How many squares on a 5-foot grid does a 5-foot radius spell affect?

Question

We had a situation come up regarding this term and how it affected spells.

In the spell Moonbeam, for example, it says a 5-foot radius cylinder appears. Does this mean that from the center of square it extends 2.5 feet into the next square hypothetically hitting up three squares or does this mean from the edge of one the target square to the five feet and five feet the other direction effectively covering only two squares for a total of 10 feet between total range of both squares?

I understand that radius means half the distance of a circle from the center point. The spell is not the issue but the understanding of radius as it pertains to the spell, as there are other spells that are worded similarly such as Fireball, etc.

Essentially we are asking, does the spell in the example effect one square or three? This would be saying the edge of the initial square is the point of origin and not the center of the square for the total distance of ten feet.

I had been working under the understanding that the radius is half of the distance and therefore dragging a ruler from the center of where I want the spell to take effect would get me the area of effect.

It's much easier to do this with Fireball, due to the larger area to effect, but this one has such a small area and therefore sparked the debate. We are using a grid system to mark the distance, etc. We play within the digital realm of roll20.com.

Answer 1

Under the default rules there are no squares and the caster is free to pick any point in 3D space; the 5-foot radius then extends from that point and if any creature is touched then it is affected.

I assume you are using the Playing on a Grid variant on page 192 of the Player's Handbook. In which case your caster still decides which point in 3d space to target and your DM decides which squares are affected.

Alternatively, you can use the variant to the variant rule on p. 251 of the Dungeon Master's Guide which says:

Choose an intersection of squares or hexes as the point of origin of an area of effect, then follow its rules as normal. If an area of effect is circular and covers at least half a square, it affects that square.

So your Moonbeam affects the 4 squares that touch the intersection. A 15 foot radius fireball affects 32 squares (a 6x6 area with the corners missing).