I actually derived it with a couple of other people. A middle C is about 262 Hz. A note above middle C's frequency is 262*2^(x/12), where x is the number of half-steps above C.

So for example C# is one half-step above C, so its frequency is 262*2^(1/12), or about 278.

Edit: whoops, I forgot that we were deriving it for my B flat trumpet, 262 is actually B flat. So normally, a C is 278, a C# is 278*2^(1/12) or about 294 (it works the same, just one step higher).