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I've been playing 5e for a while now, and mercifully this hasn't come up yet, but it's definitely on it's way.

When a caster casts burning hands, how is that properly mapped onto a standard 1" battle mat? The easy response is a 3x3 square, and that's the method I've told myself I'm going to use. But is there a better template?

The 3x3 grid works great if the caster casts on a corner, it matches the description of a cone perfectly (each square is 5', 10, 15' away for the purposes of grid math). However, when a caster casts the spell in a cardinal direction (N/S/W/E), that math breaks down. now a second or even third square is adjacent with a 3x3 square and the spell description has fall apart.

What are the appropriate grid shapes for a 15' cone?

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The nerd joke in my campaign is that pi equals 4, which would be the case for your 3x3 square "cone". Square cones and fireballs are certainly the easiest option, but not the most realistic one. – Tobold Aug 22 '14 at 13:05

Right now there isn't an official rule. According to Mike Mearls and the Wizards Team that will be an option spelled out in the Dungeon Master's Guide.

However this has been an issue for 3.5, Pathfinder, and 4e. You can use this diagram from the Pathfinder SRD to make a ruling on applying a spell's area of effect to a grid until the DMG is released.

Spell Effect diagram

The diagram addresses firing from a corner of a square and from a side of the square.

D&D 4e has an alternative set of shapes for Area of Effect. I don't have an open content diagram to display but those with access to the D&D 4e rules may wish to use them in lieu of 3.5/Pathfinder. Certainly 4e interpretation is easier to adjudicate than the odd shapes of 3.5/Pathfinder.

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Folks, post your own answers please. – Brian Ballsun-Stanton Aug 22 '14 at 12:34
"this has been an issue for 3.5, Pathfinder, and 4e" -- Not 4e. 4e is very explicit about using squares for everything (well, everything except walls). – Brian S Jan 13 '15 at 15:10
Cones in 5e are not 90° wide. That poses a problem with using the diagrams from 3.5e. – SevenSidedDie Aug 11 '15 at 19:43

Guidance for mapping areas of effect defined by continuous lines onto discrete grid squares or hexes is provided on page 251 of the DMG in the section on using miniatures in combat.

It's short and sweet: follow the rules for laying out the shape of the area "as normal" to find what targets are under/within the shape; for circular areas, at least half of the square/hex must be covered to be affected.

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Here are some examples of the areas affected by a 15-foot cone cast at different angles.

The point of origin is shown at an intersection between squares (as recommended in the DMG), and also centered on the side of the square for attacks in a cardinal direction (which is more intuitive).

Here are all the squares that are touched by the cone:

15-foot cone area of effect

15-foot cone area of effect, with point of origin in line with center of square

Here are all the squares that are 50% or more covered:

15-foot cone area of effect (50% or more covered)

15-foot cone area of effect (50% or more covered), with point of origin in line with center of square

This is probably as close as you can get to the standardized shapes of previous editions.

A more generous interpretation in keeping with the spirit of the rules would be to say that the cone hits any creature whose circular base is overlapped:

15-foot cone area of effect with circular bases

15-foot cone area of effect with cirular bases, with point of origin in line with center of square

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A cone in 5e is defined such that

A cone's width at a given point along its length is equal to that point's distance from the point of origin.

That is a 53-degree cone, not a 90-degree cone as 3.5e used. Thus the diagrams given from the Pathfinder SRD are not applicable.

If you don't want to just eyeball it you have 2 choices:

  1. (requires advance preparation) Create a scale template on a piece of 1" grid paper. Overlay it on your battle grid in the direction your caster wants to direct their cone. If more than half a square is covered, consider the square to be affected
  2. (easier to do on the fly) Create two "measuring sticks" (strip of paper or whatever) scaled to the map grid, to represent 15' lengths. Place one extending from the edge or corner of the caster's square in the direction the caster wishes to aim the spell. Place the other at the far end at 90 degrees which represents the maximum width of the cone at its end. Draw the imaginary diagonals from the ends of that width measure back to the origin.

Both of these methods allow the caster more flexibility than the pre-gridded approaches. The caster can aim the spell in any direction they like (rather than just the 8 compass points and diagonals) to attempt to hit as many enemies and avoid as many friends as possible.

Once you've done it a few times, you'll probably be able to eyeball it in all but the most complex battles.

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The real answer is to use a hex map. I've never understood the resistance to them, as they solve so many problems. Movement makes more sense, too.
You'll note that video games, which aren't mired in layers of legacy graph paper, almost always use hexes because the geometry is just more consistent. Spells on a hex map

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Hex maps do make movement in two of the cardinal directions slower. It is a drawback. – Tim Seguine Sep 20 '15 at 15:03
Your cones are slightly wider than they should be (those are 60° cones, but cones in 5e are ~53°). Also note that 5e doesn't require that a spell's point of origin be centred on a space, allowing them to be placed anywhere. (This also doesn't really help anyone who is using a square grid. There are good reasons for using a square grid, as numerous video games also do.) – SevenSidedDie Sep 20 '15 at 19:29

The way my group does this is by superimposing lines over the squares to approximate who gets hit. If the line goes over an icon at all, they get hit. Granted this is mostly for online play, but it works on tabletop as well, if you are willing to delay the game to get the exact cone shape overlayed.

As long as you use consistent rulings, it won't make much of a difference. D&D 3.5 had rules for fitting grid spaces, which created non anti-aliased triangles rather than cones, so you'll always have to compromise somewhat when using a grid and curved geometries.

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