So where to start? We’d better first calculate how many SARS-CoV-2 particles there are in the world. To do that, we’ll need to know how many people are infected. (We’ll assume humans rather than animals are the most significant reservoir for the virus.)

Of all the people who are infected now, those who got infected yesterday will contribute a little to the total count. Those who were infected a couple of days ago will contribute a little more. Those infected three days ago a little more still. On average, people infected six days ago will have the highest viral load. This contribution will then decline for people who were infected seven or eight or nine days ago, and so on.

Let’s work with a value in the middle of this range (the geometric mean) at 10 billion. When you add up all the contributions to the viral load of each of the 3 million people who became infected on each of the previous days (assuming this 3 million rate is roughly constant) then we find that there are roughly two hundred quadrillion (2x10¹⁷ or two hundred million billion) virus particles in the world at any one time.

V = 4 π r³/3Assuming a 50 nanometre radius (at the centre of the estimated range) of SARS-CoV-2 for the value of

*r*, the volume of a single virus particle works out to be 523,000 nanometres³.

*very small*volume by the

*very large*number of particles we calculated earlier, and converting into meaningful units gives us a total volume of about 120 millilitres (ml). If we wanted to put all these virus particles together in one place, then we’d need to remember that spheres don’t pack together perfectly.

## Close sphere packing

If you think about the pyramid of oranges you might see at the grocery store, you’ll remember that a significant portion of the space it takes up is empty. In fact, the best you can do to minimise empty space is a configuration called “close sphere packing” in which empty space takes up about 26% of the total volume. This increases the total*gathered volume*of SARS-CoV-2 particles to about 160ml – easily small enough to fit inside about six shot glasses. Even taking the upper end of the diameter estimate and accounting for the size of the spike proteins all the SARS-CoV-2 still wouldn’t fill a Coke can.

It turns out that the total volume of SARS-CoV-2 was between my wife’s rough estimates of the teaspoon and the swimming pool. It’s astonishing to think that all the trouble, the disruption, the hardship and the loss of life that has resulted over the last year could constitute just a few mouthfuls of what would undoubtedly be the worst beverage in history.

*Correction: The estimate of the number of virus particles – 2x10¹⁸ or two billion billion in the world at any one time – should have read 2x10¹⁷ or two hundred million billion. This doesn’t change the estimated volume of the SARS-CoV-2 in the world, which still stands at 160ml.*

*Christian Yates, Senior Lecturer in Mathematical Biology, University of Bath This article is republished from The Conversation under a Creative Commons license. Read the original article.*