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Premise

XCOM Interceptor weapons can down a Battleship. While this causes significant damage, we will do a GPE calc for this. 

Calc

We have several potential ends for this calc. As a low-ball, we could say that the ships are hovering like this one. However, that is rarely the case. By this time, the mission becomes an invasion to be countered on foot, not in the air. 

Fighter Jets are certified to fly at 41,000 feet, or 12496.8 meters. We'll use this, since logically an Interceptor would be unable to fight them at higher altitudes. 

For scaling in that image, an Apache Helicopter is 58 feet long, or 17.678 meters
Battleshipscaling

The green line is a helicopter.

Helicopter = 8 px = 17.678 meters

Length of First Segment = 261 px = 576.745 meters

Height of Ship = 81 px = 178.990 meters

Length of Second Segment = 216 px = 477.306 meters

We can add the lengths, they just needed to be calculated separately due to the gap. We will calculate volume under the assumptions that the ship, due to irregular shape, is generally a rectangular prism and it is at least 2/3 as wide as it is tall (which looks about right from eyeballing it, but we have no means of scaling this). 

Total Volume = (576.745 + 477.306) x 178.990 x (178.990 x 0.67) = 22625280 m^3

We will assume 50% hollowness for the sake of making up for irregularities and the portion of the ship that would contain the crew. Notably, this seems to be a fairly small portion. 

So 11312640 m^3. We will treat this with the density of steel, at 8050 kg/m^3. 

Mass = 9.107e10 kg. 

Now, Interceptors can gun this down out of the sky. Let's calc it. 

PE = mgh, where m = mass (9.107e10), g = gravity (9.8 m/s), and h = height (12496.8). This nets us 1.115e16 Joules, or Small City level

Tally

Battleship Gets Sunk: 2.67 Megatons of TNT, Small City level

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