# Calculating the loss on exchange rate

TL;DR: What is the proper way of calculating the exact loss (due to the exchange rate(*)) on a currency exchange transaction?

(*) I'm not interested in other costs, like commission fee.

Longer example: AKA what I assume is the 'proper' way:

Let's say I'm a tourist in the EU and I want to buy `100 EUR` for `USD`. I check the official exchange rate, which today (26.12.2018, according to Google) is `1 EUR = 1.139 USD`. Let's assume this is the 'official' exchange rate, and work with this.

Now, if I find a place that sells me `1 EUR` for `1.2 USD` and I buy `100 EUR`, then I will spend `1.2 * 100 = 120 USD`. But, if I could have bought the `100 EUR` for the official rate, I would have spent only `1.139 * 100 = 113.9 USD`.

So, on the transaction, I have lost `120 - 113.9 = 6.1 USD` which is `6.1 / 1.139 = 5.36 EUR`.

Question: is the above calculation correct? If not, then what are the issues, and what would be the correct way to calculate the loss?