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

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.

• This is false: "Muscle loss during t1 to t2 = Weight loss - fat burnt". I'm no expert but the literature clearly makes a necessary & useful distinction between muscle mass and "fat-free mass" (FFM), which includes other bone and soft tissue. Also your previous question indicates you're using bioelectrical impedance via a scale, which has low enough accuracy that this formula needs to take ± a substantial % into account. Sep 3, 2020 at 8:05
• let assume recorded body fat is accurate. I just want to know the calculation. Does the mass of bones and soft tissues change over time during weight loss? @DaveLiepmann Sep 3, 2020 at 9:05
• I don't know whether non-muscular FFM changes during weight loss but I assume it does. I'd bet that the change is negligible compared to the error propagated by inaccurate body fat measurements at t1 and t2. Sep 3, 2020 at 9:34
• Why do you want this formula? Sep 3, 2020 at 9:35
• Would the results of the calculation tell you anything? Isn't the solution for your anxiety the same regardless – strong resistance training? Sep 3, 2020 at 11:19

## 2 Answers

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.

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.

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.

• I am afraid to say that what Alberto Nunez says has no rational basis. Yes, a very significant portion, even the majority, of weight loss can be explained by water loss, but that does not imply in any way that it is, and certainly not that it must be. Water losses are typically the consequence of glycogen depletion, since glycogen is stored in its hydrated form in the muscles an liver. However, fat can be lost, and that loss maintained, without glycogen loss, and indeed, entirely without a loss of hydration.
– POD
Sep 5, 2020 at 4:16
• It should be mentioned, also, that whilst it is very common for muscle to be lost in conjunction with fat loss, especially in the discipline of bodybuilding, that is more a function of how that fat is lost, and at what rate. There is absolutely no necessity to lose fat-free mass in conjunction with fat mass.
– POD
Sep 5, 2020 at 4:27
• @POD - I believe the rational basis is the water associated with tissue loss. His opinion certainly isn't the highest form of evidence and I'm not aware of any studies looking at this in depth, but given the nature of his profession I would imagine that his insight was appropriate here. And while some muscle loss is common, especially when getting super lean like bodybuilders do, it's hardly impossible to maintain or even gain muscle mass - especially as a beginner which the question asker seems to be. There was even a study I came across recently that showed it can be done in trained people. Sep 5, 2020 at 16:42
• researchgate.net/publication/… Sep 5, 2020 at 16:42
• I agree. However, if water is directly associated with muscle tissue itself—for example, through blood supply—then we would normally include that in our assessment of ‘lean’ or muscle mass. The common belief that water accounts for a significant portion of weight loss is based on the fact that it does when we adopt restrictive diets and/or high-intensity training regimens, which can deplete muscle and liver glycogen almost entirely. And since these regimens are a cultural norm in some circles, it is, for those who follow those cultural norms, true. But it is not true more generally.
– POD
Sep 6, 2020 at 1:59