I was using your body comp calculator recently, and comparing it against calculations submitted by my students. The male results were coming out correctly, but the female results were consistently off. In looking into it further, it appears that the body-density values were accurate for both sexes (we were using 3-site formulas), indicating that the Jackson-Pollock formulas to calculate body-density from sum of skinfolds were correct.
However, for females the BF% from body-density was incorrect, and this appears to be due to the inappropriate use of the male Siri equation (%BF = (495 / density) - 450, when the female Siri equation should have been used: %BF = (501 / density) - 457.
This makes a difference of over 1% BF when finding female BF%. On a related note, this page uses the general-population/white equations for finding BF% from density. Because of the substantially greater FFM density in Black individuals, this equation underpredicts their BF% fairly substantially. If there was another input for ethnicity to distinguish between Black and non-Black, the calculator accuracy would improve.
Thanks for considering my concerns,
Clayton Peterson, PhD
Hi Dr Peterson,
Thank you for your comments and your concerns. Our calculator has been available on ExRx.net since 2001 and you are the first to request additional alternative formulas. I've actually been using these same formulas in calculating body composition since 1985, when my professor (and mentor) would take my skinfold measurements every 1 to 4 weeks for the next several years throughout my undergraduate and graduate studies at Kansas State University. I've performed countless skinfold body compositions myself throughout this time and since. It was an invaluable tool in determining the effects of training and dietary modifications for both myself and others I had assisted. Around 1992, I created fitness assessment software used by the Department of Kinesiology at KSU for many years. It utilized these same formulas including the Siri formula to convert body density estimates to body composition values. Although I became aware of the various alternative formulas specialized for various populations sometime later, I continued to use the Siri formula for the body composition calculator you see on our site today.
Since it's been such a long time since I last looked at these formulas and the relevant literature, I had one of our interns reexamine these references to refresh my memory on this topic, I also did additional research myself so I could respond more appropriately to your email.
Although the Siri Equation used male subjects to derive its formula (Siri 1956), the Siri Equation has long been considered a standard method in which to calculate body fat from both men's and women's body density estimates (Morrow 2016, ACSM 2014, NSCA 2012, Heyward 2004, Noble 1986).
In fact, Jackson, Pollock, and Ward (1980) used the Siri equation in calculating percent body fat when they developed a formula for predicting body density for women. This is the same formula we have used on our site all these years, in addition to the equation for predicting body density for men (Jackson 1978)
Admittedly these early 2 compartmental model equations (lean and fat body mass) such as the Brozek and Siri Formulas have been known to produce systematic prediction error when applied to population subgroups or individuals whose Fat Free Body Density varies from the assumed value (1.1 g/cc). Multi-compartmental model formulas have since been developed which take in consideration variations of bone density in certain populations. (Heyward 2004)
Since the Siri equation has long been used to estimate body composition in all populations, including being used in conjunction with the women's body density formula as utilized on our calculator, the more recent formulas for specific populations offer alternative methods to the Siri formula which still continues to be so widely used.
As you may be aware, there are many dozens of these alternative formulas to address many different populations and age groups (Heyward 2004, ACSM 2014), so it becomes a matter of how specific the tester wants to be in choosing a body composition formula. Even with the most relevant formula to a specific population, it will always be an estimate of body composition due to individual variations. The challenge then becomes, how many and which ones of these specialized equations we should offer to address most or all populations. Then there remains the issue of which formula to use if the individual belongs to more than one population. Even when a definite population can be identified, there's still variations of bone density to factors such as genetics, nutrition, and degree of conditioning from certain types of exercise between individuals.
I agree a specialized equation for women and various ethnic populations may be a nice option to offer, but test evaluators will still face the above mentioned issues. Although applying a special formula for every population may be somewhat more accurate, for all intents and purposes, the Siri Equation appears to offer a reasonably accurate estimate of body composition allowing for insightful comparisons for all populations which is quite useful as the participant continues to be retested over time, as I done over the decades as both a subject and test administrator. I also believe that using skinfold measurements offer many district advantages over more expensive (eg: hydrostatic or body pod) or more indirect and questionable methods (eg: bioelectrical impedance), particularly for repeated comparisons over time.
We're currently developing a fitness assessment mobile app (Android & iOS) allowing the user to collect pretesting data, customize testing batteries, send reports, save all data for later comparisons, and offer exercise prescriptions. We plan on eventually providing a wider range of assessments and equations in future versions as compared to the free calculators found on our site, which may include offering alternative equations to the Siri formula to more precisely predict body composition in various populations. We appreciate you using ExRx.net as a classroom resource.
ACSM (2014) ACSM's Guidelines for Exercise Testing and Prescription, Walters Kluwer, 9th Ed, 70.
Heyward V, Wagner D (2004). Applied Body Composition, Human Kinetics, 2nd ed, 8, 215, 217-218.
Jackson AS, Pollock ML (1978). Generalized equations for predicting body density of men. British Journal of Nutrition. 40: 497-504,
Jackson AS, Pollock ML, and Ward A, (1980). Generalized equations for predicting body density of women. Med Sci Sports Exerc. 12: 175-182.
Morrow JR, Mood DP, Disch JG, Kang M (2016). Measurement and Evaluation in Human Performance, Human Kinetics, 5th ed, 204.
Noble BJ (1986). Physiology of Exercise and Sport, Times Mirror / Mosby College Publishing, 352.
NSCA (2012) NSCA's Guide to Tests and Assessment. Human Kinetics, 26.
Siri WE (1956). Body composition from fluid spaces and density: analysis of methods. United States Atomic Energy Commission Report UCRL-3349 [Donner Laboratory of Biophysics and Medical Physics. Univ. California. Berkeley, California].
I really appreciate your thorough and reasoned reply. I understand the slippery slope one encounters when making specific accommodations for different populations: where does it end? I also understand that every body-composition assessment involves many underlying assumptions and should be thought of as an educated approximation.
I think we disagree on the final verdict: I think the evidence suggesting fundamental differences between males and females, as well as between Blacks and non-Blacks, is convincing enough to justify including those parameters in a model for predicting body composition. But I understand your decision, and it is well-reasoned.
Lastly, thanks for providing such a wonderful compilation of resources for all things exercise. It is one of the sites I most consistently share with my students.
Clayton Peterson, PhD
Skin Fold versus Circumference Measurements
Hi, I am currently writing my dissertation on the effects of Sports Supplements on Body Fat % and the comparison of tools as a measure. I have thoroughly enjoyed using your website as a source and was interested how your body fat % calculator works. The skinfold calculator identifies both 3 and 7 site calculators BUT I have found many websites and equations require waist and forearm circumferences. Could you please explain how that is not required by your calculator. If possible any reading on this matter would be greatly appreciated. I look forward to your response. Once again a great resource!
These formulas have been around for many decades. The references are provided near the bottom of the mentioned calculator. You can look at those studies up on PubMed. They will give you a comprehensive understanding of the science involved in these formulas.
When I was in college (KSU), many soldiers from Fort Riley, who were considered overweight when measured by circumference measurements, would set appointments with our lab and pay money to have their body composition (with lung volume) tested because it was much more accurate than measuring girths as they do in the Army. But obviously, that requires a specialized laboratory equipment, and a higher level of expertise to administer such tests.
In a clinical setting, skinfold measurements offer a more practical alternative in estimating body composition and is more accurate thAn the alternatives like bioelectrical impedance, near infrared, ultra-sonic, MRI, and circumference measurements, etc. In my experimental methods class, I also conducted a study comparing skinfold measurements with a formula using waist circumference in college men who weight trained. In this study, we found that if men had an enlarged musculature of the midsection (i.e. developed Erector Spinae, Obliques Rectus Abdominis), that circumference measurements would under estimate lean body weight therefore increasing the estimated percent body fat.
In a clinical setting, you will need to look at the changes of body composition occurring over time since there is a degree of measurement error with skinfold and even circumference measurements. For this reason, these indirect measurements have not been considered accurate enough for academic research examining body composition cha nges over time. Wilmore, et. al. (1970).
You can also do more research in this area on PubMed.
Wilmore JH, Girandola RN, Moody DL (1970). Validity of skinfold and girth assessment for predicting alterations in body composition, Journal of Applied Physiology, 29 (3), 313-317.