[RPG] What exact dimensions does a physical cone AoE template need to have

area-of-effectdnd-5eminiaturespropsspells

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):

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.
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.
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?

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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

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[RPG] Can a lake of eternal fire be created with the spell blast of flame

The spell creates fire and projects it away from you in a cone. The difference between this spell and, say, fireball, is that the fire is no longer magical once it's projected, and thus overcomes Spell Resistance.

Natural fires require fuel to maintain themselves for long. Once the spell is no longer maintaining the flame, it should quickly dissipate, assuming it wasn't cast into a field of dry grass or over a pool of oil. Note that lesser acid orb from Complete Arcane and Spell Compendium is also Conjuration(Creation) with an Instantaneous duration and creates neither an object nor a creature, simply a (non-magical, after leaving the caster) spell effect.

Orb of force is clearly meant to work like orb of acid, although this explanation is going to belong more on Physics.SE than RPG.SE. Force, in real world physics, is transferred between objects when they touch. Ergo, rather than "breaking" or "bouncing off", an orb composed entirely of force should be absorbed by a target (or by the ground or scenery on a miss) on impact. This is what does the damage of the spell - raw kinetic force being transferred to a relatively-stationary target.

Of course, the spell in this case probably shouldn't have the [Force] descriptor, as DnD [Force] has absolutely nothing to do with real-world force, as indicated by the fact that [Force] has full effect on incorporeal creatures and force should have none. If you (or your DM) want to rule orbs of [Force] continue to exist after striking a ghost or object, go for it. (However, both [Force] and force can be assumed to be weightless and noncorporeal, so rather than falling to the ground or filling a ball pit, they should probably keeping bouncing like that one scene in Men in Black until it escapes to outer space...)

[RPG] How does orienting a cube-shaped spell work in three-dimensional space

This can get surprisingly complicated.

So the first point is, you don't need to use any grid at all. In that case, rotating the cube is natural and you are right with the \$L\sqrt 3\$ diagonal case.

If you do use the grid however, it gets muddy. Dnd measures distances not in normal way, but just as a maximum of coordinates (this is a weird way of saying that diagonal movement costs the same as non-diagonal).

So either you sort of rotate the grid temporarily (in your head) to figure out the area of effect, in which case it works the same as the fist case, even though now you distance from the target is only \$L\$.

Or the grid stays and then you start studying the theory of metric spaces to figure out how does a cube in this situation even look like. The easiest to imagine would be the 45° rotation (2D) case, in which (C- caster, T-Target):

   X
  XXX  
CXXXXT
  XXX
   X

Or to be more srict with the rules about origin and faces (the caster is by the south-west face facing towards north-east):

   X
  XXX  
 XXXXT
C XXX
   X

Notice how the diagonal is 5 squares (or 25 feet) long, while the side is 3. But this feels a bit cheatsy since the concept of cube here is not very well defined.

Finally, note that DMG p.249 has rules/guidelines on how many targets does each shape "usually" hit for theater-of-mind and similar approaches. For Cube it states size/5 (round up), so 15 ft cube gives you around 3 affected targets (in situations where exact positioning is not a top priority).

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This can get surprisingly complicated.

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