Twin Star Exorcists — Rokuro Shoots a Hyperbeam

As requested by Nibbler3100, I am going to calculate the destructive power of the following feat from Twin Star Exorcists.

First of all, I need a frame of reference for size. Rokuro, the actor of this feat, is a 14-16 year old Japanese male. In Japan, males ages 10–16 average in height between 140–170 cm. Since Rokuro is described as being 'short', I will consider the 10-year average (140 cm) the low end estimate and the 16-year average (170 cm) as the high end estimate.

Beam Diameter:

Low End
$35.5px/307px*140cm=16.188925cm$
High End
$35.5px/307px*170cm=19.65798cm$

So, the beam Rokuro fires should be approximately 16–20cm in diameter. Seeing as how the diameter does not appear to change over distance, I can now use this to scale the rocks.

At first, I assumed these rocks were all roughly the same size floating at different distances from the viewer's perspective, but when I looked at the last image showing the rock fragments, they appear to be consistent with the assumption that the rocks are different sizes floating at the same distance from the viewer. So, I am going to assume that they are different size rocks floating roughly the same distance from the viewer's perspective. Not only is this supported by the evidence, it makes things easier for me. For convenience, I will be approximating the volume of the rocks to simple right circular cones, using their greatest diameter and height available. I determine the distance between the rocks and the beam by measuring from their assumed center of mass.

Beam Diameter:

Low End
$22.2px=16.188925cm$
High End
$22.2px=19.65798cm$

Rock #1

Diameter:
$254.3px/22.2px*16.188925cm=185.4434076cm$
$254.3px/22.2px*19.65798cm=225.181281cm$

Height:
$255px/22.2px*16.188925cm=185.953869cm$
$255px/22.2px*19.65798cm=225.801127cm$

Volume:
$pi*(185.4434076cm/2)^{2}*185.953869cm/3=1674158.7762517cm^{3}$
$pi*(225.181281cm/2)^{2}*225.801127cm/3=2997500.7553618cm^{3}$

Rock #2

Diameter:
$272.6px/22.2px*16.188925cm=198.7883323cm$
$272.6px/22.2px*19.65798cm=241.3858321cm$

Height:
$279px/22.2px*16.188925cm=203.4554098cm$
$279px/22.2px*19.65798cm=247.0529977cm$

Volume:
$pi*(198.7883323cm/2)^{2}*203.4554098cm/3=2104842.71856cm^{3}$
$pi*(241.3858321cm/2)^{2}*247.0529977cm/3=3768619.6365cm^{3}$

Rock #3

Diameter:
$110.1px/22.2px*16.188925cm=80.2883176cm$
$110.1px/22.2px*19.65798cm=97.4929571cm$

Height:
$143px/22.2px*16.188925cm=104.2800129cm$
$143px/22.2px*19.65798cm=126.62573cm$

Volume:
$pi*(80.2883176cm/2)^{2}*104.2800129cm/3=175984.4999462cm^{3}$
$pi*(97.4929571cm/2)^{2}*126.62573cm/3=315091.781618cm^{3}$

Rock #4

Diameter:
$181px/22.2px*16.188925cm=131.9907856cm$
$181px/22.2px*19.65798cm=160.2745254cm$

Height:
$182px/22.2px*16.188925cm=132.7200164cm$
$182px/22.2px*19.65798cm=161.16002cm$

Volume:
$pi*(131.9907856cm/2)^{2}*132.7200164cm/3=605330.1154324cm^{3}$
$pi*(160.2745254cm/2)^{2}*161.16002cm/3=1083814.45296cm^{3}$

Since Rock #5 is almost completely in shadow, I cannot accurately measure it. However, looking at the fragments it left behind suggests that it had similar volume to the smallest rocks (#3 and #4), so I will assume it has the same volume as the smallest measured rock to establish a low end estimate for it.

Now that I have volumes, I can estimate destructive energy needed to break them. Since the majority of fragments shown are obviously still pretty large in comparison to the original rocks, I don't think anyone will begrudge me if I only consider using the value for simple fragmentation.

Rock #1:

$1674158.7762517cm^{3}*8J/cm^{3}=13393270.2J=0.003201TonsTNT$
$2997500.7553618cm^{3}*8J/cm^{3}=23980006J=0.005731TonsTNT$

Rock #2:

$2104842.71856cm^{3}*8J/cm^{3}=16838741.75J=0.0040246TonsTNT$
$3768619.6365cm^{3}*8J/cm^{3}=30148957J=0.007206TonsTNT$

Rock #3/5:

$175984.4999462cm^{3}*8J/cm^{3}=1407876J=0.0003365TonsTNT$
$315091.781618cm^{3}*8J/cm^{3}=2520734.25J=0.0006025TonsTNT$

Rock #4:

$605330.1154324cm^{3}*8J/cm^{3}=4842641J=0.001157TonsTNT$
$1083814.45296cm^{3}*8J/cm^{3}=8670515.6J=0.002072TonsTNT$

Total Energy

Low End:
$37890404.88J=0.009056TonsTNT$
High End:
$67840947.26J=0.016214TonsTNT$

Merely Fracturing the rocks themselves equals a lower end Small Building Level destructive feat.

...Wait, we're not done yet!

Since the rocks are floating a distance away from the beam but are still destroyed by its passing, that means inverse-square law comes into effect when attempting to determine the strength of the source.

Rock #1

Distance:
$398px/22.2px*16.188925cm=290.2338821cm$
$398px/22.2px*19.65798cm=352.4268569cm$

Required Energy:
$(290.2338821cm)^{2}/(16.188925cm)^{2}*13393270.21J=4304739011J=1.028857TonsTNT$
$(352.4268569cm)^{2}/(19.65798cm)^{2}*23980006J=7707428128J=1.84212TonsTNT$

Rock #2

Distance:
$407.3px/22.2px*16.188925cm=297.0157291cm$
$407.3px/22.2px*19.65798cm=360.6619568cm$

Required Energy:
$(297.0157291cm)^{2}/(16.188925cm)^{2}*16838741.75J=5668034794.5J=1.354693TonsTNT$
$(360.6619568cm)^{2}/(19.65798cm)^{2}*30148957J=10148343649J=2.425512TonsTNT$

Rock #3

Distance:
$346.1px/22.2px*16.188925cm=252.3868cm$
$346.1px/22.2px*19.65798cm=306.4696864cm$

Required Energy:
$(252.3868cm)^{2}/(16.188925cm)^{2}*1407876J=342185541.5J=0.081784TonsTNT$
$(306.4696864cm)^{2}/(19.65798cm)^{2}*2520734.25J=612666752J=0.146431TonsTNT$

Rock #4

Distance:
$469px/22.2px*16.188925cm=342.0092731cm$
$469px/22.2px*19.65798cm=415.2969746cm$

Required Energy:
$(342.0092731cm)^{2}/(16.188925cm)^{2}*4842641J=2161334591.7J=0.516571TonsTNT$
$(415.2969746cm)^{2}/(19.65798cm)^{2}*8670515.6J=3869765619.4J=0.924896TonsTNT$

Rock #5

Distance:
$352px/22.2px*16.188925cm=256.6892626cm$
$352px/22.2px*19.65798cm=311.6941046cm$

Required Energy:
$(256.6892626cm)^{2}/(16.188925cm)^{2}*1407876J=353951521.5J=0.084596TonsTNT$
$(311.6941046cm)^{2}/(19.65798cm)^{2}*2520734.25J=633733173J=0.151466TonsTNT$

Total Energy

Low End:
$12830245460.5J=3.066502TonsTNT$
High End:
$22971937321.8J=5.490425TonsTNT$

Fracturing the rocks from the apparent distances equals a lower-middle end Large Building Level destructive feat.