Realistic gun ranges for late nineteenth-century warships

At what ranges did late nineteenth-century warships realistically expect to fight?

Roughly 6,000-8,000 yards at the outside and often nearer 4,000 yards in practice, where armor would be hard pressed.

The answer places likely maximum fighting ranges around 6,000-8,000 yards, with about 4,000 yards a plausible practical range. These figures distinguish a gun's nominal reach from the distance at which contemporary fire control could support an effective engagement. At such distances even substantial armor faced a severe test. That reality shaped the tradeoff between adding protection and preserving a ship's speed, armament, and other qualities.