What exact dimensions does a physical cone AoE template need to have?

Question

I am trying to get a precise set of measurements for cone-shaped areas of effect so that I can craft a physical template to use as an overlay when playing with miniatures. I want to get it right the first time.

The problem is that the rules for the shape of a cone AoE aren't very precise, and when you start looking at them closely, there are a bunch of inconsistencies. These are “good enough” when playing without a grid, or when only needing a grid-shaped approximation of the area of effect, but they are causing me difficulties with crafting an accurate physical template.

There are three incompatible interpretations of the maximum length of a cone (PHB, p. 204; emphasis mine):

A cone's area of effect specifies its maximum length.

… which each lead to slightly different template constructions (using a 30' length as the working example):

1. You can use the maximum length as the centreline of an isosceles triangle.

   This would give a template that has a centreline 30' long, but edges beyond the “maximum” length that are ~33.5' long. The end of the area of effect would be a flat plane. This shape would encourage players to aim off-centre to use the “bonus” length offered by the edges.

2. You can use the maximum length as the edges of an isosceles triangle.

   This would give a template with no portion farther than the maximum away, but with a centreline length that is only ~27.8'. The end of the area of effect would be a flat plane. This shape would motivate players to do off-centre aiming in order to get full use of the maximum-length edges of the template.

3. You can use the maximum length as a radius of a conical section of a sphere (a spherical cone).

   This would result in a template with a rounded end, with all points on that arc exactly the maximum length away from the point of origin.

Which of these interpretations of the definition of a cone's area of effect is the correct one to base my template design and construction on?

Answer 1

Which of these interpretations of the definition of a cone's area of effect is the correct one to base my template design and construction on?

Answer: Option 1

You say:

The problem is that the rules for the shape of a cone AoE aren't very precise, and when you start looking at them closely, there are a bunch of inconsistencies.

and

There are three incompatible interpretations of the maximum length of a cone

I disagree. It is clear what precise shape they describe, and it is the simplest way to describe and use a cone area of effect in this game, particularly given (but not limited to) the game supports the use of a grid and miniatures. It is quick to use, easy to understand, does not require a calculator or trigonometry, is difficult to argue about and you can draw it easily on any scale.

The rules as written:

Areas of effect (PHB p.204)

A spell’s effect expands in straight lines from the point of origin.

Cone (PHB p.204)

A cone extends in a direction you choose from its point of origin. A cone’s width at a given point along its length is equal to that point’s distance from the point of origin. A cone’s area of effect specifies its maximum length.

There is also a picture on that page showing the shape produced.

Areas of effect (DMG 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.

Explaining how these rules work together, the process to follow when defining a cone area of effect is:

• Choose an intersection of squares/hexes as the point of origin - i.e. a corner of a square, often the one the caster is standing in;

• Draw a straight line away from the origin of the effect to the range of the spell as stated in the description. This is always in multiples of 5', the size of a standard square on a D&D map, in your example 30', which is 6 standard sized squares/hexes on a grid;

• The width, or more accurately diameter, of the cone at any point along the line above is equal to the distance from the point of effect at that point. As an example this means that at 10', or 2 standard squares, along the line from the origin the cone is 10', or 2 standard squares, wide.

• This implicitly defines a flat bottomed cone, as shown in the diagram on p.204 (though you have to be careful with illustrations, in this case it is accurate). It has a width at it's furthest extent along the straight line equal to the length of that line. A 30' cone will extend 6 squares from its origin and be 6 squares wide at it's fullest extent. All straight lines, no curves.

This precisely describes option 1.

Option 2 and option 3 are definitely not what the RAW describe.

As to encouraging players to cast "off centre", yes of course. A player will probably set the orientation of an area of effect to maximise the number of targets whatever the rules are. They will do it to reduce the amount of unwanted collateral damage as well.

As a related aside, it is important to remember that a grid (if used) is a meta-game guide and does not exist for the characters in the game world in any way, so there is no "correct" orientation for them, just the one that reaches/effects the desired target(s).

DM judgement is required when the cone is not cast parallel to the ground or if the ground is not flat. The DM will have to adjudge what is effected but I strongly suggest you avoid too much discussion and definitely avoid calculators and trigonometry. It should be done as much as possible "by eye" and what is fun and good for the game rather than what is exactly precise. The DM should use the following rule to decide if any parts of the area of effect are blocked:

Areas of effect (PHB p.204)

A spell’s effect expands in straight lines from the point of origin. If no unblocked straight line extends from the point of origin to a location within the area of effect, that location isn’t included in the spell’s area. To block one of these imaginary lines, an obstruction must provide total cover

Answer 2

Option 1 is correct.

Let me quote the first sentence of the Cone description:

A cone extends in a direction you choose from its point of origin.

That is, the cone is defined by the direction you shot it in, which is the axis of the cone. As such, it makes the most sense to refer to the other properties of the cone in terms of the axis. And indeed, the next sentence describes the width of the cone at any given point in terms of its length. The only previous direction specified is the direction you're aiming the cone.

Whichever way you go, the purpose here is to decide whether or not a given target is inside the cone. If you are using the optional grid rules from DMG 250, then all of your math is rounded to the nearest square. In any of your options, the margin of error is about half a square for the 30' template. Coincidentally, the margin of error for DM judgement is also about a half square.

If you're still having trouble deciding, then my suggestion would be to cut out (or draw in a CAD program) the actual candidate arcs and overlay them to see how different they actually are. I think you'll find the difference is minimal.

Finally, remember that turnabout is fair play. If you do let that Burning Hands 30' cone stretch out to 33.5' at the edges, then the red dragon's fire breath will as well.

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Side note: if you were to use option 2, the width at any given point along that length would still depend on that point's distance from the origin. This would result in a slightly fatter cone than approach 1.

Answer 3

If you use the simple geometry suggested in the PHB, this is simple.

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

So at 5' out, it's one square wide, at 10' out, it's 2 squares wide, at 15' out, it's 3 squares, and so on. See the two examples on the left side of the picture below for simple, straight lines.

Shooting out at 45 degrees gets a bit more tricky, as the distances go horizontal and vertical, but at each distance away, if you are 6 squares out, there are six total squares horizontally and vertically from that point.

Answer 4

Similar to CultOfTheD20's answer, I drew a picture. The blue are 15' cones, green extending to 30' cones. No matter the angle you hit approximately the same number of squares.

1. Determine your ending center point (at cone length)
2. Determine the end points of the far edge (half the length to either side)
3. Draw the triangle back to the origin

Squares more than half covered are hit. Squares that are iffy fall to DM's discretion.