How to get body composition with values summing up to the total body weight

luca_roby I have the same question. And no answer, but a (qualified?) guess: If body water is calculated from both fat and muscle the result gets to within a few kilos. It does for me. For your example above the calculation would be:
Weight = ((Fat + muscle) x 56.4%) + fat + muscle + bones, i.e.
Weight = ((13.0 + 24.4) x 0.564) + 13.0 + 24.4 + 2.5 = 61 kg 

For myself (I'm a 88 kg male) I get within 2 kg. from my recorded weight
... but it's just a guess!

Would, too, love to know if anyone has any insights!?

I'm seeing the same issue. Can we get a response from Garmin on what the measurements actually mean? I've compared these numbers with those from my doctor's equipment and the body fat and water measurements are very close. His scale doesn't show Skeletal Muscle Mass and Bone Mass. Instead it has something called "Dry Lean Mass." That value is about 2/3 of the number shown for Skeletal Muscle Mass. I've tried all kinds of manipulations to get the numbers to line up and I can't even get close.

Thanks Bytecrawler - that's very interesting info.

Bytecrawler , petkir

Good job!
Following your ideas and assuming that the discrepancy between the actual body mass (measured by the Index S2 Scale) and the sum of the values converted in kg of the different body elements derives from the fact that the Body Water is also included in Skeletal Muscle Mass, Body Fat and Bone Mass, the problem is to find the right percentages of body water included in the other body composition factors.

petkir used the midpoints of the interval values given by ChatGPT

Body fat: 10-15%            midpoint:12.5%
Muscles: 60-65%            midpoint:62.5%
Bone Mass: 10-20%        midpoint:15%

With these values, decreasing the values given by the scale to get a dry mass in kg and summing those values to the total body water reported by the scale there is an error of about -4% (54.8 kg vs 57.0 kg). Good but not much satisfying.

Bytecrawler used slightly different values to reduce the discrepancy.

I have now used Excel "Solver" to find the optimal solution.
(In Excel-Data-Solver you select the cells with the percentages used and tell Excel to change their value to minimize the total error calculated in another cell)

The result is a 0% error !
Excel gave me the following values for the water content:
Body fat: 19.60%            
Muscles: 50.73%
Bone Mass: 4.78%

Not much far from petkir values.

I've used my weight data of 22-02-2023 (those of my OP) and the more recent data of 30/03/2023 to generate the above 3 "optimal" percentages.
I've then used another set of data (from 19-03-2023) to validate the model and check its reliability. With this new set the error is just -0.06% (57.57 vs 57.6).
Maybe these parameters are the ones used in the S2 scale inner (and hidden) algorithms.

In the image below there is the Excel sheet with the calcs.

A sure fact is that the percentages produced by the scale (i.e. in the body fat and the body water) show a great variability on a day by day basis, variability much greater than what is reasonable to expect.
That's a sign of a high level of uncertainty in the measurement process and that's probably the reason why Garmin doesn't show a detailed breakdown in kg of the different body components.

Anyway, in the long period, averaging several values, can give some ideas about possible meaningful changes in the body composition (i.e. if one starts doing much more exercise).

It would be useful if other users could check this model with their data.
It would also be fine if someone from Garmin could give us some more insight.

I think you're on to something. I ran this with my numbers and the numbers were consistently low by about 4%. I took a stab and assumed the discrepancy was primarily in muscle mass because the water content in muscle mass reduces with age and I suspect that at 68 years old, I have a few years on most of you. Taking the water percentage down to about 47.4 % got me to within .0003% +/- 0.2 % and a std deviation of less than .001%

Thanks Bytecrawler .  I've modified the model with more weight data records (my weight data for 58 days). In my previous post I only used 2 days so it was just a first trial.

It seems that for my data the optimal percentages for the water content are now

Body fat: 20%            
Muscles: 50%
Bone Mass: 8%

That produces a discrepancy of about a ± 0.1 kg between the scale reported mass and the sum of the 4 components recalculated masses. And yes, I'm 60 years old (a little younger than you)..Can you check your data with the new % parameters?

I still needed to bring down the water percentage for muscle mass. I suspect the percentages need to be tailored to the individual.

That make sense. Probably Garmin's algorithm uses also the individual age to make the decomposition. I can't check that out having only my personal (60 yo) data sets.