# Body Composition Calculations

Back in December I ran an article called What Does Body Composition Mean where I looked a little bit at the different components of the human body and how they integrate to determine body composition.  Following up from that piece, I want to talk more about body fat percentage, what the numbers tell you and how they can be used to determine how changes in body composition will affect the overall percentage.

Determining Body Composition from Body Fat Percentage

As I discussed in the article What Does Body Composition Mean, when you know the amounts of fat and lean mass present in the body, you can calculate body fat percentage.  Now, I’m not going to talk about different methods of measuring body fat percentage in this article; that will be the topic of a future article.

For the time being let’s assume I have a magic wand which I can wave to determine someones body fat percentage.  I want to show you how to do some basic calculations with those numbers in hand.

So I wave my wand it tells me that the 200 pound athlete standing in front of me has 10% body fat. First let’s determine what his actual body composition, in terms of pounds of lean body mass and fat are.

To calculate how many pounds of fat he has, we simply multiply his total weight by the body fat percentage (expressed as a decimal, so 10% becomes 0.10) that I determined with my magic wand.

200 pounds * 0.10 = 20 pounds of fat

Now we subtract the total amount of fat that he has from his total weight to determine how much LBM he has; keep in mind that LBM includes muscle, bone, organs, etc.  It’s not just muscle mass.

200 pounds – 20 lbs fat = 180 pounds of lean body mass (LBM).

So our hypothetical athlete has 10% body fat, 20 pounds of fat and 180 pounds of lean body mass.  We can now use those values to do a number of calculations which I’ll show below.

How Will Changes in Body Composition Affect Body Fat Percentage

Since folks usually want to alter their body fat percentage, it’s instructive to look at how changes in either total fat mass or lean body mass will change overall body fat percentage.  I want to look at the situation where our hypothetical athlete either loses pure fat, gains pure muscle, or gains muscle while losing fat.

Keep in mind from above that our athlete is 200 pounds with 20 pounds of body fat.  Let’s look at what happens if he gains 5 pounds of fat with no change in LBM, gains 5 pounds of LBM with no change in fat, or manages to gain 5 pounds of LBM while losing 5 pounds of fat.  The changes to his overall body composition appear in the table below.

 Condition Fat Mass LBM Total Weight Body Fat Percentage Starting 20 180 200 20/200 = 10% Lose 5 pounds fat 15 180 195 15/195 = 7.7% Gain 5 pounds muscle 20 185 205 20/205 = 9.7% Lose 5 lbs. fat/Gain 5 lbs. muscle 15 185 200 15/200 = 7.5%

One thing to note about the above calculations is that losing fat has a much larger impact on body fat percentage than gaining the same amount of muscle. I bring this up as it’s often recommended that people gain muscle to lower their body fat percentage.  Except that it doesn’t work very well; simply losing fat has the major effect.

In the above example, losing 5 lbs of fat decreased body fat percentage by 2.3%; gaining 5 lbs of muscle only decreased it by 0.3%.  Even gaining muscle while losing fat only dropped the total percentage by 2.5%, a small effect over just losing fat.

I’d also note that you don’t have to do the calculations as if pure fat loss or muscle gain is occurring. You can plug any changes you want into the above values to see how varying changes in fat mass and LBM will affect the overall body fat percentage.

Determining Goal Weight for a Given Body Fat Percentage

A question that comes up quite a bit is how much fat someone will need to lose to reach a certain body fat percentage, given that they know where they are now.  Assuming you have starting numbers for fat mass and total weight, there is a fairly easy calculation to do this.  I’d note that this calculation assumes that the total weight lost is fat mass; that is, there is no muscle loss.  This isn’t always such a good assumption.

The equation to determine goal weight is the following:

Goal Weight = Current Lean Body Mass / (1-Goal Body Fat percentage as a decimal)

By percentage as a decimal I mean this, if the goal is 10% body fat, that becomes 0.10.  20% becomes 0.20.  15% body fat becomes 0.15.  5% body fat becomes 0.05.  Got it?

So let’s take our same lifter from above who is 10% body fat at 200 pounds, he has 20 pounds of fat and 180 pounds of lean body mass. Let’s say he wants to get to 5% body fat (in decimal form, 0.05), how much weight does he have to lose?

Goal Weight = 180 / (1 – 0.05) = 180/0.95 = 189 pounds

That means that his goal weight is 189 pound down from a starting point of 200 pounds.  So he’d have to lose 11 pounds of fat to drop from 10% body fat to 5% body fat.

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