Ceiling area is just the room footprint, which makes the arithmetic the easiest on this site. Coverage is the variable, and it is worse than walls because ceilings are more often textured.
Texture changes everything
A smooth ceiling behaves like a wall: about 350 square feet per gallon per coat. Knockdown drops it to roughly 300, and popcorn to 250 or less.
Popcorn also cannot be rolled aggressively. The texture is glued-on aggregate and a wet roller worked back and forth peels it. One slow pass with a three-quarter inch nap, or spray it.
Flat sheen, always
Ceiling paint is flat for a reason. Any sheen picks up every roller lap, every seam and every framing imperfection under raking light from a window.
Dedicated ceiling paint is also thicker than wall paint so it drips less overhead, and most brands go on pink or blue and dry white so you can see where you have been.
Two coats over stains will not work
Water stains bleed through latex no matter how many coats go on. Spot-prime the stain with a shellac or oil-based stain blocker first, then paint.
This is the single most common ceiling repaint failure, and the fix costs about eight dollars in a spray can.
Cutting in a ceiling is its own job
The perimeter of a ceiling has to be brushed before the roller goes anywhere near it, and on a textured ceiling that line will never be crisp against the wall.
The usual fix is to paint the ceiling first and slightly onto the wall, then cut the wall colour to the corner afterwards. Wall paint against a straight edge is far easier to control than ceiling paint against a textured one.
Allow an extra quarter of a gallon for the cut-in band. It is a narrow strip, but on a large room it is thirty or forty linear feet of brushwork.
Why ceilings show every flaw
Ceilings are lit almost entirely by light coming across them from windows and fixtures, which is the worst possible angle for hiding a roller mark, a lap line or a patched spot.
That is the real reason ceiling paint is flat rather than merely a preference. A flat film scatters light and hides the texture underneath; anything with sheen reflects it and reveals every imperfection.
Work in sections that stay wet at the edges, keep the roller loaded, and finish each pass in the same direction. Stopping halfway across a ceiling and coming back to it later is what creates the line you will see for years.