The real world physics (and a little chemistry) of a Fireball spell

The most important question for a GM (or other players) to ask when the party spellcaster enthusiastically yells, “I cast Fireball,” is “are you sure about that?”

Let’s start with some context: IRL, one of the things I do is volunteer as a firefighter, so I have a little bit of experience at observing fire behaviour outdoors, and have seen more than enough training video about fire behaviour in enclosed spaces to be very wary of it. I've also both GMed and played when Fireball has been cast and the physics and chemistry of what should happen not been considered; the magic fire just burns. Even better, I have been at the hot end of a Fireball going off when a clever DM did understand the consequences and let the party experience them first hand.

As one of the defining spells of the D&D experience, Fireball is going to be cast by one of your game’s magic wielders at some point. But have you, or they, considered how fire and explosions behave, and what that explosion might do if it’s not in the middle of an open field?

Let's quickly take a look at what the current 5e and 5.5e descriptions of Fireball have to say.

The 2014 Player's Handbook block for Fireball reads:

So far, so uncontroversial. How about the 2024 version (which is the same in the SRD 5.2.1, as expected):

So, similar enough to the 2014 version so as to make minimal difference for this post's purposes, except that it doesn't mention the spread effect, which will be an important part of the discussion below.

For the purposes of the sourcebooks, and playing the game rules-as-written, Fireball would appear to manifest, burst into flame, and vanish, more or less instantly. However, if you want to play a more interesting and realistic homebrew, I've done some description and analysis below that you might want to use whole cloth or in part.

A little sulfur and a little bat guano. What's happening here? In terms of the incendiary and explosive chemistry it's important.

Sulfur is flammable, and this property has been known and understood in written texts since pre-Christian times. It was certainly being used by the Chinese as a component for black powder by 808 AD. Chemically, gunpowder deflagrates (burns slowly) rather than detonating. Sulfur here is acting as a fuel and accelerant.

Bat guano has been used in Mesoamercian civilisations as a crop fertiliser for over 1000 years, and in the West since the early 1800s. It is a rich source of nitrogen, potassium, and phosphates. Guano can be processed in kilns to produce potassium nitrate (saltpetre, KNO₃), another major component of gunpowder.

In combination, sulfur and potassium nitrate are two of the principal components for gunpowder (along with carbon). The sulfur reduces the temperature necessary for ignition and serves as a fuel and the potassium nitrate breaks down during the ignition reaction to provide oxygen.

For D&D purposes, let's assume that our two components form a magical, carbonless gunpowder under high pressure and containment (that's how you get gunpowder to detonate rather than deflagrate) that ignites rapidly (thanks, sulfur) and changes state from compressed solid to aerosilised powder or gas and burns hot and fast (thanks potassium nitrate).

At this point we have a basic chemical how for a Fireball. It's the what happens where this starts to get interesting. To horribly misquote Douglas Adams in The Hitchhiker's Guide to the Galaxy:

The sourcebooks have always described Fireball as a "20' radius sphere". That's fucking enormous. By comparison, a 10m diving platform tops out a hair under 33'. Imagine a ball of fire with x, y, and z axes all larger than the height of a diving platform.

But how big are we really talking? The volume of a sphere with radius 20' (~6.1m) can be calculated with the formula:

V=4/3πr3

Wolfram Alpha tells us that's 33,510ft³, which is 948.9m³ in not-USA numbers. Here's where the bat guano hits the fan.

The spell description states, "[a] bright streak flashes from you to a point you choose within range and then blossoms with a low roar into a fiery explosion." Based on the physics and chemistry that we're very much glossing over here, but paying a little more attention to the firefighting training I've received, a few things are happening. Let's enumerate them:

1. The sulfur and guano are somehow being thrown out in a highly contained, compressed, and mixed form to as much as 150' (45.72m) away, at which point, some form of magical ignition (that we can choose to ignore the actual chemistry of for the purpose of this post) occurs.
2. The ignition of the spell's material components potentially does two things that cause the "low roar":
   • the material components rapidly expand into a cloud of flammable aerosolised powder or vapour that fills the 40' sphere in the instant before ignition and we're hearing the outward displacement of air and would feel that as wind moving past us if we were close enough, and;
   • at the instant of ignition, the nascent fireball, undergoing a state transition, draws in oxygen from the surrounding air to act as feedstock for the explosion and we're hearing that air move toward the ignition point and would again feel the wind from this as air moving from behind us toward the spell (assuming we're facing it).
3. The cloud that has expanded (we're not going to do the science for the Ideal Gas Law, as I last did this kind of physics in high school and I'm a writer and designer by trade, not a physicist) to fill the volume it is in and as described above, the cloud ignites from the centre of the spell and burns rapidly outward.

Now, if we're in an open field, an arena, a large temple, a big cave or other large open space we're doing okay here and our spell goes off doing the expected 8d6 damage to whatever foe happens to be standing in the way.

But we're not here for the easy way out, are we?

Ground burst or air burst?

As we've postulated above, the cloud of gas or dust that is the fuel for the fireball expands and fills the available space evenly out from the point of origin. Again, if we're in a big open space and we cast that point of origin to be 20' or more above the ground, we get a standard Fireball. In explosive terms, that's an air burst.

But how often in our games are we in places like that when we feel the need to cast terrifying death flames? Not often I'll warrant. Far more frequently, we're somewhere at least partially enclosed.

So, what's going to happen? I'm glad you asked.

From our math above, we learned we generate 33 thousand-ish cubic feet of fire once the Fireball goes off. Exciting! If we think about that in terms of D&D's stereotypical map of 10' cubes, that's 33-and-a-bit of those cubes we're about to fill with fire. Thanks to the generosity of Dyson Logos, we have a wealth of maps we can demonstrate this on, but let's choose this one - The Ancient Temple of Torrel. Let's make some helpful assumptions about this map and place ourselves and some foes on the map:

• the squares on the map are 5', so a human, or human-sized creature, fills one square
• the hall, as drawn, is 70' long and 15' wide, and while we don't have a definitive ceiling height, let's decide it's also 10' high (as it's a subterranean excavation), that gives the room a total volume of 10,500ft³, or 31.3 per cent of the volume of a Fireball
• 10ft³ is an area 2x2 squares and 2 squares tall, with a total volume of 1,000ft³, so the blast fills 33½ cubes

Our party is made up of :

• Nekkolir Rubyborn, a 5th level dwarven paladin with 29hp
• Vaktith, a 6th level silver dragonborn cleric with 25hp
• Thogaxon, a 6th level tiefling rogue with 24hp
• a 5th level gnome wizard by the name of Flamdoosip, rocking 20hp

They have just emerged from the stairs connecting Level 1 to Level 2 and entered the large hall on the second level. At the far end of the hall, their presence has disturbed a pair of now-irritated minotaurs, who look to be about to engage. Initiative is calculated, and for whatever reason the Fates have chosen, our friend Flamdoosip goes first, announcing, "I cast Fireball!"

At this point, our DM, aware of the discussion we've been having here, and a touch amused by the chance of a TPK through misadventure (and inclined to allow a do-over if things go very badly), lets the spell be cast, asking where the wizard is casting the origin point.

While blessed with good Intelligence, our wizard has low Wisdom, his player having chosen that as a dump stat. He targets the spell to the wall between the columns behind the minotaurs, and 10' off the floor, as it's the furthest point available in the hall. Not the worst decision in the circumstances; he's allowed for the radius of the sphere to be far enough away not to blow back on the party, but has completely failed to account for the fact they are in an enclosed space.

Loosing a Fireball in this space results in what is effectively a ground burst. The fireball has nowhere to go except expand out from the wall and into any nook or cranny it can find. Shit is, as they say, about to go down.

Let's see how much space this fireball takes up. As we know, it has a volume of 33,510ft³, or 33½ 10'x10'x10' cubes. Real-world physics indicates that the aerosol/vapour will fill out to any place it can. If it ignites in the process, the flaming ball will behave similarly. The pressure wave and flame from the blast will smash open doors, climb the stairs to level 1 and descend the stairs to Level 3.

What does that look like (I don't have the skill to animate this, so you're going to have to be satisfied with the after version)?

The image below shows the spread on Level 2. I've decided the pressure wave can't blow counter-swung doors out, though in reality, it probably would. I've also not mapped the effect on Levels 1 and 3, so the spread shown is about 75% of the full potential spread.

The 2024 Player's Handbook states that Fireball deals equal damage to all creatures in the blast, so rolling we get 29hp damage. There's a chance to reduce damage to half with a successful Dexterity saving throw.

Let's see how those saves go against the DC 15 Flamdoosip casts at. For simplicity, I'm going to assume each monster and character has the stats either in their 2024 Monster Manual stat block or the standard class array on p38 of the 2024 Player's Handbook:

• Jason, our first minotaur with 75hp, rolls a 2 and takes the full force of the blast, reducing him to 46hp
• Kylie, our second minotaur with 76hp, rolls 6 and also gets the entire load, reducing her to 47hp
• Nekkolir, the closest member of the party to the ignition has a Dex of 10 and no modifiers, rolls 16 for a successful save and takes 14hp damage, reducing him to 15hp
• Thogaxon has a Dex of 15 for +2 and rolls a 7, resulting in a modified 9 and is reduced to 0hp
• Vaktith has a Dex of 8—a -1 modifier—and rolls 13, a modified 12 and is also at 0hp
• Flamdoosip, our trigger-happy caster with a Dex of 12 for a +1 modifier, rolls a 14 and tops it up to 15, saving and taking 14hp damage, leaving him with 6hp