Hello everyone. You may not see me around much, since this here is quite the only reason why people even know... let's just get on with why this exists.

__Premise:__[]

__Premise:__

Just going to exclaim this out right now, this in no way is created to discredit the calculation that we use the Average Mountain Destruction blog we currently use for most feats regarding mountains being destroyed in many fictions that do that. I personally believe as a placeholder for it, it's not bad. But if I were to be personally honest, especially since I brought the concept up in my own blog, I feel like I have an obligation to say what I believe. The calculation itself uses pixel scaling to figure out the radius of the base. Not to say there's anything wrong with pixel scaling, but let's remember this factor. Most Mountain Destruction feats either have a visual or don't. If they have visuals, then go ahead and figure out the radius via pixel scaling. But I am focusing on the situation where no such luxury exists, where it is a statement that has been approved to be legitimate, but no given visual to be able to figure the volume of the Mountain. Since such a specific radius in the standard Mountain Destruction blog we currently use can't just suddenly apply to every Mountain. But there is something we can do about it.

__Solution:__[]

__Solution:__

As I brought in my own blog regarding Mountains, I brought up this concept called angle of repose which basically describes the idea that the steepest angle of descent or dip relative to the horizontal plane to which a material can be piled without slumping. This leads me to believe that long standing mountains won't have an average angle of more than 45°. Hence, following trigonometry leads me to assume that the radius of the Mountain is equal to its height.

__Calculation:__[]

__Calculation:__

Now from this point, it would be a simple get the volume, have the Destruction Values at the draw, and be done, right? Well, it's a bit more complicated about that. You see, what people don't tell you is, get this, it's up in the air what even is the Standard Height of Mountains. On one hand, the wiki currently sees that 609.6 meters to be the minimum height for Mountains, which is backed up by the UK government's and Whittow's Dictionary of Physical Geography definition of the Minimum requirement. But then again, geologists would point out that some definitions also include a topographical prominence requirement, such as that the mountain rises 300 metres (984 ft) above the surrounding terrain. Even at one point, the U.S. Board on Geographic Names defined a mountain as being 1,000 feet (305 m) or taller but has abandoned the definition since the 1970s and left it in the air what the minimum requirement is. However, the UN Environmental Programme's definition includes these as the following for a "mountainous environment". It also goes as far as to say anything lower than 300 meters isn't considered a mountainous environment. With that being said, I won't be picking sides, but instead be giving both options to see whether or not one is preferred over the other. With that all being said, let's now begin.

__Volume for Mountain of 300 meters height__: pi*300^2*(300/3) = 28274333.8823 m^3 or 2.827433e+13 cm^3

__Volume for Mountain of 609.6 meters height__: pi*609.6^2*(609.6/3) = 237226659.27 m^3 or 2.37227e+14 cm^3

__Destruction Yields for a 300 m Mountain:__[]

__Destruction Yields for a 300 m Mountain:__

- Fragmentation (8 J/cc) = 2.2619467e14 Joules,
**Town level+** - Violent Fragmentation (69 J/cc) = 1.950929e15 Joules,
**Large Town level** - Pulverization (214 J/cc) = 6.05070745e15 Joules,
**Small City level** - Vaporization (25700 J/cc) = 7.2665038e17 Joules,
**Mountain level**

__Destruction Yields for a 609.6 m Mountain:__[]

__Destruction Yields for a 609.6 m Mountain:__

- Fragmentation (8 J/cc) = 1.897816e15 Joules,
**Large Town level** - Violent Fragmentation (69 J/cc) = 1.6368663e16 Joules,
**Small City level+** - Pulverization (214 J/cc) = 5.0766505e16 Joules,
**City level** - Vaporization (25700 J/cc) = 6.0967339e18 Joules,
**Mountain level**

While I am at it, why not include the Minimum height for Japanese Mountains because Lord knows how many Manga/Anime/LN/etc. are going to pull that off. Anyways, their generally accepted definition for a Mountain is 1000 meters, so yeah.

__Volume for Minimum Height of a Japanese Mountain:__ (1/3)*pi*1000^2*1000 = 1.04719755e9 m^3 or 1.04719755e15 cm^3

__Destruction Yields for minimum requirement of a Japanese Mountain:__[]

__Destruction Yields for minimum requirement of a Japanese Mountain:__

- Fragmentation (8 J/cc) = 8.37758e15 Joules,
**Small City level** - Violent Fragmentation (69 J/cc) = 7.2256631e16 Joules,
**City level** - Pulverization (214.35 J/cc) = 2.241002757e17 Joules,
**City level+** - Vaporization (25700 J/cc) = 2.6912977e19 Joules,
**Island level**

__EDIT: Trigonometry Edition__[]

__EDIT: Trigonometry Edition__

Now this was something I thought about for a long time ever since introducing it to this blog. This will also be tackling the idea of steeper mountains and much... wider mountains that the base calculation won't be able to cover, so this would be something to dispel that uncertainty. That very concept would be something I would ask in a question: *What about mountains that didn't follow the 45°-45°-90° triangle?* Now, I will be introducing the 30°-60°-90° triangle!!!

Now, I did say that triangles with two 45° angles have an equal radius to their height, but what do we do with right triangles with 30° and 60° angles with only the height of the right triangle? Well, there are options we have:

- base = height × tan(β); β is the angle closest to the height.
- base = height ÷ tan(α); α is the angle opposite to the height.

Honestly, you can use any of them as both are equally interchangeable, but I will use both for the sake of an example. Starting with the 300-meter tall mountain.

*Radius of 300 m Mountain (Steep):*300 × tan(30) = 173.2050808 meters*Radius of 300 m Mountain (Wide):*300 × tan(60) = 519.61524227 meters

Now for the classic Mountain Height.

*Radius of 609.6 m Mountain (Steep):*609.6 ÷ tan(60) = 351.9527241 meters*Radius of 609.6 m Mountain (Wide):*609.6 ÷ tan(30) = 1055.8581723 meters

And for the Japanese Mountains, just in case.

*Radius of Japanese Mountain (Steep):*1000 × tan(30) = 577.3502692 meters*Radius of Japanese Mountain (Wide):*1000 ÷ tan(30) = 1732.0508076 meters

Now time to crunch for the volumes.

__Volume for Mountains of 300 meters in height__:[]

- Steep Mountain: pi×173.2050808²×(300÷3) = 9424777.96076938 m^3 or 9.42477796e12 cc
- Wide Mountain: pi×519.61524227²×(300÷3) = 84823001.64692442 m^3 or 8.4823e+13 cc

__Volume for Mountains of 609.6 meters in height__:[]

- Steep Mountain: pi×351.9527241²×(609.6÷3) = 79075553.09 m^3 or 7.907555309e13 cc
- Wide Mountain: pi×1055.8581723²×(609.6÷3) = 711679977.81 m^3 or 7.1167997781e14 cc

__Volume for minimum Japanese-approved Mountains__:[]

- Steep Mountain: (1/3)×pi×577.3502692²×1000 = 349065850.39886592 m^3 or 3.4906585e14 cc
- Wide Mountain: (1/3)×pi×1732.0508076²×1000 = 3141592653.58979324 m^3 or 3.141592654e15 cc

Now for the destruction, I am going to order it from Steep to Wide Mountains, starting from Steep Mountains.

__Destruction Yields for a 300 m Mountain:__[]

__Destruction Yields for a 300 m Mountain:__

- Fragmentation (8 J/cc) = 7.5398224e13 Joules,
**Town level** - Violent Fragmentation (69 J/cc) = 6.5030968e14 Joules,
**Large Town level** - Pulverization (214 J/cc) = 2.0169025e15 Joules,
**Large Town level** - Vaporization (25700 J/cc) = 2.4221679e17 Joules,
**City level+**

Now onto Wide Mountains.

- Fragmentation (8 J/cc) = 6.7858401e14 Joules,
**Large Town level** - Violent Fragmentation (69 J/cc) = 5.852787e15 Joules,
**Small City level** - Pulverization (214 J/cc) = 1.815212e16 Joules,
**Small City level+** - Vaporization (25700 J/cc) = 2.17995e18 Joules,
**Mountain level**

__Destruction Yields for a 609.6 m Mountain:__[]

__Destruction Yields for a 609.6 m Mountain:__

- Fragmentation (8 J/cc) = 6.326044e14 Joules,
**Large Town****level** - Violent Fragmentation (69 J/cc) = 5.456213e15 Joules,
**Small City level** - Pulverization (214 J/cc) = 1.6922168e16 Joules,
**Small City****level** - Vaporization (25700 J/cc) = 2.0322417e18 Joules,
**Mountain****level**

Ditto

- Fragmentation (8 J/cc) = 5.6934398e15 Joules,
**Small City level** - Violent Fragmentation (69 J/cc) = 4.9105918e16 Joules,
**City level** - Pulverization (214 J/cc) = 1.5229952e17 Joules,
**City level** - Vaporization (25700 J/cc) = 1.8290175e19 Joules,
**Island level**

__Destruction Yields for minimum requirement of a Japanese Mountain:__[]

__Destruction Yields for minimum requirement of a Japanese Mountain:__

- Fragmentation (8 J/cc) = 2.7925268e15 Joules,
**Large Town level+** - Violent Fragmentation (69 J/cc) = 2.4085544e16 Joules,
**Small City level+** - Pulverization (214 J/cc) = 7.4700092e16 Joules,
**City level** - Vaporization (25700 J/cc) = 8.9709923e18 Joules,
**Mountain level**

Hit [it] baby one more time-

- Fragmentation (8 J/cc) = 2.513274e16 Joules,
**Small City level+** - Violent Fragmentation (69 J/cc) = 2.1676989e17 Joules,
**City level** - Pulverization (214 J/cc) = 6.723008e17 Joules,
**Mountain level** - Vaporization (25700 J/cc) = 8.073893e19 Joules,
**Island level**

**Afterword:**[]

So in the end, what did we learn from all this? Well, when following the angle of repose, the wiki standard for Mountain height's values certainly lowered down by a bit, while the minimum requirement for Japanese Mountain height strikingly resembles the values in the Average Mountain Destruction blog. So... that's it, I suppose.

**EDIT (4/10/2024): I do hope that this new edition I added can be adopted as common practice if I get enough support on that notion.**