For our fifth Design & Technology Lecture, Ben Craven (Tutor for PDE1 at GSA), gave us a talk on the importance of a ‘back-of-the-envelope’ calculation. A ‘back-of-the-envelope’ calculation is an informal mathematical computation, often performed on a scrap of paper such as an envelope. A ‘back-of-the-envelope’ calculation uses estimated or rounded numbers to quickly develop a ballpark figure. The result should be more accurate than a guess, as it involves putting thought to paper, but it will be less accurate than a formal calculation performed using precise numbers and a spreadsheet or calculator.

Among physicists, these ‘back-of-the-envelope’ calculations are often called Fermi problems, after Enrico Fermi (seen below), the Nobel prize-winning physicist who was known for his ability to come up with solid estimates based on what seemed the flimsiest of data.

So I decided to set myself one of these sorts of questions and have a go at solving it. As I was in my local coffee shop at the time unfortunately I didn’t have the ‘back-of-an-envelope’ to hand, so I grabbed a napkin instead!

**Question:**

If everyone in the world went for a swim in the ocean at the same time, how much would the global sea level rise?

**Assumptions:**

Half the volume of a human is submerged when swimming / floating.

Surface area of the ocean remains constant.

**Answer:**

0.73 mm

To summarise, breaking a problem down to what you know and what you need to guess at, can give you a really good intuition into the uncertainty of the answer. Seeing how the pieces fit together gives you a better understanding of what parts of the problem are important and what parts are not. I think that it’s undoubtably great practice and something that I will try my best at doing more.