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I'm aware of two body fat percentage formulas I'm using to track my own health, both described here:

  1. the US Navy method which takes into account your waist, neck, and height (and hips for women); and
  2. the BMI method, which is a function of your BMI (hence, weight and height) and age.

As a scientist, I'm curious what the error is on these. The linked page reports a BFP out to the tenths, which is claiming that they can calculate almost down to an ounce (~10 g) how many pounds of fat there are on someone's body. That seems like too high of precision.

Of course, these don't converge, there's almost 4 lbs (2 kg) of difference between these metrics when I multiply my BFP by my weight.

So, how much error do these measurements have?

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I don't know if there are canonical references for these measurements. I've found a couple references that seem good enough for an order-of-magnitude estimate, though.

Latour, A. W., Peterson, D. D., & Riner, D. D. (2019). Comparing Alternate Percent Body Fat Estimation Techniques for United States Navy Body Composition Assessment. International Journal of Kinesiology in Higher Education, 3(4), 93-105.

Latour et al compare gold standard estimates with Dual Energy X-ray Absorptiometry (DEXA) with US Navy-style estimates based on circumference. There are some differences according to how exactly circumference is used in the US Navy method, and differences for men versus women, but overall standard error of estimate ranged from 3.42-4.21%, in absolute percentage points, with Pearson correlations between methods ranging from .732 to .819. However, there was also an offset in their sample; the mean DEXA for men was 19.3 versus 16.1 using the Navy method, and DEXA for women was 26.9 versus 27.5 using the Navy method. This could reflect systematic differences in the population that the Navy estimates were based off of versus the study population in this study's sample.

He, M., Tan, K. C. B., Li, E. T. S., & Kung, A. W. C. (2001). Body fat determination by dual energy X-ray absorptiometry and its relation to body mass index and waist circumference in Hong Kong Chinese. International journal of obesity, 25(5), 748-752.

This study compared BMI and DEXA estimates and found a standard error of estimate of 4.6% in a regression with BMI only, and 4.3% including age; they also found a standard error of estimate of 4.4% using waist circumference (again, as far as I can tell these are all absolute measurements and assume normality of residuals). This is using an in-sample estimate of the correlation again, though, so you might expect errors to be greater in another population.

I think you'll find that these errors are large compared to the range of interesting variation in body fat. It seems that these estimates tell you very little compared to what would otherwise be apparent from visual inspection. BMI rather notoriously fails when applied to athletes and bodybuilders, for example, who can clearly be observed to have low body fat, whatever a BMI measurement would suggest.

In closing I wanted to again emphasize that these are absolute percentages, so if you estimate body fat % to be, say, 20%, and error is 4%, you would say that within 1 standard deviation you're looking at a range of 16-24%.

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  • I'm running some numbers based on some other studies I found and they're pretty close to what you've got here. Feb 16 at 21:58
  • @AzorAhai-him- Aye, I looked at a couple other studies as well in different populations and they were all in rough agreement. I would guess that individual differences make up a lot of the discrepancies, so probably if you had a gold standard measurement for one person alongside a BMI or circumference measurement, you could use changes in BMI or circumference to fairly accurately track changes in body fat, but for a baseline measurement it seems like they'd only be worth using on a population level.
    – Bryan Krause
    Feb 16 at 22:08
  • Funny though, the Navy method produces a larger value for me than the BMI method, although Latour found the opposite pattern. Feb 16 at 22:33
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    Underwater weighing done properly and DEXA scans are the gold standards in bodyfat calcs. BMI is a joke, circumference isn't much better. A well done 9 site skinfold caliper test can get near to DEXA standards, but the accuracy goes down with the 5 and 3 site versions, or if it's not properly done. Skinfold takes a bit of practice.
    – JohnP
    Feb 17 at 15:27
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    I found data suggesting similar estimates of 4-8% cool that it converged, less cool that BMI is essentially randomly associated with BFP lol. Feb 21 at 19:57
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Frankenfield, D. C., Rowe, W. A., Cooney, R. N., Smith, J. S., & Becker, D. (2001). Limits of body mass index to detect obesity and predict body composition. Nutrition, 17(1), 26–30. https://doi.org/10.1016/S0899-9007(00)00471-8

Frankenfield and colleagues reported an immense variation between BMI and BFP below a BMI of 30 (obese, or 25% BFP in men and 30% in women according to the same study).

The r^2 value for predicted versus measured body fat/height^2 was 0.567 in men with a BMI below 30 kg/m^2 and 0.996 in men with a BMI above 30 kg/m^2 (corresponding values for women were 0.933 and 0.998, respectively).

enter image description here

Solid circles: men; open: women

From this graph we can also estimate that the SD of the measurement error is 3-4.5 absolute percent, which aligns neatly with Bryan Krause's answer, which is large relative to the range of BFP values of under 25/30%.

Bowden, R. G., Lanning, B. A., Doyle, E. I., Johnston, H. M., Nassar, E. I., Slonaker, B., ... & Rasmussen, C. (2005). COMPARISON OF BODY COMPOSITION MEASURES TO DUAL-ENERGY X-RAY ABSORPTIOMETRY. Journal of exercise physiology online, 8(2).

Bowden and colleagues used DEXA as the gold standard in a sedentary sample. They similarly found a correlation of r=.551 for BMI and DEXA. They provided enough stats in their paper I was estimated the SD of difference between the BMI method and the DEXA measurement as 7.5% in men and 8.1% in women which is nearly half the BFP measurements of the skinniest participants, although my analysis was constrained by lack of information, and the true value is probably smaller.

They also calculated a linear model regressing DEXA on skin fold (SF) and biolectrical impedance analysis (BIA), finding similar values (although the SE of the regression isn't the same as the SD of the difference):

A step-wise multiple regression analysis was calculated revealing SF as the greatest predictor of DEXA with 67.5% of variability explained (r2=0.675) followed by BIA (12.1%) and BMI (2.6%). Total variability explained was 82.2% (R2=0.822). Beta weights were calculated for BIA (0.457), SF (0.425) and BMI (0.197).

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