How do airlines calculate the cost of a Brompton?
This is a hard question to answer. Not only does each airline  have its own rules as to handle bicycles or what they consider oversized luggage — the airline counter staff at check-in have “discretion” which usually boils down to a degree of capriciousness. The checkin counter staff may or may not follow their own airline’s posted guidelines in terms of overweight, size, contents, or how much they charge. Usually this discretion is in your favor (ie they will waive the charge or lower it) but not always, especially if you come in with an attitude. In other words, there’s no consistency in what you’ll be charged unless you are obviously under weight, under size, and have non-surchargable contents. 

That all being said, it’s still helpful to know the rules ahead of checking in so you know how much they charge for overweight and oversized luggage, versus how much they charge for a bicycle. 

A bare brompton in a light bag (like the b-bag) will usually be underweight and just under the nominal size. Many hard cases will push it to oversize and some will push it overweight. 

However, if you know the bicycle charge versus the overweight or oversize charge, you can go in with the following algorithm:


Approach counter and attempt to check in bicycle without any specific declaration. If the checkin clerk allows it without comment or extra charge, success!
If clerk attempts to assess oversize fee and it’s in excess of the bicycle fee, then state it’s a bicycle and get the lower bicycle fee. 
If clerk asks what’s inside, ask first how much the oversize / weight fee is. If it is less than the bicycle fee, then declare the bike as “circus equipment” or “spare parts for a mobility device” (many places calling it “sports equipment” carries a special fee too) and pay the lower fee. 


Note that I’ve found the brompton in a bag is very close to the 64 linear inches and with case can be close to the overweight limit. In those cases, it’s helpful to remove the saddle and pedals and put them in your other luggage. This will reduce both the weight and the overall dimensions as well as making it harder to break. You also want to remove all of the hinge locking bolts as those tend to snap.