10
$\begingroup$

Trying to figure out how much a 1 foot tall fairy would realistically weigh using these 2 guidelines

  1. Fairies are just scaled down humans.
  2. Their bones are not hollow because their flight is assisted by magic.
$\endgroup$
  • 1
    $\begingroup$ Are you specifically referring to the square-cube law in your question? If not, then please elaborate further on the restrictions being placed. $\endgroup$ – Andrew Fan Sep 14 at 0:03
  • $\begingroup$ Small beings usually have very thin extremities, compared to tall ones. Consider e.g. the legs when comparing the mouse against the elephant. Please elaborate to the comment from @AndrewFan $\endgroup$ – hitchhiker Sep 14 at 19:54
10
$\begingroup$

For uniformly scaled down humans (as opposed to real life short humans), result would be simple as

$$m_{fairy} = M_{human} * (\frac{H_{fairy}}{H_{human}})^3$$

Assuming the fairy is 1 foot tall and her real life prototype is 5'6" and 120 lbs we get 0.72 pounds or 11.5 ounces.

$\endgroup$
  • $\begingroup$ What if her prototype is Cara Delavingne? $\endgroup$ – Harper - Reinstate Monica Sep 14 at 22:38
  • 1
    $\begingroup$ @ Harper Cara Jocelyn Delevingne is reportedly 173 cm tall and 51 kg light. Putting it to the formula gives 279 g, or 9.8 ounces. $\endgroup$ – Alexander Sep 14 at 23:43
9
$\begingroup$

Comparison with other humans

We can almost look at a real live example: https://www.oddee.com/item_97186.aspx

Edward Nino Hernandez is about 70 cm tall (~2 foot) and weighs 10 kg. We can actually use this to test the square-cube-law, proposed in other answers:

$$m_\text{fairy} = 80\ \mathrm{kg} \cdot \left(\frac{0.7\ \mathrm m}{1.8\ \mathrm m}\right)^3= 4.7\ \mathrm{kg}$$

So they are off by a factor of 2.

Comparison with monkeys

Let's have a look at monkeys: https://en.wikipedia.org/wiki/Tamarin

The Tamarin can grow up to $30\ \mathrm{cm}$, which is just about 1 foot and heaviest specimen weigh up to $0.9\ \mathrm{kg}$ (other units can be found in the article).

The squirrel monkey (https://en.wikipedia.org/wiki/Central_American_squirrel_monkey) also grows up to about $30\ \mathrm{cm}$ and has a maximum weight of about $0.95\ \mathrm{kg}$

Comparision with a penguin

Another animal I could think of, that is roughly that size. Penguin (https://en.wikipedia.org/wiki/Little_penguin): $1.5\ \mathrm{kg}$

Conclusion

So in conclusion I would estimate the human to weigh round about $1\ \mathrm{kg}{-}1.5\ \mathrm{kg}$, which is just a little over $2\ \mathrm{lbs}{-}3\ \mathrm{lbs}$.

$\endgroup$
  • 4
    $\begingroup$ I upvoted this answer just for sweet metric units! $\endgroup$ – polfosol Sep 14 at 13:25
  • $\begingroup$ Why was this downvoted? Please clarify $\endgroup$ – infinitezero Sep 14 at 14:28
7
$\begingroup$

Well, if they are literally just humans of the exact same proportions, but scaled up or down, we can use the Square-Cube Law to figure it out in both cases.

The skinny version is, if I understand this correctly, take this equation:

V2 = V1 ( l2 / l1 )^3

where V2 is your new Volume, V1 is the original Volume, l2 is the new length and l1 is the original length, and assume for simplicity's sake that volume exactly correlates with mass, and therefore weight.

So if a reasonably well-fed human is 6ft tall and 180lbs, then an exact scaled-up giant version at 12ft tall would be 2x the height, and therefore the weight is 180(12/6)^3, or 1,440 lbs. That's a lot.

Turning this around, if this 6ft, 180lbs human is scaled down to 1ft tall, then we're looking for 180(1/6)^3, which is about 0.83333.

So your fairies would weigh less than one pound each, with the exception of some who are enormous by fairy standards.

You can use this to get a rough estimate of weights for all sorts of creatures, big or small. Take an animal that looks the most like what you want to make, plug in its bodily proportions, and presto you have a rough idea of how much the new version should weigh. You'd be surprised just how heavy your giants are and how light the dwarfs are.

$\endgroup$
3
$\begingroup$

A 30cm fairy would need a lot less muscle relatively than a normally sized person. (Note that with a normal amount of muscle, they'd be able to jump nearly as high absolutely as a big person). They'd look probably quite skinny, and weigh less than the square-cube law would suggest, maybe 0.3kg.

$\endgroup$
1
$\begingroup$

Other answers have scaled the persons' mass by the cube of their height, and got answers of about 13 ounces. This is probably a lower bound; it assumes that a human brain can fit into a space slightly larger than a teaspoonful.

The theory of "Body Mass Index" (BMI) is that people have the longest life when their mass is roughly proportional to the square of their height. If we start with 6 feet = 180 pounds (a BMI of 24.4 kg/m²), we can extrapolate this to 1 foot = 5 pounds. This is probably an upper bound; it allows a few cubic inches for the brain.

An elliptical cylinder of water with a width of 5.4 inches, a height of 12 inches, and a depth of 2.7 inches would have a mass of five pounds. The ellipse's perimeter would be 13 inches, which is quite stout. (6 * 13" is a 78" waist!)

An elliptical cylinder of water with a width of 2.2 inches, a height of 12 inches, and a depth of 1.1 inches would have a mass of 13 ounces, and a BMI of 4 kg/m². The ellipse's perimeter would be 5.3 inches, which is scaled down from a 32 inch waist.

$\endgroup$
  • 2
    $\begingroup$ Going by BMI is a recipe to estimate a real-life dwarf. If you try to picture your water cylinders, at 1 foot tall we would get a person of cartoon proportions (which might be Ok). $\endgroup$ – Alexander Sep 14 at 2:22
  • $\begingroup$ BMI is entirely the wrong tool here. It doesn't accurately approximate either actual human scaling or theoretical square-cube scaling. $\endgroup$ – Mark Sep 14 at 23:39

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.