I don't know if there is a standard formula for calculating zoom level based on altitude but you can do some trigonometric calculations.
I assume your field of view is nadir which means
FOV(angle) = 45 degrees
Altitude in your case,
A = 400 miles = 643738 meters
and now i will assume your map extent is
1000 x 1000 pixels so number of pixels from the center of map,
n = 500 px
R is the resolution in
meter/pixel then we have the following relation:
tan FOV = n x R/A
R = A/n x tan FOV
FOV = 45,
A = 643738 and
n = 500 we get
R = 1287.5 m/px
In this case your approximate map scale is
zoom level = 7
Depends on your map extent, you can cross check resolution value in the above table and get your approximate map scale and zoom_level.
Hope this will solve your problem.