On a grid, what is the area of effect of Spirit Guardians?

Question

I'm unclear on what the area of effect of Spirit Guardians is on a grid.

The spell has a range of Self (15-foot radius).

Additionally, the description of the spell says that

You call forth spirits to protect you. They flit around you to a distance of 15 feet for the Duration.

The problem here is that on a grid, an "area of effect with a 15-foot radius" is not the same as a "all targets within a distance of 15 feet".

An area of effect with a 15-foot radius would fall under the general rules for areas of effect on a grid (DMG p.251), for example as discuss here.

The later could be interpreted as a range of 15 feet, or 3 squares away on a 5 feet grid.

On a 5' grid, what does the area look like?

Does it take one of the following shapes?

EDIT: this is not a duplicate of the Scroll of Protection question; the Scroll clearly has a cylinder area of effect, while the Spirit Guardians affects targets 15 feet away from the caster.

Answer 1

From the DMG pg. 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.

Under these rules, the area of effect of a spell originating from the center of a square would resemble the fourth example you've given.

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That said, if you find yourself lacking a graphing calculator, at the time of play or are simply looking for a quick, effective solution, the groups I've played in have found success using the optional diagonal range rule from the DMG for determining distance along diagonals, which reads as follows.

When measuring range or moving diagonally on a grid, the first diagonal square counts as 5 feet, but the second diagonal square counts as 10 feet.

This pattern is repeated in the same way for each following diagonal step.

While this is most often applied to movement, it also works well for determining the radius of a spell, as, in general, it's a fairly decent approximation of the Pythagorean Theorem. This results in a radius for Spirit Guardian that will most closely follow the third example you've provided.

As you may have noticed, this approach does not strictly match the first rule. The speed and ease of the optional strategy, however, is great enough that my groups have almost always found it preferable to the standard rule.