Today’s xkcd got me wondering how much land would we need if everyone stood six feet apart.

## Methodology

### We are all but spherical cows

If we want everyone to keep a minimum distance of $r$ from each other, the problem boils down to efficiently packing $n$ circles of radius $r$ in the smallest area possible. This can be calculated as follows:

Area of a circle with radius $r$,

Optimal circle packing density1,

Area required for $n$ people,

### Crunching the numbers

Plugging in the current world population2 and the recommended distance of 6 feet3:

we get

According to Wikipedia4, this is just shy of the land area of Portugal 🇵🇹. We could also squeeze into Hungary 🇭🇺 if some of us were willing to swim.

## Corollaries

### How many people can San Francisco fit standing 6 feet apart?

Dividing the area of San Francisco by $2 \sqrt{3} \cdot 36 \text{ft}^2$, gives us around 10.5 million people.

### Are there any countries where people couldn’t stand 6 feet apart?

1 square mile of land can have 223,563 people standing 6 feet apart. This is much higher than the most densely populated countries and territories in the world5.