Body Fat Percentage Calculator Accuracy - warning a little nerdy

jchite84

In the past, I've found myself obsessing over body fat calculators and driving that number down as my weight went down. Today, I found a data set of 252 men, a variety of body measurements and their body fat percentage as calculated by a water displacement test (Pretty much the gold standard for body fat % measuring). I decided I would see if I could create a model to measure body fat percentage based on height, weight, and abdomen measurements, and my computer program spit out some numbers and I measured their accuracy against the water displacement data provided. With a standard deviation of 4.45 % body fat, my model was accurate within 1 standard deviation of the water displacement test 66.67% of the time. So, this got me thinking, how accurate are other calculators? I used the formula used in the YMCA body fat calculator and the Covert-Bailey body fat calculator and found that they are accurate to the same standard deviation 63.4 and 49.5 percent of the time respectively.

Conclusions:
1) The smallest SD I could get was +-4.45% - and having almost 9% deviation seems too significant when you are measuring something like body fat. Though, admittedly, I am not an exercise scientist, so this could be a perfectly acceptable measurement deviation.
2) Even giving other body fat calculator a similarly wide range of deviation, the most common body fat calculators found online aren't all that great.
3) Unless you have the means and desire to invest in a water displacement test, take the numbers spit out by these online calculators with a grain of salt. Maybe it's a good thing to measure to give yourself another progress number, but the chances of it being particularly accurate, aren't that great.

For anybody who is curious, the formula my computer spit out for measuring body fat % is this [A*(-.13)+B*(-.13)+C*(2.42)]-36.61= BF% +-4.45%
A = Weight in Pounds
B = Height in Inches
C = Circumference of Waist at Navel in Inches

diegops1

Nice to know that someone else uses math to figure out the reasonableness of what someone is trying to sell. I did a water displacement test many years ago when I was an active gym rat and I was impressed with how poor the other methods were by comparison.

Pickles175

Is your calculator for men only?

Codilee87

Pickles175 wrote: »

Is your calculator for men only?

Seconded

segacs

I think the point is that no simple formula is ever going to be able to take into account all the different data points that can influence body fat. All those online calculators should be taken with a shakerful of salt.

ForecasterJason

This is interesting, thanks for sharing.

Holla4mom

Very interesting! I love the mathematical processes you went through to arrive at this.

vismal

Nice to see numbers applied to this. I tell people all the time that equations to determine body fat percentage are not very worth while. I would agree that you are correct in saying a 9% deviation is too much for meaningful use. If I got a result of 15% then I could be anywhere from 10.5 (very lean, losing more fat would only be necessary for competition) to 19.5 (plenty of fat left to lose if I desired). Also, I would argue that water displacement is not the gold standard in body fat testing. Dexascan is with water displacement being the 2nd best.

Wiseandcurious

Fascinating. Out of nerdiness, what software did you use?

The men dataset was easy to find using Google but I am yet unable to find any for women Still searching though, it would be so much fun to play around with this...

ETA: I found one but only 20 women, so if anyone finds better please post the link

jchite84

Formula would be for men only, as men were the only members of the dataset. I was planning on searching for one for all women, but I got held up by the super bowl.

@Wiseandcurious‌ I used an open source alternative to SPSS called PSPP. I did a multivariate regression with Body Fat % as the dependent variable and Weight, Height, and Waist Circumference as the independent variables. Once I got the linear model, I plugged the equation into Excel to calculate the predicted Body Fat % and High and Low estimates with 1 SD. I just popped in a logical formula to determine how often the actual percentage fell within the predicted range. I repeated the same process for YMCA and Covert-Bailey formulas (found online). One thing I did not do, but looking back I probably should have was clean out any potential outliers. It is possible that Covert-Bailey or YMCA are more accurate for body fat percentages in the in the median range, but their accuracy falls off at the extremes, but even if you picked up a slightly stronger trend of accurate cases in the middle, it's still a fairly inaccurate measure.

Wiseandcurious

Thank you for that info jchite84

If memory serves, Covert-Bailey takes into account frame size, i.e. to check its accuracy one would have to compare subsets with comparable wrist etc measurements.

I think however these formulas don't work as well for women because we tend to spread our fat differently on the body.

jchite84

Yes - Covert-Bailey requires a wrist measurement also. I factored in a wrist measurement, but it only changed the SD by .05%, but the R2 coefficient remained the same, so it didn't really make a significant difference in the output, and I feel that asking for an additional measurement gives you one more spot to mess up measuring, and distort the accuracy of the conclusion even more! And even taking the wrist measurement into account, which would seem to factor in frame size, it ended up being inaccurate the highest percentage of the time.