Thursday, March 3, 2005

Weight Estimation

We all know obesity is a problem in United States. Whenever I see a large person, two questions would automatically pop into my head:

1. How much does this person weigh?
2. How did it happen?

The second question is usually very easy to answer, but the weight question is a little tricky. Since it is socially unacceptable to directly ask a person about his/her weight, I usually try to calculate an estimation in my head.

The person in the photo is about 5' 6" tall. Using the drag-along bag as a reference scale, her hip is about 30.5" and her shoulder is about 20.8" wide. Judging by her body shape, the hip's widest point is about 40% of her total height, therefore it is about 26.4" above from the ground.

Assume her upper body is cone shaped with its base diameter to be the average of shoulder and hip width, her upper body volume is:

V_upperbody = (1/3)*(pi)* (39.6")*[(30.5"+20.8") /4]^2
V_upperbody = 6821 in^3

Since her lower body is not as filled of a cone-shape as her upper body, her lower body volume would be halfed:

V_lowerbody = (1/2)*(1/3)*(pi)*(26.4")*[(30.5"+20.8")/4]^2
V_lowerbody = 2274 in^3

The total volume is:

V_total = V_upperbody+V_lowerbody
V_total = 9095 in^3 (or 0.149 m^3)

Assuming human flesh is the same density as ground beef (950 kg/m^3), her body weight would be:

Weight = (0.149)*(950)

Weight = 141.6 kg (or 318.2 lbs)


  1. Doing all this math in your head is way too much, which is fine if you have a long walk to your car... but I think you could simply it. Just have three cases: thin, normal, fat. In the US, you can pretty much rule out the first option (thin), so you will have normal and fat left. She is obviously not normal weight, just judging by the bowling ball case she is dragging on the ground... so you can rule that one out too. The enswer should simply be fat. :-)

    And you don't even need to know the density for ground beef! So, in which engineering book did you find the density for ground beef anyway? :-)


  2. The density value of ground beef was from Heat Transfer book. I am sure you remember it, we took the same class with Phelan.

  3. Bubba what is the expected error rate in your calculation? You need to do a few more guesses and develop a height to weight least squares regression line and then compare that to a confirmed/known height to weight line. That will not only tell you the accuracy of your guess but give you a basis for a quick sight only measurement. I imagine that the line would be non-linear as the relative proportions change between bone, fat, and muscle in obese people.

  4. Seth (Bubba),

    when I trying to figure out an equivalent mass density for human flesh, lean ground beef (1090 kg/m^3) was heavier than pure beef fat (810 kg/m^3). That is why I picked the ground beef as the density.

    I did not bother to calculate the expected error rate, because this is only for approximation. All the dimensions are not actually measured, only estimated.

  5. Man, there's no way her hips are only 30.5". My waist is 32" and I weigh 165 lbs. Her hips are probably more like 38 or 40"...

  6. Casey,

    The 30.5" is width. Your 32" waist is the circumference.

    Circumference = pi * diameter

  7. So what about designing a program for camera phones that will run the equation on a person after taking the picture.. You could set up a list of the fattest people ever reported.


  8. How about actually comparing some pictures. I'm willing to send in mine to see if the formula works.
    Questions that I would like to see answered:
    Is it gender specific?
    Does the description thin, normal, fat build give enough, or should you add the excessively muscular as another catagory?


  9. Dave,

    Feel free to send those photos. I have realized in my original estimation formula, I have neglected the waist.

  10. It doesn't look like this woman weighs 318 lbs., if the 5'6" estimate is accurate. The problem is probably your assumption that a human body is roughly as dense as ground beef, when in fact ground beef is denser. Try measuring the volume of beef before and after grinding, and you'll see that the ground version is more compact.

  11. Wait.. did someone say you can rule ou the first option (thin) in the U.S? Come on people, we either invented or hold the patents on bulimia, anorexia, methamphetamines, etc., and between these borders I'm sure you are to find more women over 20 but under 90 lbs., and not just because they can't afford to eat.

    Also, have none of you ever been to Germany or Brittian?

    Now, I'll admit, we have fat fucks here in the US. Sloppy, lazy, unemployable, retarded fat fucks. Most of whom are currently working as Minutemen in Arizona or tow truck drivers anywhere, but to deny America is God-given right to claim the most sickly skinny people in the world is to deny the existence of Los Angeles.

    And you can't do that, because I live there.

    PS: I'm 6'0, 30 years old, 180 lbs. and thoroughly disgusted by fat people, at least in the visual sense, but still enamored by the personalities and lives of several fatty fat fatsos. I just wouldn't be able to boff them.

  12. Fantastic project - the problem is that we always need a reference in the image - such as the bag in this case.

    Still the idea of developing a mathematical formula to estimate body weight from height, waist, hips and bust alone is very interesting. Im certain there would be massive internet traffic for such an online calculator - especially for the very large.

    Take the girl in this photo - if we assume she IS 318lbs - she would be too heavy for conventional bathroom scales - and probably unlikely to want to weigh herself on larger public scales - or even at the doctors. but . . . . if we could offer a way of calculating her weight from measurements alone - she could find out on the internet without needing the humiliation of a public weighing - tian if you do anymore work on this please email me

  13. further to my comment above i have tested your formula (slightly adjusted)

    I know a lady and her measurements
    she is 5'11''
    bust 44
    waist 38 (this is not needed but i just want to show she is not massive all over)
    hips 58

    these are circumference figures not diameters so i dropped pi from the formula
    by adding 3" to the top body height and 2" to the lower body

    i get a result of 191kg or 421lbs

    and whilst i dont know exactly what she weighs i do know it is something like 260-280lbs - back to the drawing board i guess

  14. In Brittian (sic) we call it 'The American Disease'

  15. Yeah, never you mind that the same dysfunctional American mentality which promotes cheap, fast, fatty foods to keep its population fat and sassy is the same one that will eventually send its imperial forces across your border with a greasy, drippy side order of DEMOCRACY.

  16. "In the US, you can pretty much rule out the first option (thin)"

    Really? I am 175lbs at 6ft 3inches tall. I was born in the states and I'm not fat. Most of the people I know are pretty skinny as well. So why don't you hold your tongue before you start making rash generalizations about other countries. I bet you think I talk with John Wayne's accent, wear a cowboy hat, and listen to rock and roll too?

  17. "So why don't you hold your tongue before you start making rash generalizations about other countries." - Evan

    *Other* countries? Given that the poster you're criticising shared a class with the author (see second comment), coupled with the apparent fact that the author is in the US, I'd say they too are from the US and therefore perfectly at liberty to make assumptions about the US.

    I could be wrong, but at least I made a stab at using the thing on top of my shoulders before I posted...