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I'm pretty much looking for an easy (or not) formula for calculating the mass and/or weight of fantasy creatures on an Earth-like planet with similar gravity. My world's dragons sometimes reach over 1 km long, magically supported regardless of weight, but I would still like to add a realistic number to the weight fields of the profiles of my draconic characters. I also have turtles the size of islands (inspired by Magi-Nation, NOT ATLA) and skyscraper-tall humanoids. My question is: How does one calculate the weight or mass of such incredibly large creatures?

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    $\begingroup$ What's ATLA?What's Magi-Nation? Why would it matter in context of size question? $\endgroup$ – Mołot Jun 13 '18 at 20:43
  • $\begingroup$ Probably making a comparision with something that it's real and has those sizes. For example the Golden Bridge it's twice the size of your dragon in that context you could say that your dragon would weight 300.000 tons. $\endgroup$ – Tridam Jun 13 '18 at 20:47
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    $\begingroup$ Finding the weight of your creatures isn't the problem. The problems are: (a) finding the volume of your creatures. Tails and wings are a pain. And there's no convenient way of doing it. (b) What happens when such a creature in an earth-like environemnt takes a step. This question considers a 6km tall giant, a bit bigger than you're thinking about, but similar problems. Super large critters come with super large problems. $\endgroup$ – JBH Jun 13 '18 at 20:56
  • $\begingroup$ @Mołot ATLA is probaby Avatar: The Last Airbender. $\endgroup$ – Renan Jun 13 '18 at 21:24
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Wow. At those scales, they're not just flying via magic, they're not crushed into pulp by their own mass via magic. This is because if you grow proportionately, your weight increases much more. If you grow twice as tall and twice as wide, you've gained eight times the volume. This link walks through the math on this.

That may also give you the tools to calculate your weights, as they will follow similar mathematics.

This site says a human body weigh(s) 1.01 gram per (cubic centimeter) or 0.58 ounce per (cubic inch).

w = ρ × v where w=weight, p or rho=density, and v=volume

Google tells me that the average density of the human body is 985 kg/m3, and the typical density of seawater is about 1020 kg/m3. The average density of the human body, after maximum inhalation of air, changes to 945 kg/m3.

I'm not finding any sources on the body density of dragons, unfortunately. But you should be able to use the above equation to figure out some values that work. You may want to shift the density up or down for your creatures, especially if they have heavy armored hide, for example.

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Find a similar creature and use the cube-square law

For example a big lizard is about 3m long and weighs about 70kg. That's comparable to a tall man.

That means if we double the length and keep the proportions the weight is $70 \times 2^3 =560$.

So a really big lizard is about 6m long and weighs about 560kg. That's comparable to a small cow or smart car. The lizard is much longer but slimmer than either.

We want to know the weight of a $1000m$ long dragon. The dragon is $1000/3 = 333$ times longer than the lizard.

So the dragon weighs about $70 \times 333^3 \sim 70 \times 3.7 \times 10^7 \sim 2.6 \times 10^9kg = 2.6 \times 10^6 t$.

That's 2.6 million tons or 2.6 megatons. Maybe increase it to 3 megatonnes to account for longer legs and wings.

Now I have no idea what 2.6 million tonnes actually means. To me it's just some Really big number that might be useful for comparing to other Really big numbers. Oh so the dragon weighs 2 megatons but the island turtle weighs 3000 megatons? The turtle must be much bigger.

For comparison the Titanic was about 0.05 megatons. But again to me the Titanic is just some really big ship. Unless the dragon was next to the ship I'd have no idea which is bigger.

In either case "2-3mt" or "2-3 megatons" looks pretty slick for a bestiary profile. Maybe the word megaton is too modern for the setting. Just replace it with 'high tonne' or something more germanic.

Note: This presumes the density of the dragon is similar to the lizard. Most real animals have a density similar to water because they are primarily composed of water.

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