Xjyuk

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.

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.

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

$$m_fairy = M_human * (fracH_fairyH_human)^3$$

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.

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.