Estimating the reach of a modern 15-inch gun

How far could modern extended-range ammunition carry a 15-inch shell?

The initial estimate is about 150 km for a hypothetical 15-inch/70 gun with Vulcano-like ammunition, explicitly offered as a rough calculation.

The comparison begins with guided 5-inch ammunition and the range of the older 15-inch/42 gun. Scaling that idea to a hypothetical 15-inch/70 produces an initial estimate of roughly 150 km. The calculation is explicitly informal and is not a firing table. Its purpose is to explore what long-range artillery could mean in the confined Baltic theater. The later discussion revises the estimate upward, so 150 km is only the starting estimate.