How to calculate muscle loss during weight loss from body fat over time?

Question

I want to calculate muscle loss during losing weight from body fat recorded over time.

Let, during time t₁, the recorded weight and body fat percentage are w₁ and f₁ consecutively, and during time t₁, the recorded weight and body fat percentage are w₁ and f₁ consecutively, and during time t₂, the recorded weight and body fat percentage are w₂ and f₂ consecutively.

so my calculation is:

+-----------+---------------------+-------------+------------------------------------+
| Time      | Weight(kg)          | body fat(%) | fat(kg)                            |
+-----------+---------------------+-------------+------------------------------------+
| t1        | w1                  | f1          | w1*f1/100                          |
| t2        | w2                  | f2          | w2*f2/100                          |
+-----------+---------------------+-------------+------------------------------------+
|           | Weight loss = w1-w2 |             | fat burnt = w1*f1/100  - w2*f2/100 |
+-----------+---------------------+-------------+------------------------------------+

Muscle loss during t1 to t2 = Weight loss - fat burnt
                            = w1-w2 - ( w1*f1/100  - w2*f2/100 )

Is my calculation right? If not how can I calculate from w₁, f₁,w₂, f₂?

N.B: Why do I need this formula? because I need to know whether I am losing muscle due to diet, and exercise. So that I can maintain a healthy amount of protein and increase strength training to avoid muscle loss as I am just focused on weight loss. My weight and body fat percentages were 88.0kg and 27.4% on Jun 26. And now I'm 80.3kg and the body fat percentage is 23.5%. In 69 days I lost 7.7 kg, of which muscle loss was 2.46 kg(according to my calculation), and the fat was 5.24 kg. This amount of muscle loss is making me anxious.

Answer 1

Provided that your fat mass is lost through sustainable means—an adequate diet, hydration, and low-intensity activity—or provided that you have refueled and rehydrated after a restrictive diet and/or high-intensity training regimen, the equation you have derived is correctly balanced.

So your formula is entirely correct, provided that you can fairly assume that homeostasis has otherwise been maintained.

By extension, if your mass has been lost rapidly, through a heavily restrictive diet (one that provides significantly lower energy than your Basal Metabolic Rate, for example), and/or from a high-intensity training regimen, and if you have taken the subsequent measurement before replenishing fuels and fluid, whilst your formula is mathematically correct, it will be unreliable (as discussed in another contributor's comment, above).

I hope that helps.

Answer 2

Muscle loss cannot be inferred purely through changes in body fat percentage. The reason being that muscle is only one component of fat free mass. Experienced natural bodybuilding competitor and coach Alberto Nunez has talked about a sort of rule of thumb for weight loss which boils down to 20% of all long term weight loss being water. With this in mind, losing some fat free mass is to be expected with weight loss.

What about muscle mass specifically? Muscle mass and muscular strength are highly correlated with one another and because strength is much more easily quantified, it serves as a decent proxy for muscle mass retention. If you are losing weight and you aren't getting any weaker, then you likely aren't losing muscle. In fact, if you are losing weight and you are getting stronger in the process then you are probably managing to gain muscle.

One final point that should be made here is in regards to body fat testing methods. They are prone to error, but if done consistently, they are often internally consistent. If you are having your body fat tested less than a week or two apart from each test, don't compare those results. If anything those results should be averaged. If you want an accurate picture of what's going on with your body fat percentage, compare your results from a minimum of a month apart. Why? Because meaningful differences won't occur on a daily basis and while a weekly basis is more substantial, a monthly basis is more indicative of trends.

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Side note: While body fat percentage is an interesting metric to keep track of, it is often utilized poorly. Because of this, I would rather see the layperson to focus more on how their clothes fit as opposed to having them focus on numbers and concepts they don't understand. More often than not, the exact number doesn't matter at all, most people just want to vaguely look a certain way. If you have a good idea of what your body fat percentage is as well as the number associated with the look that you are going for, you can plan out approximately how long it will take. But if you are just guessing I would recommend just focusing on how things fit, comparing progress pictures, or hiring a professional to do the complex stuff.