How would I do this with degrees?
Depends on how exact you want to calculate it.
At infinity focus, it's simply:
2 * arctan( X / (2 * f) )
with 'X' being the horizontal, vertical, or diagonal, sensor size, and 'f' being the true focal length (as recorded in the EXIF metadata). The sensor of the FZ70 is supposed to be 6.17 x 4.55 mm.
For closer distances you also need to calculate the Magnification factor, and the formula becomes:
2 * arctan( X / ( 2 * f * (M + 1) ) )
The magnification factor is, when approximately measured from the front of the lens (exact position depends on lens design):
M = f / (So - f)
where 'So' is the object distance, and 'f' the true focal length.
You can also plug the various dimensions in my DOF output quality planner as introduced here
Do note that the cameras that you mentioned, have slightly different aspect ratios, so their field of view angles for a given relative focal length differ somewhat, depending on which dimension you calculate.