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removed 5e from title as the tag makes t clear, edited tags to match the question
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Nobody the Hobgoblin
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dnd 5e AOE templates Clarification for Area of Effect Templates

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dnd 5e AOE templates

I have seen a lot of AOE templates out there. There seems to be a lot of interpretations.

I have seen some that equate 20' squares and 20' radius circle. However, 20' squares are 4x4 squares on a 1sq=5ft map, and 20' radius circles are closer to 8x8 squares. I've seen the squares given bigger areas to make them equal and circle made into diameters, therefore smaller, to make them equal. Both are wrong, but circles do seem over powered, comparatively.

Also, there are "grid circle" templates out there, but they place the point of origin on a cross in between 4 squares. Wouldn't a centerpoint of a single square be the point of origin on an AOE that originates from the "self"?

I've seen cones that are equilateral triangles with all sides equal to the given distance of the cone (meaning they have 3 60deg angles) starting at the midpoint or corners of the square the PC is on. I've also seen them start at the midpoint or corner of the PC's square but with a 45deg angle and 2 67.5deg angles in 2 variations (the line in the middle being the distance given or the two protruding sides of the triangle being the distance given). You can also have the distance given as the center of an isoceles and at that edge the center of a perpendicular line, also the distance given. Can you start on any point of the creature's square(s)? Another version looks as though a protractor has been used with the given distance, giving the far third of the triangle a curve. Not to mention the "grid cone" which can only be used in 4 directions (not 8) given the cone necessitates a single square at the beginning.

Only lines seem to have a clearly designated template, but even they get wonky when you add the direction of attack can mean they aren't placed directly in line with the battle map grid (attacking enemies at an angle) and therefore how much of an enemy's square does the template need to cover to be considered a hit? Completely? Mostly? Over 50%? 25%? Touching at all?

I want to have clear and consistent rulings for these topics at my table to help foster fair play. Any insight?