How do I map a 15' cone to a 1" grid?

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?

• 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. Commented Aug 22, 2014 at 13:05

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:

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

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:

• Technically the 1/2 square rule for the effect to happen is only for circular areas of effects, there is no such rule for cones. (DMG p251). Still a good rule. Commented Jan 10, 2017 at 15:38
• I find this answer problematic, in that the point of origin of those cones are corners and edges of squares, instead of the middle of the square where the caster usually stands Commented Jan 12, 2020 at 13:40
• @Deltharis the DMG expressly states that an intersection should be chosen as the origin point of a spell. Commented Dec 19, 2020 at 18:10

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.

• Technically the 1/2 square rule for the effect to happen is only for circular areas of effects, there is no such rule for cones. (DMG p251). Still a good rule. Commented Jan 10, 2017 at 15:38

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.

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.

• "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). Commented Jan 13, 2015 at 15:10
• Cones in 5e are not 90° wide. That poses a problem with using the diagrams from 3.5e. Commented Aug 11, 2015 at 19:43

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.

• Wouldn't an equal distance to the point of origin create an equilateral triangle (three 60 degree angles) at any given point of the cone? Commented Jan 20, 2021 at 12:56

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.

• Hex maps do make movement in two of the cardinal directions slower. It is a drawback. Commented Sep 20, 2015 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.) Commented Sep 20, 2015 at 19:29
• @SevenSidedDie 5e cones are 60deg - if you draw a line down the middle of the cone, i.e. leave 30deg on either side, plain trigonometry says the perpendicular width at distance x in one direction is sine of 30deg times x - i.e. x/2, but you have two directions, i.e. x/2*2. So at distance x from the origin, a cone is x wide, exactly as 5e rules state. Commented Dec 30, 2020 at 0:16
• @EamonNerbonne I'm not sure where the error in your math is, but it fails a reality-check: an isosceles triangle with base of 5 facing a 60° angle is an equilateral triangle with sides of 5, which can't have a height of 5. The triangle you constructed (half the template) with A=5, B=2.5, ∠AB=90° should result in the other two angles being ~26.6° (not 30°) and ~63.4°. Double that inner angle and it's ~53°, not 60°. See this triangle calculator. Commented Dec 30, 2020 at 20:14
• @EamonNerbonne Oh, I see the error in your math. Sin(30°)*5 gets you the adjacent leg of the triangle, not the side opposite the angle. That's how you accidentally built an equilateral triangle. You wanted tan(30°)*5 to find the opposite length… which is ~2.88 before doubling—too wide. Commented Dec 30, 2020 at 20:29

As the variety of approaches here show, the rules for this aren't as clear as one might hope. Here's the understanding we have at our table.

First of all, the relevant rules from the Player's Handbook (p. 204) on the shape of a cone:

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.

A cone's point of origin is not included in the cone's area of effect, unless you decide otherwise.

One might expect that the rules from the Dungeon Master's Guide (p. 251) on translating areas to a grid might help:

Choose an intersection of squares of hexes as the point of origin or an area of effect, then follow its rules as normal. If an area of effect is circular and covers at least half a square, it affects that square.

But here we have our first bit of confusion: Is the area of effect of a cone circular? It is in 3-d space, but we usually only care about a 2-d grid projection. Honestly, even the bit about starting at an intersection seems weird to me, particularly for the spell Burning Hands that you're asking about that already states that "your outstretched fingertips" are the point of origin. So I'm mostly going to ignore the DMG rule, as I think it adds more confusion for this case than it solves.

Also, our group uses the "Optional Rule: Diagonals" (DMG p. 252), which alternates between counting 5 and 10 feet when counting diagonally. It makes the square root of 2 equal to 1½, which is certainly closer than the "core" grid rules give you (where it equals 1) and makes some of this math make a bit more sense.

So, now that we've looked at the rules, how do we apply them? In particular, the definition that "a cone's width at a given point along its length is equal to that point's distance from the point of origin" means I expect that a 15′ cone effect would cover 6 squares of the grid: 1 space (5′) away from you it should be 1 square (5′) wide, 2 spaces (10′) away from you it should be 2 squares (10′) wide, and 3 spaces (15′) away from you it should be 3 squares (15′) wide. And you could, if you wanted to, add a seventh square of yourself, if you choose to include the point of origin in the cone's area of effect.

Since we're on a grid, I'm fine with limiting direction to one of the eight "main" directions, either adjacent or diagonal to you. Let's start with going in an adjacent direction:

Of course, this can be mirrored (with box 2B north of 2A instead of south of it), or rotated in 90° increments to any of the 4 adjacent directions. Here's my logic for why this works:

• Box 1 is 5 feet away from the caster, and it's 5 feet wide.
• Boxes 2A and 2B are 10 feet away from the caster, and the effect is 10 feet wide at that point.
• Boxes 3A, 3B, and 3C are 15 feet away from the caster, and the effect is 15 feet wide at that point.

Certainly this is a bit of an "intuitive" approach, and not based on overlaying a triangle on the grid or anything, but I think it works with the way D&D does "grid math", with squares the correct distance away being affected.

If you want to "designate a corner" to try to apply the DMG rule, I think calling the effect emanating from the northwest or southwest corners of square 1 makes some amount of sense, but like I said I don't think doing so adds a lot of clarification.

What if the caster wants to go diagonally? Here's how I see it working:

Again of course, rotate in 90° increments to go to a different diagonal.

• Box 1 is 5 feet away from the caster, counting diagonally, and as just itself it's 5 feet wide.
• Boxes 2A and 2B are 10 feet away from the caster, and as they're each 5 feet away from each other, and there's two squares, the cone is 10 feet wide at that point.
• Boxes 3A, 3B, and 3C are 15 feet away from the caster. (And this is why using the diagonal option is helpful, so that 3B is 15 feet away and not 10.) The cone could be considered a bit too wide here, as 3A is 15 feet away from 3C (meaning that the total "width" could be considered 20 feet, of the 5 feet of one square plus the 15 feet it takes to get to the other side). However, as it's three squares, each 15 feet away from the caster, I think it makes the most sense. And if you weren't using the Diagonals optional rule, then the width of the cone there would be 15 feet.

If your group wanted to have the caster omit one of squares 3A or 3C when casting diagonally, I could certainly see that making some sense, but my instinct is to just allow it so that there are three squares affected 15′ away.

At least diagonally it's clear which corner the effect emanates from for the DMG rule.

Again, this is more based on counting and intuition rather than geometry, but using a grid with D&D in general seems to be based more on counting squares than trying to measure like a tactical wargame. Working like this works well enough for our group.