The Math & Formulas

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Skinny Girl's Quest for Muscle
Getting Started Part 1: Doing the Body Math

One would think that figuring out body stats is a fairly easy process given the right tools such as a weight scale, body fat scale or calipers, measuring tape, and a few formulas. However, the process has become more of an ordeal than I originally planned. Finding my stats, or my "starting point" for this journey is a complete process in itself.

Why Do You Need To Know Your Stats Anyway?

Stats are important because without knowing how much body fat (or lean mass) you are packing, it's difficult to tell if you are making any progress in your program. Additionally, I use lean mass to estimate how many calories I need to consume to both 1) maintain existing lean, and 2) build new muscle.

I could start working out and completely blow off this first step, but there is a chance that my effort in the gym isn't building muscle, but rather depleting muscle (from such problems as over training, under training, incorrect training, etc.) If I didn't measure a starting point, it may take sometime before I notice a problem develop. By then I've wasted a lot of time depleting muscle instead of gaining muscle. If you consider that muscle can be added at a rate of 1 to 2 pounds per month(1), not realizing that you've lost a few pounds could put you almost a half a year behind your potential.

Another issue is knowing how much to eat. This can be done in several ways. The most popular is what I call the guessing game (or just eating what ever you like, when ever you want). This is likely the diet that most of us follow. When you consider that in 2003, it was estimated that 66% of the population was overweight(2), and, 8% to 9% of the population is underweight (3), it's easy to tell that this type of diet may not be the ideal.

Another method is to use your age and current weight, and an "activity factor" to determine the number of calories that you should consume in a day. The activity factor takes into consideration the calories you burn everyday just being who you are whether that's an active person, a sedentary person or someone in the middle. If done correctly, this is more accurate than the guessing game method. However, weight isn't the best measure for determining how to support your lean mass as the two (weight and lean mass) can be quite different numbers in different people. Let's assume you lead a very healthy life and frequent the weight room at the gym. In this scenario, you could be 200 lbs with a 20% body fat rating.

To find your "lean" (how much muscle you're packing around on your frame) you could estimate that:

200 lbs x 17% fat = 34 lbs of fat
200 lbs - 34 lbs of fat = 166 lbs of lean mass

Now, just for fun, let's estimate that your frame (the bones in your body) take up approximately 14% of your total body weight(4))

166 lbs x 14% = 28 lbs of bone

So, our athletic person who weighs 200 lbs with 17% body fat has 138 pounds of muscles and 28 lbs of bones to support.

Less Athletic Scenario

Now, let's look at our Less Athletic specimen, who is the same weight (200 lbs) but has 28% body fat.

200 lbs x 28% body fat = 56 lbs of fat
200 lbs - 56 lbs of fat = 144 lbs of lean mass
144 lbs - 28 lbs of bone (14%) = 116 lbs of muscle

Our Less Athletic person who weights 200 lbs, has only 116 pounds of muscle. That's 22 lbs less than the Athletic person who weight the exact same amount. If you are eating to maintain lean (or to build lean) it makes sense to eat for your lean mass instead of eating for your total weight.

BMR - Basal Metabolic Rate - Feed Your Body

Now, let's apply a BMR (Basal Metabolic Rate) formula to our two scenarios to see how many calories each one should consume in a day to maintain current weight. The formula that I will use is the Katch-McArdle formula. This is one of the formulas that takes lean mass into consideration.

The first step is to convert pounds of lean body mass into kilograms.

Scenario: Athletic

Convert Lean Body Mass to Kilograms:
lean body mass in pounds: 166 x 0.4536 = 72.3 kilograms
Where 0.4536 is the conversion factor from pounds to kilograms.

Now the formula ( P = 370 + (21.6 x Lean Body Mass) )
Where P stands for total heat production at rest (how many calories you burn when doing nothing.

P = 370 + (21.6 x 75.3)
P = 1,996 calories per day

Scenario: Less Athletic

lean body mass in pounds: 144 x 0.4536 = 65.3 kilograms
P = 370 + (21.6 x 65.3)
P = 1,781 calories per day

Now in the event that our Less Athletic individual eats like the Athlete, that will create an excess of 215 calories per day, or over 6,500 calories per month. At this rate, everything else equal, the Less Athletic individual is eating enough to gain an additional 22.5 pounds every year. Whether or not the Less Athletic individual will actually gain those 22.5 pounds is largely dependent upon many other factors which I'll address in future blog posts. It should not be assumed that just because someone is overweight, that they are by definition overeating.

Activity Factors: Do More, Eat More

We're not quite done yet. We still need to consider activity level. An activity level can be applied to the above formula to take into account the calories burned through the activities we do in our daily lives. Activity factors typically look like:

* Sedentary x 1.2 extra calories
* Light Exercise x 1.38 extra calories
* Moderate Exercise x 1.55 extra calories
* Heavy Exercise x 1.73 extra calories
* Very Heavy x 1.9 extra calories

These factors are applied to the BMR so in the case of the Athlete who needs 1,996 calories per day, the amount would be multiplied by one of the above factors. For example, if we wanted to apply the "Moderate Exercise" factor:

1,996 x 1.55 = 3,094 calories per day

Activity Factor: A Twist

Because we're all so different in the way we perform activities and exercise, my preferred method of calculating activity is slightly more precise. Here's where I deviate from the standard formula. First, I assume that my lifestyle without added exercise is "Sedentary" (I work a desk job and do your standard everything things such as gardening, cooking, cleaning, etc.) However, I do exercise, don't get me wrong. But, I track every single exercise event with a heart rate monitor with provides me with a total calories burned reading when I'm done. After tracking the calories burned, I calculate daily averages over time. Instead of applying a factor greater than 1.2 (the Sedentary factor), I just add a whole number to my BMR under a Sedentary scenario.

Under the Athlete scenario above, the calculation would look like this:

BMR = 1,996
Sedentary Adder = 1,996 x 1.2 = 2,395
Actual Average Calories Burned/Day = 500 + 2,395 = 2,895

Are you keeping up okay? Because, there is still one step left.

Do You Want To Stay The Same Or Is It Time For Change?

Let's say our Less Athletic individual wants to LOSE weight and has done all of the math above and ended at a caloric intake per day value of 2,000 calories. Now this individual also knows that losing weight is a gradual process and has set a goal of 1 pound per week. Under this theory, the Less Athletic individual either needs to burn 1 additional pound per week through exercise, or needs to eat fewer calories.

Let's assume every pound is worth 3,500 calories. 3,500 divided by 7 days (one week) equals 500 calories per day. By exercising to burn an additional 250 calories, and by eating 250 calories less (1,750 total per day) the math works out to 1 pound of weight loss a week. Did you notice that I said the "math" works out to 1 pound of weight loss every week? I did that on purpose. We're all very different and different foods, exercise, stresses, medications, body cycles, hydration levels, etc., impact us differently. Therefore, you can make a very general assumption, but when applied to a real life scenario, one must be patient and allow for adjustments or abnormalities. Additionally, there are many other factors that determine weight. The use of these formulas alone is not correct for determining why any one individual is over or under weight.

Next time we'll apply this math to my "starting point" and discuss what exactly I mean by starting point and how accurate it is or is not. Until then -- go do something athletic!


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references

(1) Still working on a good reference for this "common knowledge" statement.
(2) http://www.cdc.gov/nchs/products/pubs/pubd/hestats/overweight/overwght_adult_03.htm
(3) http://www.todaysdietitian.com/newarchives/tdjan2008pg56.shtml
(4) William W. Reynolds and William J. Karlotski (1977). "The Allometric Relationship of Skeleton Weight to Body Weight in Teleost Fishes: A Preliminary Comparison with Birds and Mammals". Copeia: 160–163.
(5) http://www.thefactsaboutfitness.com/news/cals.htm

Other Notes: pounds to kilograms conversion is a rounded version of the value used at onlineconversion.com

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