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 such as this only concerns a 2D 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 comparable 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.
Our Formulas
Basically 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 Line
The 5 x 30ft line is extremely easy. In fact the formula is given to us in the name. Basically, 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 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 pertaining to 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 only 6 blocks in area again. Since we are not shooting it diagonally we do not lose any area and add the point of origin to the area of effect. That’s 7 blocks if we shoot it in a cardinal direction! Check it out in the graphic below!
Which is better?
If we use our Breath Weapon in a cardinal direction we are able to clip more boxes with it. Therefore, we can hit 7 enemies instead of 6. Clearly the cone is the best then.
Not so fast! If we shoot our cone diagonally we will end up hitting 6 enemies just like the 5 x 30ft line. Plus, the cone will only hit things a maximum distance of 15ft away from it. The line doubles the distance, but does sacrifice the width to do so.
I guess it depends on how you want to position yourself. If you are in an open room and can get up close and personal with the enemy without much fear of friendly fire (literally) hitting a companion in melee range of your target, the cone is CONSIDERABLY better.
If you are in a hallway the 5 x 30ft will be able to reach much further down the hallway than the cone could at 15ft.
So if we’re going by our goal of finding what mathematically will inflict the most amount of damage for the enemy, a 15ft cone shot directly in front of you or to your side will do the most potential damage because it will hit 7 blocks instead of 6.
Originally published at dungeonsolvers.com on June 4, 2015.
