As you all know I am playing as a dragonborn, which is cool because normally I play humans or elves in fantasy games so the change is welcomed. The main reason I chose dragonborn was because of the breath weapon. It’s a fun ability and can deal a lot of damage in the early levels of D&D 5e.
When choosing your draconic ancestry as a dragonborn, you have a decision between what type of damage you’d like to do (and have resistance to!) as well as what type of AoE attack you would like it to be. I wrote a post detailing what the best draconic ancestry is for you min-maxers out there!
A grid gives us a 2-D view of the battlefield. We are going to assume that the grid accounts for each square being 5 ft. by 5 ft. or 25 sq ft. in size.
We are not accounting for how high the line or the cone will reach, simply because well, it’s irrelevant. Everything can be done on a 2-dimensional plane because we are hitting enemies in front of us in some way. All we care about is if the Dragon Breath will reach them at all.
Our Breath Weapon Choices
Breath Weapon: a 5 by 30ft. line OR a 15ft cone
The damage type choice is not the point of this post, but we’ll say Fire as it can be easily compared in this post since it has a choice of being a line or a cone. This is where the geometry portion of the post comes into play.
Which one will do more damage? Trick question, they both do the same damage dice!
Which one covers more space and subsequently will hit more enemies and therefore do more damage? That’s the question we’ll hopefully have an answer to.
This will require us to find the area of each shape. Now we’ll have to simplify the cone quite a bit, but thankfully the player’s handbook and some other D&D resources did all that for us.
We also must consider that we are going to be comparing both of the Breath Weapons in their largest form, meaning that they will not be shot diagonally, but instead from a cardinal direction (N, S, E, W) so they will not lose any area.
The 5 x 30 ft. Line
The 5 x 30ft line is extremely easy. The formula is given to us in the name. The line is not exactly a line, but a rectangle. It is a rectangle because it has 4 sides. The width is 5ft on both sides of the line, and the length is 30ft long on both sides. A rectangle is a shape with 2 sets of parallel sides (4 sides total) and this matches the description perfectly. Therefore the formula is simply the area formula of a rectangle:
Area of a Rectangle = base x height
The base, in this case, is the width, and the height is the length.
The 15 ft. Cone
I tried quite a few different equations to determine the area of the cone, but the numbers never came out correctly. Then I read the rules on cones in the spellcasting section of the Player’s Handbook.
“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.” -pg 186
This means that a cone in D&D rules is not a formula, but a summation (a few numbers added together). The further the fire travels out of the Dragonborn’s mouth, the more it expands. It adds a block of space on our grid for each block it travels until it reaches the end of its length of 15ft. This will be easier to explain by doing the math out rather than attempting to make a formula.
5 ft. x 30 ft. Line Math
Let’s start with the easy math. The 5 x 30 ft. line of fire would be a dragonborn of brass draconic ancestry. According to our formula, we’d have to find the length and the width to find the area. Well, thankfully this part is plain as day so we have our values right from the get-go. Let’s plug in our values to the equation and solve:
Brass Dragon Breath Weapon = 5 ft. x 30 ft. line of fire damage
= 150 sq ft. of fire damage
So, the line will hit 150 square feet worth of enemies. That’s a pretty decent-sized line. Since we’re using a grid, this means that it’s 6 squares long if we shoot it in a straight line. Below this paragraph is a great visual of what I’m talking about.
15 ft. Cone Math
If we decided to choose gold or red draconic ancestry, we’d have a 15 ft. cone of fire as our Breath Weapon. This means that our cone begins at the mouth and extends out 15 ft. (height) and has a diameter of 15 ft. at its base.
The 5e Player’s Handbook has laid out the rules for how cones work in D&D. Essentially, the further the fire travels out of the dragonborn’s mouth, the more it expands. Therefore we add a block of space on our grid for each block the Breath Weapon travels until it reaches the end of its length of 15 ft.:
Gold/Red Dragon Breath Weapon = 5 ft. * 1 block + 10 ft. * 2 blocks + 15 ft. * 3 blocks = 150 sq ft of fire damage
150 sq ft. of fire damage? That means it’s still only 6 blocks of space. Unlike other editions of D&D angles are no longer considered when shooting out a cone attack. Instead, you use the specified length of the cone to determine how many blocks are in the last line of the cone.
It’s difficult to explain in words, so check out the diagrams I made down below.
Which is better?
No matter how you aim for either attack you’ll be able to hit a maximum of 6 squares of creatures. Mathematically speaking, they’re equal so neither of which is necessarily better.
In practice, however, I feel that the 15 ft. cone gives you the most bang for your buck, especially as a front-line character. You’re able to get in the thick of things and can have more opportunities for groups of enemies to swarm in front of you.
As shown by the diagrams you also get a bit more creativity with the 15 ft. cone. You can decide where to put that second set of squares. Either on the right or the left. The 5 x 30 ft. cone is more at the mercy of the space that you’re in and you don’t have as many different ways to shoot the breath weapon.
That being said, if you are in a hallway the 5 x 30 ft. will be able to reach much further down the hallway than the cone could at 15 ft.
Unfortunately, this is one of those scenarios where better is subjective. My personal preference is going to be the cone attack, but there’s no theoretical difference.