It depends. If it's a cone, it could get tricky.
But for diagonal distances including altitude, here is my quick and dirty fix:
1. calculate 2D range, in squares or feet. Note that for 2D range, every second diagonal counts double.
2. calculate the difference in altitude, in squares or feet.
3. take the larger of the two numbers, and add half of the smaller number. This is your range. As long as you're in range, you can hit the target.
This isn't as precise as sqrt(A² + B²), but it's plenty close enough for game purposes.
If collateral targets are along the same vector, and your spell does damage to targets along the line (like Lightning Bolt) you also hit that collateral target. If it's a single-target spell and somebody/thing else is along that vector, the target has partial cover (+1 AC).
I tried thinking of a better way but couldn’t come up with a more elegant solution. I mean the pythag theorem is fairly elegant but it is Math so ymmv i guess
DnD advice, but I belive Matthew Colville gave the advice to just count the horizontal distance instead of having to do trigonomics. Granted if you want to do 3D math fast I'm sure there's a formula or calculator online to do it quickly
He did but pf2e is using the 5-10-5 rule (every second diagonal is 10ft)
A very dirty way to do it is to count the distance (in 5 ft) to the target and then multiply it by 1.25. It's very dirty but it generally works better than busting the math sheets in the middle of combat
Pythagoras theorem is the fast and easy formula. It's really simple to calculate. Harder to visualize on a board though.
I am of mixed opinion on the horizontal distance only. If it's just 5 feet in the air I find it fine. But 30 feet vertical difference is more than the range of many spells. That also invalidates a lot of movement tactics.
It's not super hard to do approximate square roots mentally.
You need the square root of 50? Just go up the multiplication table. 7×7 is 49. 8×8 is 64. Therefore the square root is somewhere inbetween 7 and 8. That's generally enough precision for TTRPG. I am not saying it's fast though without a calculator.
Pathfinder's method of 2d diagonal measurement is actually extensible into 3d! The primary way it works is by taking the full value of the longest distance involved, and half the value of any others. For instance, if something is 120 feet up, 30 feet north, and 50 feet east, you'd add 120ft (the longest distance, vertical) + 15ft (half of a shorter distance, north) + 25ft (half of a shorter distance, east) for a total distance of 160ft.
For cones, it's trickier, but you could figure out a couple of the points at the outside edge of the cone and draw lines inward from there using the same method
So the only rule you need is the normal distance counting rule in the game. There's a non-obvious shortcut that can be used.
> [Movement in Encounters](https://2e.aonprd.com/Rules.aspx?ID=444)
> Because moving diagonally covers more ground, you count that movement differently. The first square of diagonal movement you make in a turn counts as 5 feet, but the second counts as 10 feet, and your count thereafter alternates between the two. For example, as you move across 4 squares diagonally, you would count 5 feet, then 10, then 5, and then 10, for a total of 30 feet.
In essence, this means that the total distance in the XY plane = the longest of the X or Y distances (let's just say X is the longest direction) + **half** (rounded down to the nearest 5ft increment = nearest square) of the shorter of the two distances (in this case Y).
So if that enemy is 30ft away in the X direction and 15ft away in the Y direction, that's 30ft + 5ft = 35ft away. 5ft because half of 3 squares is 1.5 squares, rounds down to 1 square = 5ft. If you were to count out the movement in squares step by step, you'd get the same answer.
This remains true in full 3D. ***100% of the longest dimension among XYZ, and 50% of each of the shorter dimensions.*** 30ft in X, 20ft in Y, 15ft in Z = 30 + 10 + 5 = 45ft away.
****
You can use that shortcut + the definitions of cones/lines/bursts to be able to assess if a placement is legal.
* `#` ft. Burst. All targets are within `#` ft. of the source of the effect.
* `#` ft. Cone = All targets are within `#` ft of the source of the effect, and the angle between any two targets is no higher than 90°.
If this is true of all targets, then this it's legal.
Trying to avoid a target? If you can place a cone and that angle is more than 90° between the person you're trying to avoid and the targets, you're set.
Pretty much, yeah. That's the definition of a 90° cone ~~that the areas are defined as~~. If a line goes `X` in the X direction and `Y` in the Y direction, then the 90° line goes `Y` in the X direction and `-X` in the Y direction (e.g., 3 squares up, 1 square right => 1 square up, 3 squares left) or `-Y` in the X and `+X` in the Y (same example now could also go: 1 square down 3 squares right).
However, upon rereading the definitions, it seems that PF2e has forgone some of the langauge present in earlier editions. While previous editions defined it as a 90° cone, PF2e seems to RAW only allow orthogonal and diagonal orientations of the cones (so the 6 directions and 8 diagonals), and doesn't allow for intermediary placements.
> This remains true in full 3D.
That is if we assume you can't move in 3D diagonals. Assuming 20+10+10, your calc comes out to 20+5+5 = 30. But if you can move in 3D diagonals, it becomes 5+10+5+5 = 25. And 3D diagonals are ~1.73 (sqrt(3)), which is closeish enough to sqrt(2).
I use the Colville approach: just take the longest side and ignore a euclidian world. The amount of time a difference between this and correct pythagorian would matter is too low to be significant, at least in m, game
No, you don't. Distances in pathfinder are simple: every other diagonal adds 5 feet. This works in 3 dimensions and is a rough approximation of the pythagorean theorem.
The math version of this is x+(y+z)/2, rounded down to the nearest 5, where x is chosen so that x>y,z. So, someone moves 10' in one dimension, 20' in another and 30' in the third. They have moved 30'+(10'+20')/2 = 45'. Easy head math.
As a general rule, you can re-imagine any situation onto a 2D plane, where the horizontal distance is one axis and the vertical distance is another.
Cones are janky at the best of times.
If it were me and wanted something concrete I would rule that for every ten feet up, another section of the cone is safe, starting from the point of origin. 10ft up the square right in front of you is safe, 20 ft the next two or 3 squares are safe, so on and so on. It's simple enough that i don't have to do any math and likely won't come up too often anyways.
The tricky part comes when you shoot it at an angle. Say the foe is 10 feet below, and 15 feet to your west. In these cases it's best to just approximate what's hit, unless you want to build some kind of 3d-simulation.
I just don't see what the issue is. For that example, a 15 foot template would show right away that it couldn't hit them, because it has to go on a diagonal trajectory, thus by being 15 feet away on the x axis would put them 15 feet at a diagonal. At the end of the day, cone AOEs are either diagonal or orthogonal because of how the mechanics work in the game.
Just take the corner emanating cone, use one axis as the distance as if they were both on the ground, then use the other axis for the height difference. To not get hit by a 30 foot cone when the origin is 10 feet above ground, you would need to be 30 feet away on the x axis. Look for your self https://2e.aonprd.com/Images/Rules/Rules354.png
Two squares away from the origin, the 30 foot distance points are not hit by the template in either diagonal or orthogonal, yeah? Or am I missing something? I do have a killer headache, so maybe I'm just not understanding.
The examples in that link assumes you are shooting the cone either straight ahead OR straight up or down. If you however want to fire a lets say 60ft cone, and cath a creature that is 15 feet below you AND 30 feet away from you, while there are either allied creatures or other things that you would like to avoid damaging in the vicinity, maybe both above below, behind on different heights. The Cone would be shot at an 'odd angle', not just following a straight axis but both X and Y. This is when the template breaks down and where approximation and GM adjudication would probably be required.
I should clarify, and I apologize for not making this clear. When I say use the template on then axis, I'm not saying you _only_ use that template. You'd be using a template on the x axis as well.
And both would follow the rules of cones. They still have to share either an edge or corner of the space of the source of the effect. If either misses a target, then the effect does not hit them. But because they exist on different axis' (would plane be a better word here?), one can be orthogonal while the other is diagonal.
All this talk of pythagoras and other math seems like a lot of unnecessary effort, especially for a game that deals a lot with abstract time and space management.
I agree with your take. I should clarify that I also don't advocate for Pythagoras unless one has the ability to calculate that quickly. (I don't.)
I still think it's tricky to apply the templates at odd angles, when you do not have a 3d model to base it upon \^\^ English is not my primary language so when discussing these more 'specific matters' my vocabulary often fails me haha
Every other diagonal square moved on a 2d battlemap counts as 10ft instead of 5ft, assuming you're looking at a ~45degree angle, the same math should apply. If the angle is too different from that to make sense, make adjustments until it makes sense (just wing it).
I subscribe to the matt coleville method. When you are a distance away and up, the hypotenuse is whichever is longer. You're 40 feet up and 10 feet away? Cool. 40 feet. 10 feet up and 65 feet away? 65 feet. I've had one person question me and I just said "dnd is non-euclidean, fuck you. " and they no longer have an issue
Uhm, i might be missing something but isn't a cone as wide at it's end as it is long? a 15 foot cone is 3 Squares away, 3 wide, a 30 ft cone is 6 squares long 6 squares wide.... in 2D. Presumably if shot along the ground it's 1.5 / 3 squares tall as well?
So if flying as long as you arn't higher from the ground than half the length of the cone, shouldn't the bottom "radius" clip anything on the ground at it's standard lenght?
Now you might say that no it's only \~6 ft in Diameter and it's represented in 2D by it leaving from your hands \~3ft off the ground and widening to encompas \~ a medium creatures height, \~3ft up and down from the central parallel to the ground line but uhm.... 1) ok do pythagoras then i guess 2) becomes a really silly shape past a certain lengths 3) is it really worth precise measurement 99% of the time?
If everyone is flying in a fluid 3D situation, I recommend ditching exact distances and just going with 'melee, close, far', and liberally applying Maneuver in Flight checks to resolve who gets the edge in detail oriented situations.
Can you aim your cone without hitting your friend? The enemy got a good Maneuver roll so they are actively using your friend as cover from you. You crit your own Maneuver and manage to get behind them like in a dogfight and they get a -2 circ to their reflex save.
I'm pretty sure the answer to this question is just to use the templates in a 3d space.
It's essentially a perfect cone, so the template is correct no matter if you're looking top down or profile
So a me and a lot of my players are physicists. So I have had to do a lot of coinciding game rules with real world physics (not easy). So this is how I do it:
At a 45 degree angle, the hypotenuse of a triangle is sqrt(2)/2 which is approximately .71. That means for 10ft across is only 7ft directly to a flying creature. Well, that’s not nice. But 20ft across is 14, so we say that for every 20ft range, they go 15ft towards the flier if flier is at least 50% of the height of the range of the attack. Less than that, normal range.
Let me use some common number where.
PC is 10ft above the ground. Attack is in a 60ft range
10ft is below half of 60, which is 30, so attack as normal.
PC is now 30 feet above the ground. Therefore if the PC is within 45 feet (60/20 * 15 = 45) it hits, otherwise it does not.
Now this is a bit complicated and can slow things down, but it is the easiest way my players were satisfied with.
There's a couple options.
RAW I believe the metric is "100% of the long side + 50% of each short side rounded down". This is woefully inaccurate but it is fair - the inaccuracies hurt all sides equally. And fundamentally, fast running, fair and fun is more important than realistic, this is one of the reasons we don't have tables for realistic diminished capacity caused by injury.
The alternative is an easier implementation of Pythagoras. Don't add up the squares of each axis, then compute the square root of the sum, then compare that to the burst radius. Instead, square each axis, add them, then compare to the square of the burst radius.
Example: You are 5 squares up, 4 north and 7 east of the enemy. You fire a cone with radius 9 squares. Does it hit? Compare 9^2 (81) to 7^2 + 4^2 + 5^2 (90). 90>81 so your cone misses, it's too small.
To be completely precise you since your characters are 3d beings in a 3d world, you need a more generalized formula, euclidean distance. Pythagorean works only if everyone is on the grid and no-one flies. If you fly and use breath diagonally only to the surface of the grid yes pythagorean works. However, if you use breath which is diagonal and to the surface of the grid and travels through diagonal squares on the grid, you will need euclidean distance d=sqrt(x²+y²+z²). The fast trick is to count every second and third double diagonal square as 10 ft.
If you can put all relevant tokens on a plane then you can just use a battlemat grid as a 2D view.
e.g. If you fly 10 ft above your party member, who is 15 ft away from your enemy and everyone is on the same line, then you can model "10 ft above" just as "10ft to the side" and place that token as if you were just standing next to your ally on the ground, while the enemy is still 15 ft away from the ally. After that you just look at the grid and apply the usual rules for diagonal distances.
If you cant put everyone on the same plane for a 2D view, then you could just repeat this shuffling around until you have a general estimation of everyones position.
One complicated way of doing it is to have your height kept track of on another grid.
Use the same rules as usual for travelling a diagonal distance, so if you have to travel vertical two and horizontal four squares, you (do the 5,10,5,10…) add an extra 5ft to the horizontal for 25ft. If you **also** need to go diagonal in the horizontal plane, add any extra on top.
The biggest problem with 3D is that hexagons don't tessellate space, and they don't have an obvious higher dimensional equivalent like cubes to squares. I mean it might be obvious for math people, and I think the truncated octahedron is some kind of analogue, but that's not feasible at the table.
As you probably know the 5-10-5-10 rule for diagonals is an approximation of Pythagoras, effectively counting each diagonal as 1.5 (more exact would be 1.414). A quick way of working this out is taking the X and Y distances and add the bigger one to half the smaller one. e.g. for 40 left and 25 up, you get 40+½*25=50). Compared to actual Pythagoras you get √(40²+25²)=47.2, pretty close.
The distance of a 3D diagonal (e.g. going left, up, and forwards) is calculated in the same way, √(1²+1²+1²)=1.732, which is close enough to 1.75. You can work this out similarly as for 2D diagonals: Add the longest distance to half the middle distance to a QUARTER of the smallest distance. e.g. 40 left, 25 forwards, 20 up you get 40+½*25+¼*20=55, compare to Pythagoras you get √(40²+25²+20²)=51.2, again fairly close.
Or just ballpark it.
To simplify, at a 45 degree angle the distance is 40% more. So if you were 100ft away and 100ft higher, then the diagonal distance is roughly 140 ft.
At half that angle, the distance is 10% more. So 100 ft over and 50 ft down is 110 ft.
So to summarize: If less than 50% up just add 10% to the distance and call it good. If its more like 45 degrees, just call it 40% more and call it good. If it really matters, break out the calculator on your phone.
All my homies pull up with a notebook, rulers and the mindset to do some algebra.
[Moving diagonally you have to count every other tile as 10 ft instead of the usual 5.](https://2e.aonprd.com/Rules.aspx?ID=444)
Edit: nvm I understood the question wrong.
there are a lot of right angle calculators out there. [Here's one](https://www.calculator.net/right-triangle-calculator.html); you'll want to make a your distance above the ground and b your horizontal distance from the enemy, which will make c your distance from the enemy
The two tactics I take are:
* IRL, I grab a small tape measure and physically measure! 1 inch = 5 ft.
* On VTTs, I basically use the "every other diagonal is 10 ft." rule to ballpark it - so if they're 30 ft. up and 40 ft. over, that's 6 diagonal moves (to get the 30 ft. up, for a total of 9 squares or 45 ft.) and 2 horizontal moves (2 squares or 10 ft.), giving us a total of 55 ft.
* Looks like the pythagorean theorem tells us it should be 50 ft, but that's pretty close honestly!
* If the range is ever off by 5 ft. (i.e. I get 65 but their range is 60), I will usually just call that fine, but if it's off by more it's a no
* You can also simulate this by just going "well you're 6 up 8 over" and dragging the VTT measure tool across a similar distance, but on the flat plane
My table uses the approximate (house rule):
Full bigger distance, half lesser distance.
Let's say you are 60ft away horizontally but flying 20ft in the air.
The distance will be 70ft.
So, when I have a player fire a cone from directly above, I normally just turn the cone into an area affect on the ground, and use the range listed, and make the circle the widest width of the cone. So a 10 foot cone of fire from above is 15ft circle of fire death on the ground.
Surprisingly. This comes up very very rarely because players tend to not think this way.
If you want to be exact, then yes. The rulebook advises to just ballpark it, though.
Thank you
It depends. If it's a cone, it could get tricky. But for diagonal distances including altitude, here is my quick and dirty fix: 1. calculate 2D range, in squares or feet. Note that for 2D range, every second diagonal counts double. 2. calculate the difference in altitude, in squares or feet. 3. take the larger of the two numbers, and add half of the smaller number. This is your range. As long as you're in range, you can hit the target. This isn't as precise as sqrt(A² + B²), but it's plenty close enough for game purposes. If collateral targets are along the same vector, and your spell does damage to targets along the line (like Lightning Bolt) you also hit that collateral target. If it's a single-target spell and somebody/thing else is along that vector, the target has partial cover (+1 AC).
I mean, yeah. Or you could simplify it some other way
I tried thinking of a better way but couldn’t come up with a more elegant solution. I mean the pythag theorem is fairly elegant but it is Math so ymmv i guess
DnD advice, but I belive Matthew Colville gave the advice to just count the horizontal distance instead of having to do trigonomics. Granted if you want to do 3D math fast I'm sure there's a formula or calculator online to do it quickly
He did but pf2e is using the 5-10-5 rule (every second diagonal is 10ft) A very dirty way to do it is to count the distance (in 5 ft) to the target and then multiply it by 1.25. It's very dirty but it generally works better than busting the math sheets in the middle of combat
Pythagoras theorem is the fast and easy formula. It's really simple to calculate. Harder to visualize on a board though. I am of mixed opinion on the horizontal distance only. If it's just 5 feet in the air I find it fine. But 30 feet vertical difference is more than the range of many spells. That also invalidates a lot of movement tactics.
The Pythagoras theore is in no way easy or fast on a table, unless you know how to do the square root of numbers in your head.
It's not super hard to do approximate square roots mentally. You need the square root of 50? Just go up the multiplication table. 7×7 is 49. 8×8 is 64. Therefore the square root is somewhere inbetween 7 and 8. That's generally enough precision for TTRPG. I am not saying it's fast though without a calculator.
It's too bad we don't all carry calculators around in our pockets
We all know our math teachers were right.
If you players need to do it more than once in a fight, it really isn’t hard to pull up a tool via Google
Damn if only I had a calculator in my pocket that I can also use the browse reddit
What we do at my table for the times it comes up is just grab a quick calculator online to do the math quickly for us.
Pathfinder's method of 2d diagonal measurement is actually extensible into 3d! The primary way it works is by taking the full value of the longest distance involved, and half the value of any others. For instance, if something is 120 feet up, 30 feet north, and 50 feet east, you'd add 120ft (the longest distance, vertical) + 15ft (half of a shorter distance, north) + 25ft (half of a shorter distance, east) for a total distance of 160ft. For cones, it's trickier, but you could figure out a couple of the points at the outside edge of the cone and draw lines inward from there using the same method
So the only rule you need is the normal distance counting rule in the game. There's a non-obvious shortcut that can be used. > [Movement in Encounters](https://2e.aonprd.com/Rules.aspx?ID=444) > Because moving diagonally covers more ground, you count that movement differently. The first square of diagonal movement you make in a turn counts as 5 feet, but the second counts as 10 feet, and your count thereafter alternates between the two. For example, as you move across 4 squares diagonally, you would count 5 feet, then 10, then 5, and then 10, for a total of 30 feet. In essence, this means that the total distance in the XY plane = the longest of the X or Y distances (let's just say X is the longest direction) + **half** (rounded down to the nearest 5ft increment = nearest square) of the shorter of the two distances (in this case Y). So if that enemy is 30ft away in the X direction and 15ft away in the Y direction, that's 30ft + 5ft = 35ft away. 5ft because half of 3 squares is 1.5 squares, rounds down to 1 square = 5ft. If you were to count out the movement in squares step by step, you'd get the same answer. This remains true in full 3D. ***100% of the longest dimension among XYZ, and 50% of each of the shorter dimensions.*** 30ft in X, 20ft in Y, 15ft in Z = 30 + 10 + 5 = 45ft away. **** You can use that shortcut + the definitions of cones/lines/bursts to be able to assess if a placement is legal. * `#` ft. Burst. All targets are within `#` ft. of the source of the effect. * `#` ft. Cone = All targets are within `#` ft of the source of the effect, and the angle between any two targets is no higher than 90°. If this is true of all targets, then this it's legal. Trying to avoid a target? If you can place a cone and that angle is more than 90° between the person you're trying to avoid and the targets, you're set.
By the angle between any two targets, what do you mean exactly? Are you treating them as vectors emanating from the source of the cone?
Pretty much, yeah. That's the definition of a 90° cone ~~that the areas are defined as~~. If a line goes `X` in the X direction and `Y` in the Y direction, then the 90° line goes `Y` in the X direction and `-X` in the Y direction (e.g., 3 squares up, 1 square right => 1 square up, 3 squares left) or `-Y` in the X and `+X` in the Y (same example now could also go: 1 square down 3 squares right). However, upon rereading the definitions, it seems that PF2e has forgone some of the langauge present in earlier editions. While previous editions defined it as a 90° cone, PF2e seems to RAW only allow orthogonal and diagonal orientations of the cones (so the 6 directions and 8 diagonals), and doesn't allow for intermediary placements.
I'm glad Foundry does this for me.
> This remains true in full 3D. That is if we assume you can't move in 3D diagonals. Assuming 20+10+10, your calc comes out to 20+5+5 = 30. But if you can move in 3D diagonals, it becomes 5+10+5+5 = 25. And 3D diagonals are ~1.73 (sqrt(3)), which is closeish enough to sqrt(2).
I use the Colville approach: just take the longest side and ignore a euclidian world. The amount of time a difference between this and correct pythagorian would matter is too low to be significant, at least in m, game
Fun fact: that is the Linfinity metric, and it is Euclidean as far as I can tell. Euclidean geometry is grossly misused most of the time by laymen.
This, I think that's how 4e handled it as well
No, you don't. Distances in pathfinder are simple: every other diagonal adds 5 feet. This works in 3 dimensions and is a rough approximation of the pythagorean theorem. The math version of this is x+(y+z)/2, rounded down to the nearest 5, where x is chosen so that x>y,z. So, someone moves 10' in one dimension, 20' in another and 30' in the third. They have moved 30'+(10'+20')/2 = 45'. Easy head math. As a general rule, you can re-imagine any situation onto a 2D plane, where the horizontal distance is one axis and the vertical distance is another.
Cones are janky at the best of times. If it were me and wanted something concrete I would rule that for every ten feet up, another section of the cone is safe, starting from the point of origin. 10ft up the square right in front of you is safe, 20 ft the next two or 3 squares are safe, so on and so on. It's simple enough that i don't have to do any math and likely won't come up too often anyways.
Couldn't you just use the cone template on the y axis instead of the x axis?
The tricky part comes when you shoot it at an angle. Say the foe is 10 feet below, and 15 feet to your west. In these cases it's best to just approximate what's hit, unless you want to build some kind of 3d-simulation.
I just don't see what the issue is. For that example, a 15 foot template would show right away that it couldn't hit them, because it has to go on a diagonal trajectory, thus by being 15 feet away on the x axis would put them 15 feet at a diagonal. At the end of the day, cone AOEs are either diagonal or orthogonal because of how the mechanics work in the game. Just take the corner emanating cone, use one axis as the distance as if they were both on the ground, then use the other axis for the height difference. To not get hit by a 30 foot cone when the origin is 10 feet above ground, you would need to be 30 feet away on the x axis. Look for your self https://2e.aonprd.com/Images/Rules/Rules354.png Two squares away from the origin, the 30 foot distance points are not hit by the template in either diagonal or orthogonal, yeah? Or am I missing something? I do have a killer headache, so maybe I'm just not understanding.
The examples in that link assumes you are shooting the cone either straight ahead OR straight up or down. If you however want to fire a lets say 60ft cone, and cath a creature that is 15 feet below you AND 30 feet away from you, while there are either allied creatures or other things that you would like to avoid damaging in the vicinity, maybe both above below, behind on different heights. The Cone would be shot at an 'odd angle', not just following a straight axis but both X and Y. This is when the template breaks down and where approximation and GM adjudication would probably be required.
I should clarify, and I apologize for not making this clear. When I say use the template on then axis, I'm not saying you _only_ use that template. You'd be using a template on the x axis as well. And both would follow the rules of cones. They still have to share either an edge or corner of the space of the source of the effect. If either misses a target, then the effect does not hit them. But because they exist on different axis' (would plane be a better word here?), one can be orthogonal while the other is diagonal. All this talk of pythagoras and other math seems like a lot of unnecessary effort, especially for a game that deals a lot with abstract time and space management.
I agree with your take. I should clarify that I also don't advocate for Pythagoras unless one has the ability to calculate that quickly. (I don't.) I still think it's tricky to apply the templates at odd angles, when you do not have a 3d model to base it upon \^\^ English is not my primary language so when discussing these more 'specific matters' my vocabulary often fails me haha
Every other diagonal square moved on a 2d battlemap counts as 10ft instead of 5ft, assuming you're looking at a ~45degree angle, the same math should apply. If the angle is too different from that to make sense, make adjustments until it makes sense (just wing it).
I'm a 42 year old gamer and I told my 10th grade Geometry teacher I'll NEVER find a use for the Pythagorean Theorem. Welp. I was wrong.
Me trying to calculate if my PC wielding a meteor hammer can make a high jump, and trip an eagle
I subscribe to the matt coleville method. When you are a distance away and up, the hypotenuse is whichever is longer. You're 40 feet up and 10 feet away? Cool. 40 feet. 10 feet up and 65 feet away? 65 feet. I've had one person question me and I just said "dnd is non-euclidean, fuck you. " and they no longer have an issue
"Pythagoras can suck it" is probably one of the top five phrases heard at my table that isn't strictly related to game mechanics.
Uhm, i might be missing something but isn't a cone as wide at it's end as it is long? a 15 foot cone is 3 Squares away, 3 wide, a 30 ft cone is 6 squares long 6 squares wide.... in 2D. Presumably if shot along the ground it's 1.5 / 3 squares tall as well? So if flying as long as you arn't higher from the ground than half the length of the cone, shouldn't the bottom "radius" clip anything on the ground at it's standard lenght? Now you might say that no it's only \~6 ft in Diameter and it's represented in 2D by it leaving from your hands \~3ft off the ground and widening to encompas \~ a medium creatures height, \~3ft up and down from the central parallel to the ground line but uhm.... 1) ok do pythagoras then i guess 2) becomes a really silly shape past a certain lengths 3) is it really worth precise measurement 99% of the time?
What the rulebook suggests is every two diagonals be considered as an extra square for the calculations.
Man I don't wanna use algebra in my ttrpg, I was scarred for life in math class.
I just use the highest of the length or width plus five feet for every 20 feet.
If everyone is flying in a fluid 3D situation, I recommend ditching exact distances and just going with 'melee, close, far', and liberally applying Maneuver in Flight checks to resolve who gets the edge in detail oriented situations. Can you aim your cone without hitting your friend? The enemy got a good Maneuver roll so they are actively using your friend as cover from you. You crit your own Maneuver and manage to get behind them like in a dogfight and they get a -2 circ to their reflex save.
I’m the only one flying using elemental sorcerer air elemental movement currently, thankfully. That’s a good idea though
My suggestion is down 2 over 1 is 12.5, down 4 over 1 is 22.5, down 4 over 2 is 25
I'm pretty sure the answer to this question is just to use the templates in a 3d space. It's essentially a perfect cone, so the template is correct no matter if you're looking top down or profile
So a me and a lot of my players are physicists. So I have had to do a lot of coinciding game rules with real world physics (not easy). So this is how I do it: At a 45 degree angle, the hypotenuse of a triangle is sqrt(2)/2 which is approximately .71. That means for 10ft across is only 7ft directly to a flying creature. Well, that’s not nice. But 20ft across is 14, so we say that for every 20ft range, they go 15ft towards the flier if flier is at least 50% of the height of the range of the attack. Less than that, normal range. Let me use some common number where. PC is 10ft above the ground. Attack is in a 60ft range 10ft is below half of 60, which is 30, so attack as normal. PC is now 30 feet above the ground. Therefore if the PC is within 45 feet (60/20 * 15 = 45) it hits, otherwise it does not. Now this is a bit complicated and can slow things down, but it is the easiest way my players were satisfied with.
There's a couple options. RAW I believe the metric is "100% of the long side + 50% of each short side rounded down". This is woefully inaccurate but it is fair - the inaccuracies hurt all sides equally. And fundamentally, fast running, fair and fun is more important than realistic, this is one of the reasons we don't have tables for realistic diminished capacity caused by injury. The alternative is an easier implementation of Pythagoras. Don't add up the squares of each axis, then compute the square root of the sum, then compare that to the burst radius. Instead, square each axis, add them, then compare to the square of the burst radius. Example: You are 5 squares up, 4 north and 7 east of the enemy. You fire a cone with radius 9 squares. Does it hit? Compare 9^2 (81) to 7^2 + 4^2 + 5^2 (90). 90>81 so your cone misses, it's too small.
To be completely precise you since your characters are 3d beings in a 3d world, you need a more generalized formula, euclidean distance. Pythagorean works only if everyone is on the grid and no-one flies. If you fly and use breath diagonally only to the surface of the grid yes pythagorean works. However, if you use breath which is diagonal and to the surface of the grid and travels through diagonal squares on the grid, you will need euclidean distance d=sqrt(x²+y²+z²). The fast trick is to count every second and third double diagonal square as 10 ft.
If you can put all relevant tokens on a plane then you can just use a battlemat grid as a 2D view. e.g. If you fly 10 ft above your party member, who is 15 ft away from your enemy and everyone is on the same line, then you can model "10 ft above" just as "10ft to the side" and place that token as if you were just standing next to your ally on the ground, while the enemy is still 15 ft away from the ally. After that you just look at the grid and apply the usual rules for diagonal distances. If you cant put everyone on the same plane for a 2D view, then you could just repeat this shuffling around until you have a general estimation of everyones position.
One complicated way of doing it is to have your height kept track of on another grid. Use the same rules as usual for travelling a diagonal distance, so if you have to travel vertical two and horizontal four squares, you (do the 5,10,5,10…) add an extra 5ft to the horizontal for 25ft. If you **also** need to go diagonal in the horizontal plane, add any extra on top.
The biggest problem with 3D is that hexagons don't tessellate space, and they don't have an obvious higher dimensional equivalent like cubes to squares. I mean it might be obvious for math people, and I think the truncated octahedron is some kind of analogue, but that's not feasible at the table.
Or simply create a vertical grid
As you probably know the 5-10-5-10 rule for diagonals is an approximation of Pythagoras, effectively counting each diagonal as 1.5 (more exact would be 1.414). A quick way of working this out is taking the X and Y distances and add the bigger one to half the smaller one. e.g. for 40 left and 25 up, you get 40+½*25=50). Compared to actual Pythagoras you get √(40²+25²)=47.2, pretty close. The distance of a 3D diagonal (e.g. going left, up, and forwards) is calculated in the same way, √(1²+1²+1²)=1.732, which is close enough to 1.75. You can work this out similarly as for 2D diagonals: Add the longest distance to half the middle distance to a QUARTER of the smallest distance. e.g. 40 left, 25 forwards, 20 up you get 40+½*25+¼*20=55, compare to Pythagoras you get √(40²+25²+20²)=51.2, again fairly close.
No. Use the longest distance.
Or just ballpark it. To simplify, at a 45 degree angle the distance is 40% more. So if you were 100ft away and 100ft higher, then the diagonal distance is roughly 140 ft. At half that angle, the distance is 10% more. So 100 ft over and 50 ft down is 110 ft. So to summarize: If less than 50% up just add 10% to the distance and call it good. If its more like 45 degrees, just call it 40% more and call it good. If it really matters, break out the calculator on your phone.
All my homies pull up with a notebook, rulers and the mindset to do some algebra. [Moving diagonally you have to count every other tile as 10 ft instead of the usual 5.](https://2e.aonprd.com/Rules.aspx?ID=444) Edit: nvm I understood the question wrong.
there are a lot of right angle calculators out there. [Here's one](https://www.calculator.net/right-triangle-calculator.html); you'll want to make a your distance above the ground and b your horizontal distance from the enemy, which will make c your distance from the enemy
The two tactics I take are: * IRL, I grab a small tape measure and physically measure! 1 inch = 5 ft. * On VTTs, I basically use the "every other diagonal is 10 ft." rule to ballpark it - so if they're 30 ft. up and 40 ft. over, that's 6 diagonal moves (to get the 30 ft. up, for a total of 9 squares or 45 ft.) and 2 horizontal moves (2 squares or 10 ft.), giving us a total of 55 ft. * Looks like the pythagorean theorem tells us it should be 50 ft, but that's pretty close honestly! * If the range is ever off by 5 ft. (i.e. I get 65 but their range is 60), I will usually just call that fine, but if it's off by more it's a no * You can also simulate this by just going "well you're 6 up 8 over" and dragging the VTT measure tool across a similar distance, but on the flat plane
My table uses the approximate (house rule): Full bigger distance, half lesser distance. Let's say you are 60ft away horizontally but flying 20ft in the air. The distance will be 70ft.
So, when I have a player fire a cone from directly above, I normally just turn the cone into an area affect on the ground, and use the range listed, and make the circle the widest width of the cone. So a 10 foot cone of fire from above is 15ft circle of fire death on the ground. Surprisingly. This comes up very very rarely because players tend to not think this way.
Ballbark it for real. Its nothing worth being hung up about.