focus – How to calculate depth of field at different resolutions

I have a DSLR (EOS 60D) and I use hyperfocal pro when setting up astro-photography.
At lower resolutions though, such as in video mode, how can I calculate the depth of field?

The field of view barely changes so there is not much crop, but there is no continuous auto-focus so I want to keep the subject in focus.

Is the DOF the same as in photography modes, assuming the same aperture and focal distance?

And if it isn’t, is there a similar app or calculator for the lower resolutions?