Sometimes when I'm off on a weird tangent I have to use a Standard Reference Human when crunching numbers. What's the average person's weight, height, surface area, volume? That sort of thing. The answer for all of these is that it depends on sex, age, ethnicity and a multitude of other factors that I ignore to make calculations easier.
It turns out that defining a Standard Reference Human is actually serious business done by various national and international organizations for safety, engineering and ergonomic requirements. It's also semi-controversial since standards that work great for a 6'0" man might not be so great for a 5'0" woman. Fortunately I can ignore all of that, grab whatever values show up in my search results and then round them off to make calculations easier.
So without further ado, my Standard Reference Human is below. All values are in metric because have you tried doing math in the Imperial system? Actual values are taken from a variety of sources.
| Key | My Value | Actual Value | Notes |
|---|---|---|---|
| Height | 200 cm | 170 cm | At 6'7" my value is grotesquely inflated, but two meters is a nice easy figure to work with. |
| Weight | 100 kg | 70 kg | Again my value is high, making our giant dude slightly overweight. |
| Volume | 100 liters | 66 liters | This number is not only easy to work with, it is also consistent with my previous two figures |
| Density | 1.01 kg per liter | 1.01 kg per liter | Life is basically self-directed seawater. A handful of other chemicals in a mix of 99% H20. |
| Surface Area | 2 square meters | 1.5 to 2 square meters | You can find anything on the internet, including skin area calculators. My number is a bit low for 200cm, but reasonable. Source: https://www.calculator.net/body-surface-area-calculator.html |
One advantage of using my larger values, besides ease of calculation, is having a built in safety margin. So if you need to calculate something that will work for the pro-wrestler sized numbers above you know that it will absolutely work with regular people.
So that's great when you want to estimate how much material you'll need to make uniforms for 10,000 soldiers or something equally wacky. But while working on another project I found myself asking “How tall would a human shaped object be if it had to contain 3 square meters?”
You could just assume a spherical human and call it a day. I find it easier to work with cubes and there you could quarter the depth, quadruple the height and get a rough rectangle shape. That could work. But luckily for us there's an equation out there that works perfectly for calculating human heights and weights.
The Body Mass Index or BMI. Scourge of power-lifters and middle-aged men getting physicals alike, this formula divides your weight by your height to get a measure of how obese you are. A range of 19 to 24 is considered healthy with figures above and below that indicating how underweight or overweight you are.
Using our Standard Reference Human above we use the following equation: Take the weight in kilograms and divide it by the height in meters squared (BMI=w(kg)/h(m)^2) or 100 kg/ (2 meters)^2 → 100/4 = 25 for a slightly overweight individual.
The fun thing about equations though is that you can flip them around and use them to solve for things you aren't supposed to. And if right now you want to bolt from this website and never come back I feel you. The way they teach math in our schools is an abomination and traumatizes millions of kids every year. Math isn't about mindless calculation and rote formulas. It's a set of lock picks for opening up the secrets of the universe. It's a damn shame it's not taught that way.
So, we can take our BMI equation and flip it around. I'd walk you through the steps but it's been decades since I did it and I was never good at it. But I know it can be done so I had WolframAlpha.com do it for me giving us the two equations below.
Height (meters) = Square Root of Weight (kg) divided by the Square Root of BMI.
Weight (kg) = BMI times the Height (meters) squared.
For our purposes we'll make the Standard Reference BMI 25, which is a bit unhealthy but is a lot easier to work with since the square root is 5. So now we can answer all sorts of silly questions, like how much does a hill giant weigh? According to Dungeons and Dragons they are 5 meters tall, so we square that to get 25, multiply that by our reference BMI of 25 and get 625 kg or about 1,400 lbs.
What about shapeshifters? Let's say you are looking for were-bears amongst the populace and despite living in a world of magic and wonder assume that conservation of mass still applies. According to Wikipedia the average weight of an adult brown bears is 217 kg, so let's solve for height. We take the square root of 217, which is around 15, and divide that by the square root of our reference BMI of 25, which is a nice easy 5 and we get 15 / 5 = 3 meters. So to find the hidden were-bears keep an eye out for any adult males who are 9'10" tall.
Feel free to play with the numbers if you want to figure out the stats for runway model were-bears or hill giants who have really let themselves go. Also a fun fact, in metric a kilogram of water is equal to a liter in size, so you if you have the weight of a person you have the volume as well within one percent.
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