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1. Diebuster! - The Excelio Variable Gravity Well approaches

The Excelio Variable Gravity Well tows the colossal Excelio blackhole behind it.

432 pixels = 30,000km
1 pixel = 30,000km/432 = 69.4444444km
69.4444444km X 309 = 21458.3333km
21458.3333km/2 = 10729.1666km

Entering that distance into the schwarzsnchild radius calculator, and the mass of the blackhole is 0.7231088206168746 X 10^34kg (or 7.23108821e33kg). The animation is a bit strange, in that the blackhole moves over but then drifts back, so we'll calc the furthest distance it travelled.

940 pixels = 21458.3333km
1 pixel = 21458.3333km/940 = 22.8280141km
22.8280141km X 129 = 2944.81382km

Timeframe is 3 seconds.

22.8280141km X 249 = 5684.17551km
5684.17551km - 2944.81382km = 2739.36169km

T = 2739.36169km/3s
= 913120.563m/s

Finally, we can get that juicy kinetic energy.

KE = (0.5)mv^2
= (0.5) X 7.23108821e33 X 913120.563^2
= 3.01460149e45/10^44
= 30.1460149 FOE

Final Results
Excelio Variable Gravity Well's kinetic energy = 30.146 FOE

Nono and Buster Machine No. 19 kick the Excelio Variable Gravity Well and kill it into the blackhole.
2. Gurren Lagann - Super Galaxy Gurren Lagann & Ashtanga sizes

As there are a few calcs I mean to make and look over involving them, and the images in the old calcs of their sizes where lost in the great PostImage crash, it's time to recalc the sizes of Super Galaxy Gurren Lagann and the Ashtanga. The second movie has the perfect shot from which to scale directly.

The diameter of the Moon is 3474.2km.

932 pixels = 3474.2km
1 pixel = 3474.2km/932 = 3.7276824km

3.7276824km X 432 = 1610.3588km

364 pixels = 1610.3588km
1 pixel = 1610.3588km/364 = 4.42406264km
4.42406264km X 878 = 3884.327km
744 + 704 = 1448 pixels
4.42406264km X 1448 = 6406.0427km

Now onto the Ashtanga.

105 pixels = 1610.3588km
1 pixel = 1610.3588km/105 = 15.3367505km
15.3367505km X 1072 = 16440.9965km

300 pixels = 16440.9965km
1 pixel = 16440.9965km/300 = 54.8033217km
54.8033217km X 1388 = 76067.0105km
54.8033217km X 584 = 32005.1399km

Final Results
Super Galaxy Gurren Lagann main body height = 3884.327km
Super Galaxy Gurren Lagann total height = 6406.043km
Ashtanga total length = 76067.011km
3. Diebuster! - Diebuster stomp

Diebuster stomps fast.
Spoiler:

The timeframe is 1 frame.

T = 1s/24
= 41.6666667ms

Diebuster has a height of 10,000km.

586 pixels = 10,000km
1 pixel = 10,000km/586 = 17.0648464km
17.0648464km X 385 = 6569.96586km
17.0648464km X 224 = 3822.52559km

Low end stomp from the knee, high end stomp the whole leg.

(Low end)
T = 3822.52559km/41.6666667ms
= 91740614.1/299792458 X 100
= 30.6013749% C

(High end)
T = 6569.96586km/41.6666667ms
= 157679181/299792458 X 100
= 52.5961133% C

Final Results
Diebuster stomp (low end) = 30.601% C
Diebuster stomp (high end) = 52.596% C
4. Diebuster! - Lal'C and Tycho talk with each other from across the Solar System

A minor feat from the end of Diebuster!

Lal'C on Earth talks to Tycho on Pluto. Looking at Endless Mike's Cowboy Bebop calc for a bit of directiong, but this should be pretty straight forward. From the time when Lal'C stops talking and Tycho begins talking.
Spoiler:

The timeframe is 11 frames.

T = 1s/24
= 41.6666667ms X 11
= 0.458333334s

The closest Pluto is to Earth is 4,280,000,000km, the furthest Pluto is from Earth is 7,500,000,000km, and on average is 5,187,000,000km away (information from here).

(Low end)
T = 4,280,000,000km/0.458333334s
= 9.3381818e12/299792458
= 31148.8216 C

(Mid end)
T = 5,187,000,000km/0.458333334s
= 1.13170909e13/299792458
= 37749.7519 C

(High end)
T = 7,500,000,000km/0.458333334s
= 1.63636363e13/299792458
= 54583.2154 C

Final Results
Lal'C communicates with Tycho on Pluto (low end) = 31148.822 C
Lal'C communicates with Tycho on Pluto (mid end) = 37749.752 C
Lal'C communicates with Tycho on Pluto (high end) = 54583.215 C
5. Diebuster! - Quatre-Vingt-Dix shatters giant ice formation

Another feat I noticed during my Diebuster! rewatch. Quatre-Vingt-Dix's initial attack is -10^12 degrees, which is below absolute zero and therefore can't be calced (both the show and the DVD booklets even say that said attack was because physics was broken), but the part afterwards can be;

Quatre-Vingt-Dix shatters the giant ice structure containing the frozen space monsters into fine dust, which falls on the Jupiter station as snow. This will take some scaling, which we can do by paying careful to the surrounding stars and gas in the Red Milky Way. The Jupiter Station is around 70km long.

Spoiler:

70km = 228 pixels
1 pixel = 70km/228 = 0.307017544km
0.307017544km X 1968 = 604.210527km
0.307017544km X 191 = 58.6403509km
58.6403509km/2 = 29.3201755km

0.307017544km X 989 = 303.640351km

0.307017544km X 1020 = 313.157895km

0.307017544km X 859 = 263.72807km

0.307017544km X 2256 = 692.631579km

0.307017544km X 865 = 265.570176km
604.210527km + 303.640351km + 313.157895km + 263.72807km + 692.631579km + 265.570176km = 2442.9386km

Volume is roughly a cylinder (really it's more curvy, but given we see most of it after it's destroyed it's hard to scale).

V = πr^2h
= π X 29.3201755^2 X 2442.9386
= 6597745.44km^3
= 6.59774544e+15m^3
= 6.59774544e+21cm^3

Pulverization of ice is 4.3919 joules/cm^3.

E = 6.59774544e+21 X 4.3919
= 2.89766382e22 joules
= 6.9255827437858510365 teratons

Come to think of it, you could also get the KE for this too. Ice weighs 919kg/m^3.

M = 6.59774544e+15 X 919
= 6.06332806e18kg

First for the expansion of the ice particles, and the distance they travelled from the ice formation...

0.307017544km X 298 = 91.4912281km

Then for the timeframe...
Spoiler:

The timeframe is 3 seconds and 17 frames.

T = 1s/24
= 41.6666667ms X 17
= 0.708333334s + 3s
= 91.4912281km/3.70833333s
= 24671.7919m/s

Finally for the kinetic energy.

KE = (0.5)mv^2
= (0.5) X 6.06332806e18 X 24671.7919^2
= 1.84536576e27 joules

Then we add on the above shattering for our final results.

E = 1.84536576e27 + 2.89766382e22
= 1.84539474e27 joules
= 441.05992829827920332 petatons

Final Results
Quatre-Vingt-Dix shatters giant ice formation (low end) = 6.926 teratons
Quatre-Vingt-Dix shatters giant ice formation (high end) = 441.0599 petatons
6. Analysis on Nono censoring the naked singularity

First, the scene itself. Splitting the blackhole causes the swartzenchild radius to fall apart and expose the naked singularity, which could lead to a second Big Bang. Nono then takes the naked singularity away to the multi-dimensional space
Spoiler:

In an interview from the DVD booklet, it mentions that they tried to depict the cosmic censorship hypothesis (and have an endnote to the scientific description of such), says that Nono seems to have already experienced her and Lal'C seeing the skylarks, so that she and Lal'C may indeed see the skylarks together at some point in the future.

Later on the same page, for another question, Kazuya Tsurumaki says that Nono watches over time for eternity.
This would mean that Nono exists outside and beyond time, and can seemingly perceive events in a non-linear manner, as well as the scientific concepts of the naked singularity and cosmic censorship being researched.
Earlier from this same booklet, it points out the singularity has infinite mass and zero volume.

Nono holds the naked singularity in her hands, and even just one hand.
Spoiler:

This is not new information; it's been around for a few years. But I looked for Diebuster! interviews, and found this;
http://www.style.fm/as/13_special/mini_070130a.shtml
I'm going to try get this properly translated by a human and not just a machine, but from what I can see of it? "Multi-dimensional space" is a mistranslation of "multiverse" (this happens quite a bit with translation; "multi-dimensional labyrinth" in Gurren Lagann really translates to "Multiversal Labyrinth"). So Nono has taken the naked singularity from the universe into the further multiverse.

A previous interview (or part of this interview), says that the last episode is developed on the universe scale, but is concentrated on Lal'C's story (once again, I'll need to get a proper translation of this).
http://www.style.fm/as/13_special/mini_070129a.shtml
So to sum up, Nono and Buster Machine #19 splitting the Excelio Variable Gravity Well's blackhole caused the blackhole to fall apart and expose the naked singularity, which would have lead to another Big Bang. Nono censors the singularity, holds the infinite mass singularity in her hands, and takes it beyond the universe into the further multiverse, where she transcends time and watches over it for eternity.

And for the cherry on top, Nono seems to have some kind of intangibility in this form too.
7. Lio-Hen - You can't freeze us

From Lio-Hen, one of the two prequels to Promare.

Vulcan shoots Lio with an ice rocket launcher, but Lio just melts his way out, without even wearing his Burnish Armour either. Once again using the height of 5 feet 9 inches (or 1.7526m) for Lio.

1347 pixels = 1.7526m
1 pixel = 1.7526m/1347 = 0.00130111359m
0.00130111359m X 201 pixels = 0.261523832m

66 pixels = 0.261523832m
1 pixel = 0.261523832m/66 = 0.0039624823m
0.0039624823m X 286 = 1.13326994m
0.0039624823m X 1075 = 4.25966847m
4.25966847m/2 = 2.12983424m

Said ice burst is also thick enough to contain Lio's bike from front to back.

58 pixels = 1.13326994m
1 pixel = 1.13326994m/58 = 0.0195391369m
0.0195391369m X 2126 = 41.540205m
41.540205m/2 = 20.7701025m
0.0195391369m X 1235 = 24.1308341m
24.1308341m/2 = 12.0654171m

Volume as an ellipsoid.

V = 4/3πabc
= 4/3 X π X 12.0654171 X 20.7701025 X 2.12983424
= 2235.70961m^3

Once again using the mass of solid air, as it's too hard and dense to be the 1.003kg's of air in it's gaseous form. Ice has a density of 919kg/m^3.

M = 2235.70961 X 919
= 2054617.13kg

Keep in mind that this isn't just ordinary ice, but ice that can freeze Burnish Flames (somehow).

Given said fires can evaporate a frozen lake and worse, they should be at least 100°C. Specific heat of air at this temperature is 1.005 kilojoules.

E = 2054617.13 X 1.005 X 100
= 206489022 kilojoules
= 206489022000 joules

And of course we'll add the heat fusion of oxygen of 13800 joules/kg.

E = 9311452.37 X 13800
= 128498042706 joules

E = 206489022000 + 128498042706
= 334987064706 joules
= 80.0638299966539 tons of TNT

Lio then melts his way out, evaporating the ice.

279 pixels = 1.13326994m
1 pixel = 1.13326994m/279 = 0.00406189943m
0.00406189943m X 1431 = 5.81257808m

Volume of the area melted as an equilateral triangular prism.

V = √3/4w^2h
= √3/4 X 5.81257808^2 X 4.25966847
= 62.3180758m^3

M = 62.3180758 X 919
= 57270.3117kg

The heat fusion of ice is 3.33 X 10^5 joules/kg (or 333000 joules/kg), as well as the the heat of vaporization, that being 2.26 X 10^6 joules/kg (or 2260000kg).

E = 57270.3117 X 333000
= 1.90710138e10 joules

E = 57270.3117 X 2260000
= 129430904442 joules

The specific heat of water is 4.18 joules/kg.

E = 57270.3117 X 4.18 X 100
= 23938990.3 joules

E = 1.90710138e10 + 129430904442 + 23938990.3
= 1.48525857e11 joules
= 35.4985317877629 tons of TNT

Final Results
Vulcan freezes Lio = 80.064 tons of TNT
Lio escapes ice = 35.499 tons of TNT
8. Promare - Absolute Zero Heat Death Cannon

Krazor X fires the Absolute Zero Heat Death Cannon and freezes a volcano. Said weapon is also designed to work against solar flares.

Finding the scaling is a bit tricky, but there's a way to get an estimate of the power on display here, as we can scale part of the beam to Lio de Galon's "ear", which in turn we can scale from a sedan it dwarved. The average length of a compact sedan is 177.2 inches, or 4.50088m.

50 pixels = 4.50088m
1 pixel = 4.50088m/50 = 0.0900176m
0.0900176m X 25 = 2.25044m

87 pixels = 2.25044m
1 pixel = 2.25044m/87 = 0.0258671264m
0.0258671264m X 1133 = 29.3074542m

Keep in mind too this isn't even the full beam, just what we can scale from. But it's better than nothing, so let's continue on.

10 pixels = 29.3074542m
1 pixel = 29.3074542m/10 = 2.93074542m

It gets even closer to the volcano, but that's the best scale I have to go with.

2.93074542m X 1228 = 3598.95538m

362 pixels = 3598.95538m
1 pixel = 3598.95538m/362 = 9.94186569m
9.94186569m X 396 = 3936.97881m
3936.97881m/2 = 1968.48941m
9.94186569m X 654 = 6501.98016m
6501.98016m/2 = 3250.99008m

Keep in mind that ultimately the volume would be even higher because of all the spikes pointing out. Anyway, volume as an ellipsoid.

V = 4/3πabc
= 4/3 X π X 1968.48941 X 3250.99008 X 3250.99008
= 8.71471082e10m^3

Ice weighs 919kg/m^3 (the ice is a solid, so it would absolutely weigh a lot more than it would as just gas).

E = 8.71471082e10 X 919
= 8.00881924e13kg

A pyroclastic flow (the ashcloud produced by a volcano) is between 400°C to 800°C, so we'll go with a low end and a high end.
https://science.howstuffworks.com/nature/natural-disasters/volcanic-ash.htm
(Low end)
Specific heat of air is 1.005 kilojoules.

E = 8.00881924e13 X 1.005 X 400
= 3.21954533e16 kilojoules
= 3.21954533e19 joules

We'll also add the heat fusion of air/oxygen, that being 13800 joules/kg.

E = 8.00881924e13 X 13800
= 1.10521706e18 joules

E = 3.21954533e19 + 1.10521706e18
= 3.33006704e19 joules
= 7.9590512428298278991 gigatons

(High end)

E = 8.00881924e13 X 1.005 X 800
= 6.43909067e16 kilojoules
= 6.43909067e19 joules

The heat fusion is still going to be the same from above, so let's add them together.

E = 6.43909067e19 + 1.10521706e18
= 6.54961238e19 joules
= 15.653949282982791757 gigatons

Final Results
Absolute Zero Heat Death Canon (low end) = >7.959 gigatons
Absolute Zero Heat Death Cannon (high end) = >15.654 gigatons

This is actually pretty accurate compared with the energy of an average solar flare (around 10^20 joules). Lio de Galon withstands the Absolute Zero Heat Death Cannon for almost a minute, and it's Burnish flames overwhelms and disables Krazor X, though it too is destroyed.
9. Promare - Big robots are fast robots

Given the size of the mechas in this movie, it comes at not surprise that they'd be really fast.

1. Krazor X punch
1:11

Lio de Galo catches Krazor X's punch. To note how impressive this is, I'll point out the timeframe;
Spoiler:

The punch happens in the span of 1 frame. Take notice also Lio de Galo reacts to and catches this punch in said frame.

T = 1s/24
= 41.6666667ms

Given Krazor X is over 148m tall, this is going to be super fast. Reminder that the average length of a compact sedan is 177.2 inches, or 4.50088m.
Spoiler:

50 pixels = 4.50088m
1 pixel = 4.50088m/50 = 0.0900176m
0.0900176m X 925 = 83.26628m

T = 83.26628m/41.6666667ms
= 1998.39072/340.29
= Mach 5.87261077

It would also be possible to get kinetic energy for this, but given that would take a lot of fiddling around...maybe another time.

2. Lio de Galon's kick
1:43

Krazor X punches Lio de Galon across the city, but then Lio de Galon leaps back in the span of about a second and kicks Krazor X in the face. Krazor X's shoulder blade is 36.6187169m tall.

= 2*atan(45/(1664/tan(70/2)))
= 1.468238481122232653 degrees

Entering the values of size and degrees into the angscaler, we get a distance of 1428.9m to Krazor X. Now for the timeframe.
Spoiler:

Timeframe is 1.02 seconds.

T = 1428.9m/1.02s
= 1400.88235/340.29
= Mach 4.11673088

Final Results
Krazor X's punch = Mach 5.873
Lio de Galon's kick = Mach 4.117
10. Promare - Size of Lio de Galon & Krazor X

Given this will be relevant in future calcs, it's time to calc the size of the Promare mechs.

1. Deus Ex Machina/Lio de Galon height
Until I become aware of Lio's official height, I'll use the height I used in the other calcs, that being 5 feet 9 inches, or 1.7526m.

1347 pixels = 1.7526m
1 pixel = 1.7526m/1347 = 0.00130111359m
0.00130111359m X 201 pixels = 0.261523832m

139 pixels = 0.261523832m
1 pixel = 0.261523832m/139 = 0.00188146642m
0.00188146642m X 1704 = 3.20601878m

95 pixels = 3.20601878m
1 pixel = 3.20601878m/95 = 0.0337475661m
0.0337475661m X 1483 = 50.0476405m

2. Krazor X height
Krazor X is even bigger than Lio de Galon, and we can see this in their fights, when both of them dwarf cars they send flying up. The average length of a compact sedan is 177.2 inches, or 4.50088m.

50 pixels = 4.50088m
1 pixel = 4.50088m/50 = 0.0900176m
461 + 319 + 186 + 281 = 1247 pixels
0.0900176m X 1247 = 112.251947m
0.0900176m X 213 = 19.1737488m

122 pixels = 19.1737488m
1 pixel = 19.1737488m/122 = 0.157161875m
0.157161875m X 233 = 36.6187169m
36.6187169m + 112.251947m = 148.870664m

Final Results
Deus Ex Machina/Lio de Galon height = 50.048m
Krazor X height (main body) = 112.252m
Krazor X height (total) = 148.871m
11. Promare - Size of the Parnassus

A relatively straightforward calc. How big is the Parnassus. Given Promare is set in an alternate America, we'll be using the average height of an American man for Galo ( 5 feet 9 inches, or 1.7526m).

232 pixels = 1.7526m
1 pixel = 1.7526m/232 = 0.00755431034m
0.00755431034m X 1440 = 10.8782069m

132 pixels = 10.8782069m
1 pixel = 10.8782069m/132 = 0.0824106583m
0.0824106583m X 1042 = 85.8719059m

173 pixels = 85.8719059m
1 pixel = 85.8719059m/173 = 0.496369398m
0.496369398m X 409 = 203.015084m

8 pixels = 203.015084m
1 pixel = 203.015084m/8 = 25.3768855m
25.3768855m X 134 = 3400.50266m (3.40050266km)
25.3768855m X 643 = 16317.3374m (16.3173374km)
25.3768855m X 2472 = 62731.661m (62.731661km)

Final Results
Foresight Foundation tower height = 3.401km
Parnassus's height = 16.317km
Parnassus's length = 62.732km

Damn that is one ridiculously big spaceship. I'm starting to think Kray might be a bit full of shit when he said they didn't have the technology to reach the Earths core.
12. Promare - Inferno

TRAILS OF FIRE, YOU ALWAYS KNEW, THEY WOULD CARRY ME HOME, THEY'D LEAD ME TO YOU!

Galo de Lion manifests, fixes global warming by punching the planet repeatedly, sets the entire Solar System on fire and is generally the coolest thing ever. This is a calculation of cosmic proportions so sit back and brace youreselves.
Spoiler:
1. Galo de Lion's size
2:00

Galo de Lion is a really big robot.

We can scale its height from the Earth.

R = (h/2) + c^2/(8h)
= (379/2) + 2633^2/(8 X 379)
= 2476.00693 X 2
= 4952.01386 pixels

The diameter of the Earth is 12756.2km.

4952.01386 pixels = 12756.2km
1 pixel = 12756.2km/4952.01386 = 2.5759621km
2.5759621km X 641 = 1651.19171km
2.5759621km X 396 = 1020.08099km
2.5759621km X 510 = 1313.74067km
1651.19171km + 1313.74067km = 2964.93238km

2. Galo de Lion punches the Earth
2:20

Galo de Lion punches the Earth repeatedly, visibly shaking it. This should be relatively straight forward.

541 pixels = 12756.2km
1 pixel = 12756.2km/541 = 23.5789279km
23.5789279km X 522 = 12308.2004km

Timeframe is 0.10 seconds.

23.5789279km X 499 = 11765.885km
12308.2004km - 11765.885km = 542.3154km

T = 542.3154km/0.10s
= 5423154m/s

The Earth has a mass of 5.9736 X 10^24kg (or 5.9736e24kg).

KE = (0.5)mv^2
= (0.5) X 5.9736e24 X 5423154^2
= 8.7843578e37 joules
= 20.995119024856598116 ninatons

3. Promare dragon flies into the Sun
2:49

Galo de Lion summons a Burnish Dragon of astrological proportions that flies through the Solar System and slams into the Sun, then ignites the entire Solar System. The Sun is pushed back at FTL speeds, so is unfortunately uncalcable (though this does cement it at being star level in anycase), but the speed is quantifiable. The distance from the Earth to the Sun is 149,597,870km.
Spoiler:

Timeframe is 6.42 seconds.

T = 149,597,870km/6.42s
= 2.33018489e10/299792458
= 77.7266014 C

4. Complete combustion shakes the Solar System
The Promare Dragon then splits apart and ignites every planet in the Solar System, which is a very clear solar system level feat. The Promare Dragon hits every planet in the Solar System, including Pluto (yes it's still a planet in our hearts), you can even see the elliptical orbit. First off for speed. On average, Pluto is 5,906,380,000km from the Sun.
Spoiler:

Timeframe is 0.62 seconds.

T = 5,906,380,000km/0.62s
= 9.52641935e12/299792458
= 31776.7145 C

Now for the energy. The Promare dragon shakes every planet of the Solar System, as well as the Sun (thankfully this time at sub-light speeds). Scaling from Neptune, which has a diameter of 49,244km (and a mass of 1.02 X 10^26kg, or 1.02e26kg, which will come of importance soon).
Spoiler:

30 pixels = 49,244km
1 pixel = 49,244km/30 = 1641.46667km
1641.46667km X 131 = 215032.134km

Timeframe is 0.07 seconds.
1641.46667km X 140 = 229805.334km
229805.334km - 215032.134km = 14773.2km

T = 14773.2km/0.07s
= 211045714m/s

Now for the mass of all the planets shook. The Sun has a mass of 1.989 X 10^30kg (or 1.98900e30kg), Mercury has a mass of 330 X 10^23kg (or 3.3e25kg), Venus has a mass of 4.867 X 10^24kg (or 4.86700e24kg), the Earth has a mass of 5.9736e24kg (as per above), Mars has a mass of 6.39 X 10^23kg (or 6.39e23kg), Jupiter has a mass of 1.9 X 10^27kg (or 1.9e27kg), Saturn has a mass of 5.683 X 10^26kg (or 5.68300e26kg), Uranus has a mass of 8.68100e25kg (as per above), Neptune has a mass of 1.024 X 10^26kg (or 1.02400e26kg) and Pluto has a mass of 1.30900 X 10^22kg (or 1.30900e22kg)

M = 1.98900e30kg + 3.3e25kg + 4.86700e24kg + 6.39e23kg + 1.9e27kg + 5.68300e26kg + 8.68100e25kg + 1.02400e26kg + 1.30900e22kg
= 1991696029090000000000000000000kg

Given it's moving at relativistic speeds, we can get relativistic kinetic energy. Entering this value and the speed into the relativistic kinetic energy calculator and we have a result of 7.296E+46 joules, or 729.6 FOE.

Final Results
Galo de Lion's height = 2964.932km
Galo de Lion punches the Earth = 20.995 ninatons
Giant Promare Dragon flies into the Sun = 77.727 C
Promare dragons shakes the Solar System (speed) = 31776.715 C
Promare dragon shakes the Solar System (energy) = 729.6 FOE

And on a final note? This is just with the Promare that was in the Earths core. The full Promare would be even more powerful.
13. MAHARI YUWARE GAAIE SABANARE! (Promare)

0:45

Lio Fotia gets mad. The rest is history. This is gonna take a lot of scaling, so hold on...
Spoiler:

1. Lio's volcanic eruption
Earlier in the film, we get a shot of Lio near the volcano with the face on it. Given Promare is set in an alternate America, we'll go with the average height of an American man, that being 5 feet 9 inches, or 1.7526m.

15 + 12 = 27
27 pixels = 1.7526m
1 pixel = 1.7526m/27 = 0.0649111111m
0.0649111111m X 1346 = 87.3703555m
0.0649111111m X 68 = 4.41395555m

The volcano does seem to change in shape a bit with the animation style, but given that's the best we have to go with, let's go with it.

175 pixels = 87.3703555m
1 pixel = 87.3703555m/175 = 0.499259174m
0.499259174m X 2880 = 1437.86642m
1437.86642m/2 =
0.499259174m X 1691 = 844.247263m
844.247263m/2 = 422.123631m
0.499259174m X 442 = 220.672555m
220.672555m/2 = 110.336277m
0.499259174m X 803 = 400.905117m
0.499259174m X 1556 = 776.847275m

= 2*atan(175/(1556/tan(70/2)))
= 6.10069125230074683 degrees

Once again refering to our old friend the angscaler, we can determine that the volcano peak is 819.78m.

0.499259174m X 1182 = 590.124344m
590.124344m/2 = 295.062172m
0.499259174m X 2659 = 1327.53014m
1327.53014m/2 = 663.76507m

Volume as an ellipsoid.

V = 4/3πabc
= 4/3 X π X 295.062172 X 663.76507 X 663.76507
= 544541437m^3

Weight of lava/magma (or the mantle) is 3300kg/m^3.

Spoiler:

The timeframe is 0.57 seconds. Next for the speed and kinetic energy.

T = 663.76507m/0.57s
= 1164.50012m/s

KE = (0.5)mv^2
= (0.5) X 1796986742100 X 1164.50012^2
= 1.2184114e18 joules

Next to do the lava eruption that follows and covers everything. First, to take away the distance to the explosion.

L = 819.78m - 663.76507m
= 156.01493m
Spoiler:

Timeframe is 0.45 seconds.

T = 156.01493m/0.45s
= 346.699844m/s

KE = (0.5)mv^2
= (0.5) X 1796986742100 X 346.699844^2
= 1.07999606e17 joules

Finally, let's add them all together to get our final result.

E = 1.2184114e18 + 1.07999606e17
= 1.32641101e18 joules
= 317.01983986615681488 megatons

Lio's Burnish Dragon swims through the ground to Promepolis, and gets noticably closer. We can scale the distance travelled from the Foresight Foundation tower. Once again using the average American height for Galo (1.7526m).

232 pixels = 1.7526m
1 pixel = 1.7526m/232 = 0.00755431034m
0.00755431034m X 1440 = 10.8782069m

132 pixels = 10.8782069m
1 pixel = 10.8782069m/132 = 0.0824106583m
0.0824106583m X 1042 = 85.8719059m

173 pixels = 85.8719059m
1 pixel = 85.8719059m/173 = 0.496369398m
0.496369398m X 409 = 203.015084m

Jeez that's a ridiculously huge tower. Anyway, onto scaling.

= 2*atan(9/(1617/tan(70/2)))
= 0.30219874754211817347 degrees

Promepolis is 38491m away.

Timeframe is 2 seconds.
= 2*atan(8/(1617/tan(70/2)))
= 0.26862123949704258541 degrees

The Foresight Foundation tower is now 43302m away.

D = 43302m - 38491m
= 4811m/340.29
= Mach 14.1379412

Final Results
Lio's volcanic eruption = >317.0198 megatons
Burnish Dragon swims towards Promepolis = Mach 14.138
14. Promare - Lio melts the frozen lake

Finally, it's time to calc Promare at long last! Behold, the first ever Promare calc!

Lio (in his black form) evaporates the Frozen Lake just by coming in contact with it. The average height of an American man is 5 feet 9 inches, or 1.7526m.

13 pixels = 1.7526m
1 pixel = 1.7526m/13 = 0.134815385m
0.134815385m X 2880 = 388.268309m
388.268309m/2 = 194.134154m

Next up is the depth. Due to the cracks that appear from the melting, we can ascertain the ice goes all the way down.

2829 pixels = 388.268309m
1 pixel = 388.268309m/2829 = 0.137245779m
0.137245779m X 385 = 52.8396249m

The scaling's not entirely perfect, but that's the best I could get with the shots available, and keep in mind that there's also Deus Promith's lab at the bottom. Volume as a spherical cap.

V = π/3H^2(3R = H)
= π/3 X 52.8396249^2(3 X 194.134154 - 52.8396249)
= 1548337.28m^3

Ice weighs 919kg/m^3.

M = 1548337.28 X 919
= 1.42292196e9kg

It takes 333.55 kilojoules to melt 1kg of ice.

E = 1.42292196e9 X 333.55
= 474615619758 kilojoules
= 4.7461562e14 joules

But the ice doesn't just melt; it evaporates, so let's also add the energy to vaporize the water (more information on which can be found here).

E = 1.42292196e9 X 2.26 X 10^6
= 3.21580363e15

Finally, to add the two together to get our final results.

E = 4.7461562e14 + 3.21580363e15
= 3.69041925e15 joules
= 882.0313695028680741 kilotons

Final Results
Lio melts the frozen lake = 882.031 kilotons
15. Darling in the Franxx - Red Strelizia breaks through the Gran Crevasse

(Episode 15)
Spoiler:

Strelizia bursts open the giant stone hynem seal to the Gran Crevasse (with help from the 9s). To make our work easier, the official diameter of a plantation is 3km, with a height of 1.2km.

There's a brief shot of different plantations being dwarved by the Grand Crevasse, and we can also get the thickness of the seal here too.

108 pixels = 3km (3000m)
1 pixel = 3000m/108 = 27.7777778m
27.7777778m X 67 = 1861.11111m
27.7777778m X 1193 = 33138.8889m
33138.8889m/2 = 16569.4444m

2038 pixels = 33138.8889m
1 pixel = 33138.8889m/2038 = 16.260495m
16.260495m X 359 = 5837.5177m

Volume as a spherical cap. This is the formula we will be using...
https://byjus.com/spherical-cap-volume-formulas/
V = π/3H^2(3R = H)
= π/3 X 5837.5177^2(3 X 16569.4444 - 5837.5177)
= 1565527663653m^3

The 9s fragment the seal so that Strelizia can break through. Fragmentation of rock is 8000000 joules/m^3, divided by 4 for each of them.

E = 1565527663653 X 8000000
= 1.25242213e19/4
= 3.13105532e18 joules
= 748.34018164435951803 megatons

For our mass, we'll go with a low end of sandstone (2323kg/m^3) and a high end of basalt (3011 kg/m^3)

(Low end)
M = 1565527663653 X 2323
= 3.63672076e15kg

(High end)
M = 1565527663653 X 3011)
= 4.7138038e15kg

Next up we need the distance the fragments travelled (it's a direct continuation of the same scene from the last shot taken, so one pixel would still be 16.260495m).
Spoiler:

327 + 988 + 989 = 2304 pixels
16.260495m X 2304 = 37464.1805m

Lastly, we get ourselves the timeframe.
Spoiler:

0.97 seconds. Red Strelizia also flew that distance, so we can get the speed of this as well.

T = 37464.1805m/0.97s
= 38622.8665/340.29
= Mach 113.499857

Now, let's get our energy.

(Low end)
KE = (0.5)mv^2
= (0.5) X 3.63672076e15 X 38622.8665^2
= 2.71249512e24 joules
= 648.30189292543025203 teratons

(High end)
KE = (0.5)mv^2
= (0.5) X 4.7138038e15 X 38622.8665^2
= 3.51585141e24 joules
= 840.30865439770559533 teratons

Final Results
The 9s fragment the seal (individual energy) = 748.340 megatons
Red Strelizia breaks through the Grand Crevasse (speed) = Mach 113.5
Red Strelizia breaks through the Grand Crevasse (energy - low end) = 648.302 teratons
Red Strelizia breaks through the Grand Crevasse (energy - high end) = 840.309 teratons

From the looks of it Strelizia did the work actually upthrowing the seal into the sky, but even if the 9s were involved in sending it flying upwards, divided between the five of them thats still going to be over a hundred teratons each.