When playing on a grid, how many Medium creatures fit inside the area of a Scroll of Protection's barrier during combat?

Question

The description of the scroll of protection (DMG, p. 199) reads:

Using an action to read the scroll encloses you in a invisible barrier that extends from you to form a 5-foot-radius, 10-foot-high cylinder. For 5 minutes, this barrier prevents creatures of the specified type from entering or affecting anything within the cylinder.

The cylinder moves with you and remains centered on you. However, if you move in such a way that a creature of the specified type would be inside the cylinder, the effect ends.

A creature can attempt to overcome the barrier by using an action to make a DC 15 Charisma check. On a success, the creature ceases to be affected by the barrier.

As I understand, most spell effects are centered on a grid intersection (if you're using a grid, which I am) and calculate their areas that way. This item, though, centers its 5-foot radius around the creature that uses the scroll. So on a grid, this cylinder should be centered in the middle of a space, and therefore partially cover the other spaces.

Is this correct? If so, are other creatures (say, the other party members) able to fit inside in the area of effect and also be safe from the creatures the scroll targets?

It only partially covers their space, so a creature may or may not be able to affect them, which seems more ambiguous than it should.

Answer 1

The scroll's effects can cover either four or nine Medium creatures, depending on how you interpret it.

Normally, effects that are described with a radius originate from a grid intersection. When the origin is defined by a creature, such as the caster of a spell, or as in this case, a creature reading a scroll, then the intersection is one of the intersections within or adjacent to that creature's space (the corner of their square for a Medium-sized creature). So if you take the "5-foot radius cylinder" as the key part of the spell, then the effect should cover four squares. One of those would be the square of the creature reading the scroll, and three of their friends could fit in the others. This is probably the best interpretation of the rule, though the description of the effect does it's best to make it more confusing by describing the effect as remaining "centered on you" as you move. Probably that just means you can pick a new corner for it each time you move.

The alternative interpretation is that the radius of the effect of a Scroll of Protection is supposed to be interpreted as a distance from the reader of the scroll, not a radius from a point in space. Since a Medium creature occupies a full 5-foot square in combat, there are 8 squares within five feet of them (forming a 3 by three grid with the creature's square in the middle). There are some spells, like the Thunderclap cantrip, that have areas of effect that work this way, and this is also how a Paladin's Aura of Protection works.

The spell Ice Knife as originally published (in the Princes of the Apocalypse adventure, and the free Elemental Evil Player's Companion that was released alongside it) used a radius to define the area of effect for its secondary explosion. But it was changed in an errata to use a distance from the targeted creature instead.

Unfortunately the exact intentions of the designers of the Scroll of Protection are not clear, so the DM of your game will need to make a ruling on how it works at your table. You could play by the strict RAW and use a radius that's centered on a corner of the reader's square. Or you could apply a similar ruling to the Ice Knife errata and change the five foot radius cylinder to a five foot range around the reader of the scroll, which might make the effect easier to understand.

I don't think either version is going to dramatically change the power level of the scroll. A larger area is not necessarily better, since you may want to be using the protection it offers to flee though a room full of the creatures you're protected from. Having a larger area means you'll have a harder time fitting through gaps in between the enemies (since you can't push the AOE against them without ending the effect). Similarly, with the larger area, the creature at the center (who read the scroll) can't easily reach the edge of its effect, and so they probably can't fight anyone outside unless they have ranged attacks or a reach weapon.

Answer 2

As I understand, most spell effects are centered on a grid intersection (if you're using a grid, which I am) and calculate their areas that way. This item, though, centers its 5-foot radius around the creature that uses the scroll. So on a grid, this cylinder should be centered in the middle of a space, and therefore partially cover the other spaces.

You have this correct, when the target of an effect is a creature, and you are playing on a grid, the radius starts either at one of the nearest intersections between spaces, or you could start from the center of your space, since the target of the spell is Self. Either way, as cited below, a space is affected by the spell as long as its center point is covered by that spell's area.

Dungeon Master's Guide, P. 251

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.

On a square grid, this would cover 8 squares (plus the center), and on a hex grid this would cover 6 hexes (plus the center); which means that the affect of the scroll, when applied to a medium or small creature, would apply to 6 or 8 medium/small creatures in addition to the user, or more if the user is size large.