The formula you quote is the one I have used in the past, and your arithmetic appears to be correct also.
Your calulated values are pretty close (within 0.5 degree) to the values contained in this table in our Resources section. Any difference may be due to using a slightly different size for the DX frame dimensions - Nikon's DX DSLR's do vary from model to model by 0.1-0.2mm.
What figures are you getting from the online calculator(s)?
The "crop factor" is taken account of in your calculation, because you plug in the actual sensor dimension into the formula. You don't need to do anything else.
Another factor to be aware of - if you need ultimate precision - is that most lenses differ a little in focal length from the named numbers.