Equation for Realistic Falling Damage 5E

[Koningkrush]

Using the average weight and surface area of a Medium creature, I calculated approximations for distances beyond 200 feet to terminal velocity at around 1800 to 2000 feet. After staring at the Joules I came up with for a couple hours trying to think of how to convert them into damage dice, I decided to use the typical 1d6 for 10 feet, and 8d6 for 90 feet. I did this because 90 feet is the border line where death starts to become nearly certain for a typical human. 8d6 is on average 28 damage, and a commoner at 10 hp instantly dies from 20 damage.

I could make a table, but I'm not going to make 180-200 table entries for every 10 feet. In general, the book is fairly accurate with from 10 to 200 feet. Shortly beyond 200 feet, the damage goes up by 1d6 every 20 feet instead of 10. It eventually rapidly tapers off from every 30 feet to every 60 feet to 200 feet to 10000 feet etc. as terminal velocity approaches. I just use a graphing calculator, an equation solver online, or something similar to enter this in and type in a value for X (distance) to find the damage die count rounded to the nearest whole number.

One note is that this equation is highly accurate up to around 2000 feet. Beyond that however, it exponentially skyrockets if you calculate damage beyond the typical distance for terminal velocity, so just don't enter a value over 2000.

Here it is:

Y = 0.000000019X^3 - 0.00008X^2 + 0.1127X - 0.03

Damage caps out at about 58d6 for an average of 203 damage. Your level 20 fighters and barbarians might have a chance of falling from space and driving head first through a mountain top, but I doubt it (unless a barbarian uses rage to be so angry at the ground that he ends up taking 100 damage instead).

[MaxWilson]

Damage caps out at about 58d6 for an average of 203 damage. Your level 20 fighters and barbarians might have a chance of falling from space and driving head first through a mountain top, but I doubt it (unless a barbarian uses rage to be so angry at the ground that he ends up taking 100 damage instead).

203 damage is very survivable still, between Inspiring Leader, high-level Aid spells, and the fact that PCs in 5E don't insta-die unless you bring them to full negative HP in one hit. By 20th level, even a Wizard can probably take 203 damage without dying. In fact, after six seconds with a healing kit and a Healer (via feat), he'll be back on his feet and walking around.

This says some interesting things about D&D biology and physics--as does the fact that mice and elephants both take the same amount of damage from falling. One wonders whether objects in D&D actually fall at a constant velocity--maybe smaller things fall faster? Perhaps Galileo's experiments would have given a different result in D&D-land...

[Koningkrush]

There would be different damage values depending on the size. Like I said, this is for medium creatures. Redoing the calculations for all sizes just felt like a headache. If necessary, you could increase or decrease the die from d6 to d4, d8, d10, etc for higher sizes.

D&D is a world of magic, so I do expect level 20 characters to be approaching Demigod status by defying traditional physics. If this isn't your style, just say characters automatically die after 200 feet or so.

[Nifft]

I don't think there is any way to get "realism" to co-habitate in the same world as hit points.

[Mellack]

There would be different damage values depending on the size. Like I said, this is for medium creatures. Redoing the calculations for all sizes just felt like a headache. If necessary, you could increase or decrease the die from d6 to d4, d8, d10, etc for higher sizes.

D&D is a world of magic, so I do expect level 20 characters to be approaching Demigod status by defying traditional physics. If this isn't your style, just say characters automatically die after 200 feet or so.

As you say, it is a world of magic, not physics. You are making assumptions about the D&D world based on our world rules, not theirs. Their world has Pi = 4, so you have to be careful trying to make it a tie in too closely to ours.

[pwykersotz]

As you say, it is a world of magic, not physics. You are making assumptions about the D&D world based on our world rules, not theirs. Their world has Pi = 4, so you have to be careful trying to make it a tie in too closely to ours.

Slight tangent, I use the opposite approach. The rules simulate reality closely enough for a meaningful adventure to happen. That means some things like pi=4 only exist because we don't care to examine it closely enough. But if something important with relation to those calculations is brought up, it is examined in real-world applications. Like Boyle's Law and such.

I tried the rules-as-physics approach before. It was way too much overhead and it made the game too far out of touch in my opinion.

[Malifice]

203 damage is very survivable still, between Inspiring Leader, high-level Aid spells, and the fact that PCs in 5E don't insta-die unless you bring them to full negative HP in one hit. By 20th level, even a Wizard can probably take 203 damage without dying. In fact, after six seconds with a healing kit and a Healer (via feat), he'll be back on his feet and walking around.

This says some interesting things about D&D biology and physics--as does the fact that mice and elephants both take the same amount of damage from falling. One wonders whether objects in D&D actually fall at a constant velocity--maybe smaller things fall faster? Perhaps Galileo's experiments would have given a different result in D&D-land...

No, it doesnt.

You lose hit points from falling. Hit points are not merely bodily toughness. Hit points are a pool of a persons 'luck, resolve, the will to live and heath'. Losing hit points is akin to spending a fate point in WHFRP 1E - i.e. when a 20th level epic hero falls from a mountain, some lucky contrivance saves his life.

Like a giant eagle swooping in to save him at the last minute, his magic items warding him from being obliterated from the fall, getting snagged on a dead tree and dangling precariously etc.

If you want to houserule 'hit points' as 'meat only' and somehow interpret some kind of weird physics or starfish like biology from that feel free.

[Douche]

203 damage is very survivable still, between Inspiring Leader

Now you've got me picturing a guy giving an inspiring speech to himself & allies how they are going to survive the fall if they just work as a team and believe in themselves!

[CaptAl]

I understand the desire to make the game more "real". I just feel like falling is a rather ignominious way for a hero to die. That's why the rules for falling are just kind of glossed over. If you die because you made a poor choice (refusing to run from that Ancient Red Dragon at level 4) at least you have a possible story to tell. Having your high level character botch an Acrobatics check and die from falling off a cliff isn't fun or compelling. I don't need real world physics to explain a fall when disintegrate spells, water walking monks, and regenerating trolls exist in my game world.

[Douche]

I understand the desire to make the game more "real". I just feel like falling is a rather ignominious way for a hero to die. That's why the rules for falling are just kind of glossed over. If you die because you made a poor choice (refusing to run from that Ancient Red Dragon at level 4) at least you have a possible story to tell. Having your high level character botch an Acrobatics check and die from falling off a cliff isn't fun or compelling. I don't need real world physics to explain a fall when disintegrate spells, water walking monks, and regenerating trolls exist in my game world.

The Witcher 3 had realistic fall damage. If you dropped from like 10-15 feet without rolling after you hit the ground, you'd take like 1/2 your health bar worth of damage. Lethal falls were like 20 feet, lol. People on the forums complained soooo much about it. It's actually kind of funny.

[CaptAl]

The Witcher 3 had realistic fall damage. If you dropped from like 10-15 feet without rolling after you hit the ground, you'd take like 1/2 your health bar worth of damage. Lethal falls were like 20 feet, lol. People on the forums complained soooo much about it. It's actually kind of funny.

Just not very heroic to trip off a one story house and find yourself talking to your god about being clumsy. Too much real world isn't good, or we'd not need the games.

[RulesJD]

https://en.wikipedia.org/wiki/Juliane_Koepcke

Apparently level 20 Barbarians come in the form of middle-aged women from Peru.

[Slipperychicken]

I don't think there is any way to get "realism" to co-habitate in the same world as hit points.

The dnd universe already needs a pretty alien system of natural laws for its basic premises to be possible. Even before you mention magic, a good portion of monsters shouldn't be able to hold up their own weight in earth gravity.

I'd rather not enforce ideas about real-world physics only in ways that erode class balance without adding anything meaningful.

If we wanted to implement the idea that high falls always kill, we could even skip the math and go with the chunky salsa rule. If you fall out of an airplane onto something hard with no way to soften the fall, then you go splat, end of story.

[JoeJ]

If we wanted to implement the idea that high falls always kill, we could even skip the math and go with the chunky salsa rule. If you fall out of an airplane onto something hard with no way to soften the fall, then you go splat, end of story.

That reminds me of the wonderful (and system agnostic) lava rules (http://www.scratchfactory.com/Resources/LavaBanners/LavaRules.pdf).

[pwykersotz]

That reminds me of the wonderful (and system agnostic) lava rules (http://www.scratchfactory.com/Resources/LavaBanners/LavaRules.pdf).

I love those rules! I spent weeks hyping them to an old GM and then sent him the PDF. He facepalmed so hard I could hear it a city away. :smalltongue:

[bardo]

Damage caps out at about 58d6 for an average of 203 damage.

Let's be honest here... you're just trying to stop players from jumping off cliffs and surviving. Realism, if you'd excuse the pun, is out the window.

You're using the exact same wildly unrealistic approach as RAW: "fall damage = F(distance fallen)*d6", just tweaking F and removing the 20d6 cap to get more damage. This does not improve on realism in any way. You're still pretending everybody falls at the same speed, you're still pretending the ground is the same hardness everywhere, and still ignoring dozens of other factors in the extremely complex dynamics of how a body hits the ground.

If we're going to talk about it, let's talk about your real concern. Tell me, what's wrong with letting players jump off a cliff and survive?

Off-topic, this reminded me of the examples of real-world falling that were listed in the AD&D 2nd Ed. PHB. A military guy who fell 18,000 ft. and walked away unharmed, and a flight attendant who fell from 33,000 ft. and survived. Turns out both examples are true.

Bardo.

[RulesJD]

Let's be honest here... you're just trying to stop players from jumping off cliffs and surviving. Realism, if you'd excuse the pun, is out the window.

You're using the exact same wildly unrealistic approach as RAW: "fall damage = F(distance fallen)*d6", just tweaking F and removing the 20d6 cap to get more damage. This does not improve on realism in any way. You're still pretending everybody falls at the same speed, you're still pretending the ground is the same hardness everywhere, and still ignoring dozens of other factors in the extremely complex dynamics of how a body hits the ground.

If we're going to talk about it, let's talk about your real concern. Tell me, what's wrong with letting players jump off a cliff and survive?

Off-topic, this reminded me of the examples of real-world falling that were listed in the AD&D 2nd Ed. PHB. A military guy who fell 18,000 ft. and walked away unharmed, and a flight attendant who fell from 33,000 ft. and survived. Turns out both examples are true.

Bardo.

By the same token, people trip on the sidewalk and die from hitting their head after falling no more than their own body height. Happens in bar fights all the time as well.

[bardo]

By the same token, people trip on the sidewalk and die from hitting their head after falling no more than their own body height. Happens in bar fights all the time as well.

And that's why bathtubs need anti-slip stickers. In game terms these are 0 ft. falls (just being knocked prone), but in reality they can prove fatal.

Bardo.

(edit grammar)

[Talamare]

Awesome, now calculate the wingspan needed for an Ancient Dragon to fly

[Slipperychicken]

By the same token, people trip on the sidewalk and die from hitting their head after falling no more than their own body height. Happens in bar fights all the time as well.
A surprising number of people also injure themselves or die falling out of bed. A friend of mine actually wound up with a cast on her wrist, despite her reflexes. Had her head struck the ground first, she could well have died. I've also known a number of people who have incurred serious injuries from slipping on ice and tumbling to the ground.


I'm starting to think there's a case to be made for D&D-land gravity simply being lower than real-world gravity. A fall less than 5 feet is not even worth mentioning in terms of harm to a person or an object (which could potentially kill someone or break something IRL), people can survive much greater falls than they would IRL, terminal velocity is lower, a relatively fit person can effortlessly leap a 10 or 15 foot wide chasm, and a regular human's anatomy can be scaled up to that of a giant without any real drawbacks from circulation or increased weight.

[RulesJD]

A surprising number of people also injure themselves or die falling out of bed. A friend of mine actually wound up with a cast on her wrist, despite her reflexes. Had her head struck the ground first, she could well have died. I've also known a number of people who have incurred serious injuries from slipping on ice and tumbling to the ground.


I'm starting to think there's a case to be made for D&D-land gravity simply being lower than real-world gravity. A fall less than 5 feet is not even worth mentioning in terms of harm to a person or an object (which could potentially kill someone or break something IRL), people can survive much greater falls than they would IRL, terminal velocity is lower, a relatively fit person can effortlessly leap a 10 or 15 foot wide chasm, and a regular human's anatomy can be scaled up to that of a giant without any real drawbacks from circulation or increased weight.

And wearing thick Plate armor doesn't impede your swimming, at all.

[Slipperychicken]

And wearing thick Plate armor doesn't impede your swimming, at all.

It does if your strength score is less than 15. Then you get -10 speed, which applies to walking, climbing, swimming, and jumping.


If you're using encumbrance, it's 65 pounds. Even for a character with 16 strength, that takes him most of the way to "Encumbered" (80lb limit for a str 16 character), after which point his speed drops by 10ft. The armor leaves just 15lb for a single weapon, shield, and maybe a backup weapon or some ammo. In armor, you're not swimming well with anything beyond the bare essentials for a fight, and you can forget about your full adventuring kit. There's a good reason RL knights had squires and pages with them: to carry all that other stuff!

[bardo]

And wearing thick Plate armor doesn't impede your swimming, at all.

Full plate armour is my swim team's uniform. It only drags you down if you're not proficient.

Bardo.

[JackPhoenix]

https://en.wikipedia.org/wiki/Juliane_Koepcke

Apparently level 20 Barbarians come in the form of middle-aged women from Peru.

That's nothing compared to https://en.wikipedia.org/wiki/Vesna_Vulovi%C4%87


A surprising number of people also injure themselves or die falling out of bed. A friend of mine actually wound up with a cast on her wrist, despite her reflexes. Had her head struck the ground first, she could well have died. I've also known a number of people who have incurred serious injuries from slipping on ice and tumbling to the ground.

My uncle died falling out of his bed. There was even police investigation about it (just few hours before he was helping us do something at home...he lived alone and his employer was worried when he didn't get to work the next day)

[REVISIONIST]

That's nothing compared to https://en.wikipedia.org/wiki/Vesna_Vulovi%C4%87



My uncle died falling out of his bed. There was even police investigation about it (just few hours before he was helping us do something at home...he lived alone and his employer was worried when he didn't get to work the next day)

Some people, if they are lucky, die in their bed. (Sorry about your uncle, JackPhoenix). I think the point is no hero or self respecting adventurer
wants to meet an ignomious end from fall damage. From my experience, fall damage is the threat a DM uses to get the players to rollplay/skill check.
If you lead the life of a mountain climber, B.A.S.E jumper, etc., that seems akin to an adventurer in D&D. Fall damage is the DM's way of getting the players to realize the "gravity" of their situation, and should just be used when and if the players are overextending the limits of what their characters ought to be doing, or should be doing.

[EvanescentHero]

One of the characters in my game died recently because an enemy (one of the big bads of the campaign) threw her unconscious body off a cliff.

The druid dove off the cliff after her, by the way, with no real plan besides "help Thane." She survived the fall by casting meld into stone as she hit the ground, but there wasn't anything she could do for the warlock besides revive her with a healing spell. Unfortunately the warlock was out of spells, so she couldn't save herself.

[Vogonjeltz]

203 damage is very survivable still, between Inspiring Leader, high-level Aid spells, and the fact that PCs in 5E don't insta-die unless you bring them to full negative HP in one hit. By 20th level, even a Wizard can probably take 203 damage without dying. In fact, after six seconds with a healing kit and a Healer (via feat), he'll be back on his feet and walking around.

This says some interesting things about D&D biology and physics--as does the fact that mice and elephants both take the same amount of damage from falling. One wonders whether objects in D&D actually fall at a constant velocity--maybe smaller things fall faster? Perhaps Galileo's experiments would have given a different result in D&D-land...

A level 20 Fighter averages 114.5 with an average (read: +0) Con bonus. So, that means on average they would not die instantly from a fall of that height. However, they'd definitely be dying. And absent the fairly absurd luck of having someone handy with a medical kit, and/or training, they'll probably expire. Although, presumably with Indomitable the Fighter has better chances of stabilizing than most.

A level 20 Wizard with an average Con bonus (+0), would average 51.5 hit points, and thus die instantly on average from the average impact. A fantastically tough Wizard could have a +5 Con bonus for 151.5 and be tough for another 40, or 191.5...which means on average they still are dying, but with only even chances of stabilizing. Bearing in mind, that's the healthiest Wizard of all time. If they had a full Abjuration shield, they'd even be able to walk it off, on average.

Of course, they'd probably be kicking themselves for weeks over not just memorizing Feather Fall, right?

[RulesJD]

A level 20 Fighter averages 114.5 with an average (read: +0) Con bonus. So, that means on average they would not die instantly from a fall of that height. However, they'd definitely be dying. And absent the fairly absurd luck of having someone handy with a medical kit, and/or training, they'll probably expire. Although, presumably with Indomitable the Fighter has better chances of stabilizing than most.

A level 20 Wizard with an average Con bonus (+0), would average 51.5 hit points, and thus die instantly on average from the average impact. A fantastically tough Wizard could have a +5 Con bonus for 151.5 and be tough for another 40, or 191.5...which means on average they still are dying, but with only even chances of stabilizing. Bearing in mind, that's the healthiest Wizard of all time. If they had a full Abjuration shield, they'd even be able to walk it off, on average.

Of course, they'd probably be kicking themselves for weeks over not just memorizing Feather Fall, right?

Do teleportation spells conserve momentum? If they don't, a simple Misty Step/Dimension Door and you're fine.

Alternatively, a Half-Orc anything (and some other class features) can survive a fall from almost any height so long as it doesn't do double their HP in damage.

[bardo]

A level 20 Fighter averages 114.5 with an average (read: +0) Con bonus.

Standard array is: 15, 14, 13, 12, 10, 8. Adds up to 72. You get at least 2 more points from racial modifiers, which brings us to 74. 74/6 = 12.33.

Average ability score at level 1 using standard array is 12.33.

Few (if any) builds dump CON so it's pretty safe to say the average CON score at level 1 is greater than 12.33. On a level 20 fighter, after 7 ASIs, a +0 modifier isn't average it's ridiculous.

Bardo.

[Koningkrush]

I usually see these kind of statements regarding falling damage and expected no different from this.

"There are people that have fallen out of airplanes and survived! How do you simulate that?"
Well, I roll this bucket of dice and, would you look at that, the majority of them are all 1s. It seems that you fell through 27 flocks of birds on your way down and went straight into a cart of cabbages to break your fall.

"You can die from a much shorter fall than terminal velocity."
Well, I roll this handful of dice and, would you look at that, they are all 6s. It seems you landed perpendicularly on your head into a stone surface.

"Well, you can do this, this, and this to survive and this class has this much HP so this is all flawed."
Well, isn't magic something.

[Koningkrush]

A story I could share related to falling, although not necessarily related to rules, is when a player decided to thunderwave me off a cliff when my Goliath Barbarian was suffering from a failed madness save lasting for 3 minutes (Attack the person closest to you).

I happened to be launched into another player, a druid, and we both ended up going down 60 feet.

The druid rolled his falling damage, and ended up with 4 sixes and 2 fives. He died instantly.
I rolled my damage and it ended up about 22 or so. I halved it from raging to 11. I reduced it to 0 using Stone Endurance.

As a result of the rolls, the DM said that the druid broke the fall of my 340 pound Goliath. I grunted and peeled myself from the crater I made.

[bardo]

As a result of the rolls, the DM said that the druid broke the fall of my 340 pound Goliath. I grunted and peeled myself from the crater I made.

That is some fine DMing work.

Bardo.

[Vogonjeltz]

Standard array is: 15, 14, 13, 12, 10, 8. Adds up to 72. You get at least 2 more points from racial modifiers, which brings us to 74. 74/6 = 12.33.

Average ability score at level 1 using standard array is 12.33.

Few (if any) builds dump CON so it's pretty safe to say the average CON score at level 1 is greater than 12.33. On a level 20 fighter, after 7 ASIs, a +0 modifier isn't average it's ridiculous.

Bardo.

I was referring to 10 as average as that is what the system refers to as average. Adventurers are, by their nature, above average people. If the Fighter had a maximum Con bonus then, on average, they'd survive. But that's just the peak of the bell curve, it doesn't mean always. There's a significant number of Fighters with averaged hp who would still die in such a situation.

[Slipperychicken]

The chance of 20d6 rolling 114 or higher is negligible. It's less than a thousandth of a percent.

Even if we roll the fighter's hp at 10 con (19d10+10) instead of taking average rolls, his chance of being KO'd from full health by a 20d6 fall is about a tenth of a percent.

In both cases, it is nearly impossible for the fighter to die outright from the fall, though an extremely slim chance exists that he's KO'd (20d6 rolls over the fighter's hp), and then the fighter proceeds to fail three death saves and dies.

[bardo]

I was referring to 10 as average as that is what the system refers to as average. Adventurers are, by their nature, above average people. If the Fighter had a maximum Con bonus then, on average, they'd survive. But that's just the peak of the bell curve, it doesn't mean always. There's a significant number of Fighters with averaged hp who would still die in such a situation.

You're applying the general population average to a subset of the population that is known (by you) to be well-above average. It is nonsense. The average person has CON 10, but it's not relevant in a discussion about 20th level fighters jumping off cliffs. Just like the average person is 5'4" tall, but it's not relevant in a discussion about the NBA all-star dunk contest.

Bardo.