Should I include independently derived but not novel results in my thesis? I'm writing up my physics PhD thesis, and am wondering whether to include the derivation of a formula that I worked out myself. I've recently found that this work isn't actually a novel contribution to the field, as the formula (though not a detailed derivation) appears in the appendix of a 10 year old paper.

Is there any sense in including it? And, if so, how would one describe the contribution?
There is usually no reason not to include something in a thesis.  Your thesis is a place for you to give a coherent account of all your work on a topic.  There are (usually) no page restrictions, and it should serve as a reference document for future readers.

Many theses include a lot of review material, beyond just what might be contained in a literature survey.  A thesis has to contain new material, of course, but it does not all need to be novel.  There can be a lot of merit in giving detailed explanations of known results, if the reader is not necessarily going to be familiar with them in detail.  A derivation that has not previously appeared in the literature (even if the final result is known) is clearly suitable for inclusion.