How is a steady-state weight calculated?

June 29, 2008 7:18 PM

I am A years old, am H inches tall and I weigh W pounds. I burn a total of B calories per day on average (that's including exercise as well as just daily living and sleeping). I consume E calories per day. What would my steady-state weight be expected to be, and how long would it take to reach it?
posted by zaebiz to health & fitness (12 answers total)

Obviously this would be a very crude esimate anyway, but you can't even get that without knowing your sex. Basal metabolic rate depends heavily on if you are male or female.
posted by Justinian at 7:36 PM on June 29, 2008

Your question is flawed. There's steady state to be reached, unless B always equals E.

If you consistently consume more calories than you burn, you'll gain weight more or less indefinitely (see the 1200 pound man for an example). If you burn more than you consume, you'll be a little more limited by bone structure and stuff, but if you consistently run that deficit, you'll become malnourished, fall ill, and die.

Here's a little info that will help you do the math, though:

A net gain of 3500 calories is about a pound of weight gain. (give or take a little)

So, daily weight change = (E-B)*3500

(Height is irrelevant in this simplified calculation.)
posted by chrisamiller at 7:37 PM on June 29, 2008

Basal metabolic rate depends heavily on if you are male or female.

I'd amend that to read "depends heavily on what percentage of your weight is muscle and what percentage is fat". Muscle burns more calories than fat, therefore men, who tend to be more muscular, usually burn more calories as a result.
posted by orange swan at 7:38 PM on June 29, 2008

Your weight will increase whenever E is greater than B and will only be steady when E = B. You need to know how B varies with W (presumably, when you are heavier you will burn more calories per day). Are you asking someone to approximate the relationship between B and W?
posted by ssg at 7:40 PM on June 29, 2008 [1 favorite]

chrisamiller: You can actually come up with a crude formula if we know the sex of the person involved because your resting burn rate for calories increases as your weight increases, so if E is constant as the question indicates, B will eventually equal E as weight increases. Obviously depending on the initial values of B and E this could either be very quickly or not until the person is the size of the goodyear blimp.

I'm assuming this is some sort of abstract math problem and not asked in expectation of a real-world answer, because I agree looking for a real-world answer is doomed to failure.
posted by Justinian at 7:42 PM on June 29, 2008

From a Basal Metabolic Rate (BMR) calculator:

Women: BMR = 655 + ( 4.35 x weight in pounds ) + ( 4.7 x height in inches ) - ( 4.7 x age in years )
Men: BMR = 66 + ( 6.23 x weight in pounds ) + ( 12.7 x height in inches ) - ( 6.8 x age in year )

Then multiply by BMR by a factor between 1.2 and 1.9, depending on whether you're a slug or Speedy Gonzales.
posted by lukemeister at 7:47 PM on June 29, 2008

Enh, since this is so crude and inaccurate anyway, I'm going to assume you're asking about a dude. X = calories burned from exercise. I don't see how you lump all "calories burned" together and still get a meaningful answer.

B = 66 + 6.23W + 12.7H - 6.8A + X

Steady state weight achieved when B = E

So E = 66 + 6.23W +12.7H - 6.8A + X

W = (E - X - 12.7H +6.8A - 66) / 6.23
posted by Justinian at 7:52 PM on June 29, 2008

I want to reiterate that this treats your question like a theoretical math problem and I have absolutely zero confidence in the real world application of this formula.
posted by Justinian at 7:55 PM on June 29, 2008

I was thinking more like - the more I weigh, the more food I need to consume to maintain my weight - but ultimately there is a steady-state weight at which the weight I reach is "optimal" for the amount of calories I am consuming. I was thinking along these lines.
posted by zaebiz at 9:31 PM on June 29, 2008

Optimal isn't the right word; if you always eat the same amount of calories and do the same amount of exercise, there is a weight you'll naturally fall into. That weight isn't "optimal" in any sense since there is a weight you'll naturally fall into even if you eat like a pig; you'll just be fat. This natural weight increases with age as your metabolism slows.

The formula I gave is exactly what you're asking for.

Weight = (E - X - 12.7H + 6.8A - 66) / 6.23 for men.

All the variables are the ones you provided except for X, which is the number of calories you burn through exercise.
posted by Justinian at 10:15 PM on June 29, 2008

chrisamiller: "A net gain of 3500 calories is about a pound of weight gain. (give or take a little)

So, daily weight change = (E-B)*3500"

This should be: (E-B) / 3500 ...
posted by benzo8 at 1:44 AM on June 30, 2008

This should be: (E-B) / 3500 ...

Yeah - thanks benzo.
posted by chrisamiller at 7:31 AM on June 30, 2008