Calculating the weight of different sized humanoids

Question

In my world, I have relatively robust humanoids as the focal human sub-species, and a number of other human subspecies that are more gracile in build. I wanted to work out roughly how much they would realistically weigh given their builds and heights.

In my research, I've used prehistoric humans as baselines. Neanderthals were shorter, but more robust than equivalent Sapiens. Homo floresiensis added in as an additional data point. These are the figures:

• Neanderthal average: 164cm tall (5'5"), 77kg
• Upper paleolithic Sapiens avg.: 179cm tall (5'9"), 67kg
• Late upper paleolithic Sapiens avg.: 166cm tall (5'4"), 62kg
• Floresiensis est.: 109cm tall (3'7"), 25kg

This works out to Neanderthals having 0.49kg/cm, Sapiens having 0.37kg/cm for both, and H. Floresiensis 0.23kg/cm. However, square-cube law being what it is, scaling these up to make, say, a 6-foot Neanderthal gives a weight of 89kg which is not too far from the expected weight for a real-life gracile Sapiens according to BMI calculators. Not very realistic.

Perhaps it's just been too long since I took a maths class, but I can't work out what sort of formula to use to be able to plug height and a 'robustness ratio' into to be able to get a realistic weight for scaling humanoids up and down.

Criteria for a strong answer

Ideally, any calculation would be viable for calculating a realistic weight for anything from goblins up to giants. Another option for a successful answer would be a BMI chart that is scaled far enough to encompass goblins or giants.

A stellar answer would propose a method of calculation, and provide an example of it in practice that matches the figures for prehistoric humanoids above.

Edit: Played around a bit with the NHS BMI calculator.

Seems to be that Neanderthals had an average BMI of 28.6, Sapiens 20.9/22.4 respectively, and Floresiensis 21. Playing around with the calculator gave me a 6' Neanderthal as weighing 95kg with the same BMI, whereas a 6' late upper paleolithic human would weigh 75kg.

I believe this is relatively realistic for humanoids that do not differ too greatly in size to require physiological adaptations to large weight. However, it doesn't let you plug number in for 3m tall people so doesn't quite cut it. Could be useful for checking answers though.

Answer 1

The general rule here is that, if proportions are kept the same, weight is proportional to volume, which goes as the cube of a length dimension. Thus, if you double the height, you multiply volume/weight by two cubed = eight.

Therefore, if you have a man who weighs 100 kg, and another who has the same proportions (same waist to height ratio, same fraction of leg length to height, etc.), he'll weigh 800 kg.

Complicating this is the fact that, in real creatures, proportions generally change as height changes. This isn't always the case -- island dwarfism, for instance (sometimes blamed for the small size of the floresiensis "hobbit" fossils) typically changes size much faster than conventional selection can respond to the advantage of not growing unneeded bone and muscle. Otherwise, however, if you have a species that's much larger than an otherwise similar one, it will have different proportions -- thicker legs and body, thicker bones, etc. in order to support and move its greater weight.

In practice, it probably isn't far wrong to add an additional square on top of the cube of the height -- that is, instead of double height weighing eight times as much, it wouldn't be unreasonable for it to be enough thicker to weigh twelve times as much. On this basis, if you start with a real human (myself) who weighs 91 kg at 1.55 m, and "expand" him to 3m, you'd expect him to weigh:

(3/1.55)^3 * 91 kg + (3/1.55)^2 * 91 kg = about 1000 kg (simply 8x would be 728 kg)

Clearly at this scale the "thickening" is needed -- if you asked legs of merely human proportion to support that kind of weight, you'd have knees that last days, or at best weeks, bones in danger of snapping with the slightest stumble, and so forth.

This factor fits well with insects, which are the most common creatures we see in a very wide range of sizes. The biggest ones, certain beetles as big as a large mouse, are much heavier than simple cube-law from smaller beetles would suggest.

Answer 2

You can actually use BMI just be aware BMI changes with size, the formula is BMI = kg/m^2

BMI has to be increased with height because of the square cube law, which so simple formula can completely account for.

for a human of around 100cm with a gracile build a BMI of 15 (goblin), for normal human height 22 is fine for a human, over 2 meters you want something closer to 24 (slender giants). For very robust builds (football players weight lifters) you want something like 24 on the robust short end (dwarves), and 30 for normal human height, and for something over 2m you want to go to around 35 (beefy giants).

You will have a margin of error no matter what you do but a population will have a range of around +/-5 anyway, more if they have agriculture and thus fat individuals.

I used human athletes, children, pygmies, and a little estimation to get these numbers.

pygmy humans

athletes