I have a feeling this will take awhile...
Feat happens in the episode Stakes Part 8: The Dark Cloud. During the final battle against the Vampire King, the gang throws everything at the damn vampire, even a Cross-Continental volcanic eruption! Said eruption is what I will be calculating in this blog.
This Calculation is primarily based off a few statements about the inconsistent size of Ooo and as such may not be 100% accurate. I'll address the issues below in the "The Size of Ooo" sub-header.
Step #1: Volume and Mass
In this shot, Flame Queen stands at 21 PX tall. If I recall, she's around 16 or 17. The average height of a 16 year old girl is 5'4 feet, or 1.6256 meters.
The diameter of the eruption is 224 PX.
224 / 21 = 10.66666666666667
1.6256 * 10.66666666666667 = 17.33973333333334 Meters
The radius would be that in half so:
17.33973333333334 / 2 = 8.66986666667
Lets combine the 467 and 83 length lines into one as they're basically the same thing. Both lines represent the height of the eruption.
467 + 83 = 550
32 Pixels = 18.6944 Meters.
550 / 32 = 17.1875
8.66986666667 * 17.1875 = 149 Meters
This will serve as the height of the volcanic eruption.
^ Ignore that.
In that scan, we can see instead of lava, its actually a rock. Whoops.
The diameter of the lava can still serve as the diameter of the fire though.
So, the diameter of the fireball is 18.6944 meters, which is represented by 100 PX, the diameter of the rock is 58 PX.
100 / 58 = 1.724137931034483
17.33973333333334 / 1.724137931034483 = 10.0570453333 Meters
Cutting that in half to find radius.
10.0570453333 / 2 = 5.02852266665 Meters
It's pretty much spherical.
Volume = (4 × pi × r3)/3
r = Radius
(4 × pi × 5.02852266665^3)/3 = 532.610649181 m^3
Since it was thrown out of a Volcano, I will be using density of Obsidian. That is 2594.8 kg/m^3
Mass = Volume * Density
532.610649181 * 2594.8 = 1382018.11249 kg
Step #2: The Size of Ooo
Before I said the size of Ooo in size is somewhat inconsistent. We never actually see Ooo from an aerial angle so the actual size i hard to gauge. According to the Adventure Time wiki, Ooo was referred to as a Continent by Pendleton Ward and as a "Smallish" Island nation by Adam Muto, granted it doesn't source citations for either one of them. To further add to the confusion, every "globe" shot of the Earth we get is on the other hemisphere.
However in the Adventure Time short Have You Seen The Muffin Mess?, Bubblegum refers to Ooo as a continent. Since Bubblegum is a super genius, I doubt she'd exaggerate the size of Ooo. For that, I will be using Australia as a model for the size of Ooo.
So a rough length of Australia is 1843.113 kilometers.
This is the only official depiction of Ooo, I'm afraid.
So, 559 PX = 1843.113
The distance is 137 PX
559 / 137 = 4.08029197080292
1843.113 / 4.08029197080292 = 451.7110572450805 km
Step #3: Timeframe and Speed
The lava takes approximately 2.89 seconds to reach the Vampire King.
451.7110572450805 km / 2.89 seconds = 156,301.404 m/s (Mach 459)
Step #4: Kinetic Energy
KE = Mass * 0.5 * Velocity^2
1382018.11249 * 0.5 * 156,301.404^2 = 1.688144e+16 Joules
Small City level+
Other: Revising the Mass
I thought that the method as of finding the mass was't right, so I'll re do it.
The Oovian is 7 Pixels. It's so low quality it's hard to make out who it is, but most of the village folk were roughly as tall as Finn, so I'll use 1.7526 Meters. The meter has a diameter of 58 Pixels.
58 / 7 = 8.285714285714286
1.7526 * 8.285714285714286 = 14.5215428571 Meters.
14.5215428571 / 2 = 7.26077142855 Meters
(4 × pi × 7.26077142855^3)/3 = 1603.3816354 m^3
Latite, a type of Volcanic Rock has a density of 2.8 g/cm^3, or 2,800 kg/m^3
1603.3816354 * 2,800 = 4489468.57912 kg
4489468.57912 * 0.5 * 156,301.404^2 = 5.4839148e+16 Joules.
13 Megatons. City level
Conclusion and Power-Scaling
If accepted, this may downgrade the verse considerably as Ice Kings "Mountain level" feats revolve around creating/destroying small mountains, and thus should probably be downgraded to Town level. Since Fire Elementals can casually generate Volcanic Eruptions, my suggested scaling for Season 7 onward AT characters would be:
So City level AT is pretty consistent. Nice.