It’s nearly Christmas!

Time for a festive post.

No expensive Christmas trees or private jets this year — I’d like to keep the number of people going into debt to fund Christmas down.

This year we’ll rely solely on Santa.

I’ve got used to Amazon Prime delivery, but even Amazon do not have the delivery capacity of Santa… yet.

Let’s start by looking at how many gifts Santa will be delivering this year…

Examining total households (excluding persons living inside collective living quarters, such as hotels, rooming houses and other lodging houses, institutions and camps) there are 2,174,034,795 households.

There are 86,400 seconds in a day. So Santa needs to deliver to one household every 0.00003974177 seconds (86,400/2,174,034,795). No time for a snack break!

Lets for a moment ignore continents where the Christianity is less dominant (namely Asia), we have about 1 billion households. In this case Santa needs to deliver to one household every 0.0000864 seconds (86,400/1,000,000,000). Still no time for a snack break!

According to the UN, the world population in 2021 is 7.9 billion.

If we consider the official Premier League match ball, the Nike Premier League Flight which costs £125 at retail, Santa’s total bill for presents would be £987,500,000,000 (125*7,900,000,000) — almost £1 billion! Even if he chooses a relatively cheap £20 ball (or is able to negotiate a bulk discount), we’re still talking in the 100’s of billions of Pounds, £158,000,000,000 (20*7,900,000,000)

It’s hard to visualise that many people. Although I’m informed by National Geographic:

Standing shoulder-to-shoulder, the entire world’s population could fit within the 500 square miles (1,300 square kilometers) of Los Angeles.

But what do 7.9 billion presents look like?

In the interests of fairness, let’s assume each present is the same. This year everyone is getting a football (soccer ball). This makes it easier for Santa as it can be delivered in a cube shaped box.

Rules state that a size 5 ball must be 68 to 70 cm in circumference. So the maximum radius is 35cm. Let’s assume the box’s dimensions are 35cmx35cmx35cm (a cube).

Laid side by side the boxes would cover 2,765,000km (0.00035km*7,900,000,000). Placed around the equator (40,075km), the presents could be laid around the planet almost 69 times (2,765,000/40,075).

The earths surface area is 510.1 million km². One side of each box has a surface area of 0.00035km² and all boxes together, 2,765,000km². So all presents, each laid on the ground, the would cover 1/184 (510,100,000km/ 2,765,000km) of the earths surface.

ESO estimate the Pacific Ocean holds 707.5 million km3 of water. The presents, have a total volume of 2,765,000km3 (0.00035km3*7,900,000,000). They would 1/256 of the Pacific Ocean (707,500,000/2,765,000)!

Amazon’s sortable fulfillment centers are around 800,000 square feet in size (74,322 m2). Let’s assume that’s 743.22m (w) x 100m (l) x 30m (h) = 2,229,660m3 (or 0.00222966km3)… meaning Santa is going to need 6,166 of them.

An official size 5 football weighs between 410 – 450 g without packaging. Therefore accounting for the upper end of this allowance to cover potential packaging weight, the total weight of all the balls would be 3,555,000,000 kg (0.450*7,900,000,000) or 3.5 million tons.

The A380-800F (the Airbus A380 freighter) has a payload capacity of 150,000kg. So if the sleigh breaks down, Santa would need a minimum of 23,700 cargo flights (3,555,000,000kg/150,000kg). According to one source only 27 of these freighters have been produced, so would need 878 flights by each plane to distribute the presents.

Of course, the space vs weight ratio is an important factor. The A380-800F has a total hold volume of 1,134m³ (or 0.000001134km3). Yes, Santa would need A LOT more planes!

To put that into perspective, National Geographic estimate:

The world generates at least 3.5 million tons of plastic and other solid waste a day

😮

Now, Santa can’t send these presents unwrapped.

A cursory glance at Amazon shows me a 4 pack of 500cmx70cm Christmas wrapping paper for about £10. Put another way £10 buys you 0.02kmx0.0007km (a total surface area of 0.000014km2).

Each of our presents has a surface area of 7.35e-7km (0.735 m2) (6*0.00035km*0.00035km).

So one pack of wrapping paper is enough for 19.048 presents 0.000014/(7.35e-7), wrapped perfectly with no overlap and no mistakes.

But we need enough for 7,900,000,000 presents!

In total, that’s 414,741,706 (7,900,000,000/19.048) packs. At £10, ignoring any bulk discounts, that’s £4,147,417,060 (£4.1 billion) just to wrap the presents!

Thinking about the environmental cost for a minute…

Roughly about 50% of the wood is converted into wood pulp. So 50 kgs of wood would make 25 kgs of pulp. Roughly, 1kg of pulp makes 1.2 kg of finished paper. Hence, 25 kgs of pulp would make 30 kgs of paper.

Assuming a 75 GSM (grams per square meter) paper weight, our pack of paper weighs 1050g (20mx0.7m*75g) or 1.05kg or 0.00105 tonnes.

The total weight of all paper required would be about 435,479 tonnes (0.00105t * 414,741,706), requiring 8,709,580 trees (435,479/0.05).

For a frame of reference, Nature report there are about 3.04 Trillion trees on Earth. According to mvorganizing.org:

Throughout the world, about 900 million trees are cut down annually. This equates to about 2.47 million trees cut down every day.

So it would take 4 days worth of Earths tree-felling activities to supply the wood needed for Santa’s wrapping paper needs.

All that’s left now is tape. Let’s assume perfection, that is; we only need tape for one face (shout out to those who can neatly wrap presents, a skill I don’t posses). That’s 140cm of tape per box (35*4).

In total that’s 11,060,000km of tape needed (0.00140*7,900,000,000) — almost 276 times (11,060,000km/40,075km) around the world.

Quickly looking at Amazon, I can get 50m of Selotape for £1. Santa therefore needs 221,200,000km rolls of tape (11,060,000km/0.05km) at a total cost of £221,200,000.

I think we’ll save Santa Claus the need to write cards for each present this year…

- Presents: £158,000,000,000
- Wrapping Paper: £4,147,417,060
- Tape: £221,200,000
- Total cost (exc. Reindeer food): £162,368,617,060

### tl;dr

**Have a great Christmas for those celebrating!**