When own-gun armor becomes too expensive

At what gun size does protecting a battleship against its own weapons become impractical?

The trade-off becomes doubtful around 18 inches and especially at 20 inches; 14- and 15-inch protection can still make sense, but only over selected areas and ranges.

The answer rejects the idea that armor can provide complete immunity at every range. As gun caliber rises, the weight required to resist the ship's own weapons consumes too much of the design, particularly at short ranges where protection is least realistic. Designers must instead choose which vital areas and engagement conditions justify the armor burden.