Calc Little Witch Academia - Volcanic Ray

The Volcanic Ray spell melts the ground and causes lava to burst up. Continental crust ranges from 30km to 50km, which averages out at 40km (40,000m). First off, let's find the speed.

2.29 seconds. We'll split that in half for the time for the heat ray to reach below the crust and for the lava to burst up.

T = 2.29s/2
= 40,000m/1.14500s
= 34934.4978/340.29
= Mach 102.660959

Amanda is 167cm tall, or 1.67m.
139 pixels = 1.67m
1 pixel = 1.67m/139 = 0.0120143885m
0.0120143885m X 6 = 0.072086331m
0.0120143885m X 505 = 6.06726619m
6.06726619m/2 = 3.03363309m
3.03363309m - 0.072086331m = 2.96154676m

Volume as a cylinder.

V = πr^2h
= π X 3.03363309^2 X 40,000
= 1156474.26m^3

V = πr^2h
= π X 2.96154676^2 X 40,000
= 1102166.11m^3

V = 1156474.26 - 1102166.11
= 54308.15m^3

There are various densities of magma, those being basalt, andesite and rhyolite. We'll go with the average rhyolite, as that weighs the least. Rhyolite magma weighs between 2180 and 2250kg per m^3, which averages out at 2215kg per m^3.

M = 54308.15 X 2215
= 120292552kg

At last for our energy.

KE = (0.5) X 120292552 X 34934.4978^2
= 7.34036662e16 joules

Let's also get the energy for the heat ray to melt the rock. Melting rock takes 4350000000 joules per m^3.

E = 54308.15 X 4350000000
= 2.36240452e14

E = 7.34036662e16 + 2.36240452e14
= 7.36399067e16 joules
= 17.6003601099 megatons

Final Results
Volcanic Ray (speed) = Mach 102.661
Volcanic Ray (energy) = 17.600 megatons