’s sleigh does NOT run on oil.

Santa has to visit every house (with children) in the world in one night. Obviously, that requires time travel technology.

Therefore, Santa is obviously a Timelord.

Therefore, his sleigh is powered by the Eye of Harmony, the artificial black hole that powers Gallifrey and TARDIS’s in general.

I mean, obviously. https://en.wikipedia.org/wiki/Eye_of_Harmony

VatchOh, for goodness sake! Santa’s backup system for powering his sleigh (in case of reindeer failure) doesn’t use fossil fuels, it uses antimatter and dilithium crystals.

floraI thought Santa used a 5 dimensional tesseract to cross time and space. ?

tejanojimThat’s some pretty serious handwaving that doesn’t consider the payload. At around 3.5 billion persons on his list, assuming each present at half a kilogram and fitting within a 10 cm cube, that gives nearly 2 metric tons and a volume of 3.5 million cubic meters. Thus I conclude that 1. the fuel efficiency is grossly overstated and 2. his path is actually much longer due to return trips to the North Pole to reload gifts and refuel, unless he has aerial refueling arrangements with various national air forces.

craazymanmaybe everybody is getting gift certificates?

tejanojimEdit: Total payload is a bit less than 2

millionmetric tons, equal to roughly 14,000 full C5 loads.