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Suppose there is a huge creature with an ability that targets all creatures within 10 feet. For player characters, who are medium-sized, effects like this are easy enough to resolve, but what if the user is a larger creature? Does the AoE's radius start from the edge of the creature or from the center of the creature? In the above example (huge, 10ft), would that imply that only those creatures that are in the huge creature's space are actually affected?

Similarly, does Reach work the same way or is it different?

The only RAW I can find on the subject is PHB 195 (also SRD 95) where it says:

Most creatures have a 5-foot reach and can thus attack targets within 5 feet of them when making a melee attack. Certain creatures (typically those larger than medium) have melee attacks with a greater reach than 5 feet, as noted in their descriptions.

Taking a look at Cloud Giants (MM 154), their morningstar (a weapon that does not clasically have additional reach) has a reach of 10 feet. This suggests to me that reach begins at the boundary of the controlled zone of the creature, because otherwise they'd only ever be able to swing at their own feet which would be silly if for some reason two giants got in a fight. Similarly, the Pseudopod action of Gelatinous Cubes (MM 242) strikes me as the sort of attack that should attack creatures it has not yet engulfed, not the creatures already inside it.

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I can't find a direct quote pertaining to this question, but rules in 5e are generally intended to be interpreted as naturally as possible. A creature is more than just its center. Regardless of your position relative to the creature's center, if part of its body (in game terms, one of its squares) is within 10 feet of you, then the creature is within 10 feet. The same goes for weapon range.

In the end, 5e makes it pretty safe to follow your common sense. Your instincts are right: it would be pretty silly if a cloud giant with a huge morningstar could barely swing past its own body. If it seems dumb and wrong, it probably is.

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    \$\begingroup\$ That last sentence solves many rule problems. +1. \$\endgroup\$ – keithcurtis May 19 '18 at 22:56

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