So, the one day I was reading through different spells and I came across what I believe to be a simple math error in the effect of one:
…You can choose to make the wall up to 100 feet long, 20 feet high, and 5 feet thick, or a circle up to a 30-foot radius and up to 20 feet high and 5 feet thick…
We can ignore the height and thickness for this purpose as the only variable difference in volume between the two is length.
100 feet long vs. 30-foot radius.
I base the following critique on the premise that the desire is for the circle and line to have the same volume. For the purpose of volume I am going to simplify it and just refer to squares, even though they have no volume they will work for my purpose here.
100 foot long wall takes up 20 squares if they are 5-foot squares (100 / 5 = 20).
The 30-foot radius circle has a circumference of 188.5 feet (2 * pi * Radius = C)…(2 * 3.14 * 30 = 188.5). It would seem obvious already that the listed dimensions of the circle are wrong. But let’s look at the grid squares occupied.
Referring to Fig-1, a circle with a 30-foot radius occupies 28 squares.
My first impression is that the mistake made was that the Diameter was intended to be 30-feet which would make the radius 15-feet.
A 15-foot radius circle has a circumference of 94.2 feet (2 * pi * Radius = C)…(2 * 3.14 * 15 = 94.2). And since 5-foot increments are the only increments that make sense to use if the effect may need to be utilized on a gridded battle-map, then this would make sense. However, if we look at how this circle fleshes out on a grid then we will see that 20-foot radius is, in my humble opinion, the most appropriate with staying true to the original premise.
Referring to Fig-2, a circle with a 20-foot radius occupies 20 squares.
A 20-foot radius circle has a circumference of 125.7 feet (2 * pi * Radius = C)…(2 * 3.14 * 20 = 125.7)
Referring to Fig-3, a circle with a 15-foot radius occupies 12 squares.
100-foot line 20 squares
30-foot radius circle 28 squares
20-foot radius circle 20 squares
15-foot radius circle 12 squares
So even though, mathematically, it seems like the spell should be corrected to have up to a 15-foot radius; my opinion would be that it should be defined as having a radius of up to 20-feet.