The formula for doing the math is actually pretty easy and well documented. You need a database of IATA codes, latitude & longitude to feed in to the formula but once you have that then getting the maths part done is easy. Doing a ton of calculations can slow down the server a bit but if it is just a couple per page load that shouldn't be an issue. I have the code in vb.net if you want that. I'll even give you a dump of the airports table from my DB if you want that, too.

I suppose I could set up an API-ish service to just return the distances if you want that rather than doing the calculations on your own server.