CHAPTER 9
Estimating % Body Fat
Introduction
There are numerous methods around for the estimation of % body fat. The unfortunate truth is
there is not one that gives a very precise estimate of it for individual assessment. I was very
careful to title this chapter “Estimating % Body Fat” and not Measurement or Determination of %
Body Fat. Those last two titles make it sound like it is an accurate process, which it is not! This
chapter will detail the most important methods being used today.
Unfortunately there is only one way to truly know the answer to how much body fat there is in
your body and that is to blend you and dissolve out all of the lipid molecules with ether. Any other
method relies on one or more assumptions to be able to estimate not measure % body fat.
There are basically three categories of methods: Direct, Indirect and Doubly Indirect, each of
which will be addressed here. In concluding we will look at how % Body fat methods are
validated or at least the details of how validity is claimed.
Brussels Cadavre Study
A landmark study was carried out in the 1980’s where 25 bodies were totally dissected after
comprehensive anthropometry had been carried out. This was a collaboration of Bill Ross (SFU)
and Dr Jan Clarys (Frei Universitiet Brussels). Alan Martin and Don Drinkwater Ph.D. candidates
in Kinesiology at the time went over for 6 weeks to be the lead investigators for the study. The
study produced unique invaluable data on the variability of tissue densities and proportions.
“In the original Brussels Cadaver Analysis study, 13 female and 12 male cadavers, age
range 55–94 years, 12 embalmed and 13 unembalmed, were selected from about 75
cadavers on the basis of least emaciation and most normal appearance (Clarys et al.
1984). After comprehensive anthropometry, each cadaver was dissected into skin,
adipose tissue, muscle, bones, organs and viscera. Tissues were separated by six body
segments: these were arms, legs, head and trunk. The weight of any fluid separating from
the tissue was added back to the tissue weight. All tissues were stored in airtight
humidified containers until weighing. The evaporative weight loss occurring through the
dissection process, taken to be the difference between pre-dissection body weight and the
sum of all tissues after the dissection, was added back to each component in proportion to
its weight. This evaporative weight loss was considerable and varied between 2 and 3 l; it
was linearly related to the length of time the cadavers were exposed for at room
temperature. These quantities may not be surprising, considering the important but
variable amounts of water in the separate human body tissues (figure 1). Volumes and
densities of all tissues were determined by weighing the tissues underwater. A complete
dissection lasted from 10 to 15 h and required a team of about 12 people.”
You can read more about the Brussels cadaver studies in the paper I have put in the readings
column of the course web site: J. P. Clarys, S. Provyn & M. J. Marfell-Jones (2005): Cadaver
studies and their impact on the understanding of human adiposity, Ergonomics, 48:11-14, 14451461
Estimating % Body Fat
9-2
Definition of % Body Fat
Although there are many constituents of the human body when human biologists use the term
body composition they are more often than not referring to a two compartment division of Fat
and Fat-Free (Non Fat) components. Body fat has been defined as the ether-extractable
molecules of the body (Keys and Brozek, 1953). As described by Harper et al., (1977) fat is
comprised of many different molecules such as phospholipids, glycolipids, lipoproteins, derived
lipids such as cholesterol, glycerol esters of fatty acids and waxes. About 1 – 2% of all lipids are
structural lipids that are found in the nervous system. This was termed Essential Fat. This is a
term used earlier with a different definition in Table 5-3 of the Weight for Height chapter. Typical
percentages for Essential Fat for males and females were given as 1 – 5% Body Fat for men
and 3 - 8%.Body Fat for women. Unfortunately, this definition of Essential is the amount of %
Body Fat necessary for minimal healthy functioning of the body. Very different than Essential
Body Fat being the 1-2% of all lipid that is essential for nervous system integrity and function.
Beware of this difference when you read anywhere about body composition testing.
When someone has their % Body Fat estimated what is it that they have had measured. Most
people believe that it is the amount of that solid yellowish white stuff found under their skin. The
same fat that the butcher will trim off of the outside of your roast for you. Unfortunately, this is
absolutely wrong. That is subcutaneous adipose tissue. The fat that is being estimated is the
type of fat or lipid molecules that are stored in the adipocytes in the adipose tissue. If you were
to blend a person in a massive Magic Bullet then dissolve out all of the fat molecules with Ether
then that would be the Fat that is being estimated. % Body Fat is the percentage of your body
weight that is made up of lipid molecules, which would be much less than % Adipose Tissue
Mass. Adipose tissue is a storage tissue for lipid molecules thus containing all the elements of a
tissue including extracellular components such as water. It can be found both subcutaneously
and internally around organs or in the abdominal cavity. It is therefore not surprising that the vast
majority of individuals who have their % body fat measured by any method believe that they are
being told how much adipose tissue is in their body because it that that they call fat. The truth is
that all the methods estimate the amount of lipid (fat) in their bodies and not the amount of
adipose tissue.
Unfortunately, the same naming confusion exists in the scientific literature, although it is clearly
defined in the primary literature that fat is lipid and not adipose tissue the two fat and adipose
tissue are often confused in the body composition literature. For example, a paper was entitled
"Fat areas as estimates of total body fat" (Himes et al., 1980) and the terms "fat biopsy" and "fat
patterning" are almost universal. This confusion between adipose tissue and fat has led to
some serious errors. A paper proposing a simple geometrical model for the estimation of the
subcutaneous adipose tissue volume in infants, referring to this throughout their paper as the
"fat layer", (Dauncey et al., 1977). In converting from volume to mass, they selected the factor
9-3
Estimating % Body Fat
0.9 g/ml as "being the density of human fat", when they should have used the density of adipose
tissue, with its greater and much more variable value.
Alexander (1964) measured adipose tissue thicknesses and excised a portion of the internal
adipose tissue of each of 20 autopsy cases. In his report the terms fat and adipose tissue are
used interchangeably. As a result, he compares his "fat" percentages (actually adipose tissue)
with those of other workers who used densitometry or ether extraction to determine fat content.
In view of considerations such as these, the term fat should only be used to refer to the etherextractible chemical entity.
Methods for Estimating % Body Fat
The most common methods for estimating body fat are densitometry (underwater weighing,
water volumetry, helium dilution and the BodPod), whole body counting, total body water
measurement, anthropometry, bioimpedance and DEXA. Anthropometry, bioimpedance and
DEXA rely for their validation on one or more of the indirect techniques and are thus called
doubly indirect methods. A summary of the indirect methods presented here and their
assumptions are displayed in Table 9-1.
In the absence of direct methods, densitometry has long been regarded as the criterion method
(Malina,1969). Yet all indirect methods are only as good as the assumptions on which they are
based, assumptions which in each case can only be validated by dissection evidence. Table 9-1
shows the Indirect methods that will be described here and lists the assumptions required to
estimate % Body Fat using that technique.
Note that the densitometric methods all essentially measure total body volume and that in
combination with body weight, body density is calculated.
Density = Weight / Volume
units: gm/ml
Once the Body Density has been estimated it is transformed into an estimate of % Body Fat
using assumptions of constancy of density of the Fat and Fat Free Masses, as will be described
later.
For Whole Body Counting and Total Body Water estimates of the Fat Free Mass (kg) are made
and transformed into estimates of % Body Fat:
Fat Mass = Weight – Fat Free Mass
% Fat = Fat Mass / Weight * 100
9-4
Estimating % Body Fat
Table 9-1: Indirect Methods for Estimation of % Body Fat
Determine Body Density (D) via direct measurement of Body
Volume (V) and Body Weight (W a)
Whole Body
Volumetry
D= Wa /V
Determine % Body Fat by assuming constant densities of Fat and
Fat Free Masses
Determine Body Density (D) via determination of Body Volume by
hydrostatic weighing ((W a-W w)/dH2O) and Body Weight (W a)
Hydrostatic
Weighing
D= Wa /((Wa-Ww)/dH2O
Determine % Body Fat by assuming constant densities of Fat and
Fat Free Masses
Densitometry
Determine Body Density (D) via determination of Body Volume (V)
using helium dilution chamber and Body Weight (W a)
Helium
Dilution
D= Wa /V
Determine % Body Fat by assuming constant densities of Fat and
Fat Free Masses
Determine Body Density (D) via direct measurement of Body
Volume (V) using BODPOD chamber and Body Weight (W a)
BODPOD
D= Wa /V
Determine % Body Fat by assuming constant densities of Fat and
Fat Free Masses
Determine Total Body Water using isotope dilution
Total Body
Water
Isotope
Dilution
Determine Fat Free Mass by assuming constant fraction (proportion)
of Water in the Fat Free Mass
Determine % Body Fat from Weight (W a) and Fat Free Mass (FFM)
%Fat = ((Wa – FFM)/Wa) x 100
Determine total amount of Potassium (K42) in the body using whole
body counting of K40 and assuming constant fraction of K40 in K42
Whole Body
Counting
K40
Determine Fat Free Mass by assuming constant fraction (proportion)
of Potassium (K42) in the Fat Free Mass
Determine % Body Fat from Weight (W a) and Fat Free Mass (FFM)
%Fat = ((Wa – FFM)/Wa) x 100
9-5
Estimating % Body Fat
Two-compartment Models for determing % Body Fat
Because of the acceptance of densitometry as the criterion method, it will be analysed in some
detail here. Its basis is the two-component model: fat and fat-free mass (also called the non-fat
mass), and the theory is as follows:
For unit mass of a body of density D, composed of two different components of masses A and B
with densities a and b, a simple analysis yields the expression:
D
A B
( A / a )  ( B / b)
equation 1
By rearranging this one of the fractions (B) can be calculated:
B
1
ab
b
x

D ( a  b ) ( a  b)
equation 2
This enables the calculation of the body fat fraction given the whole body density, D, and the
densities of the fat and fat-free masses. Various methods have been devised for the
measurement of D, the underwater weighing technique (Behnke, 1942) being the most used and
probably the most accurate (Wilmore and Behnke, 1969; Durnin et al. 1982).The density of
human fat is reported to be remarkably constant at 0.900 g/ml (37 C) (Fidanza et al., 1953; Allen
et al., 1959), with the previously mentioned exception of brain-derived fat. Using densities of
1.067 g/ml and 1.035 glml for cholesterol and phospholipids respectively, and assuming brain fat
contains 50% phospholipid and 25% cholesterol (Mendez et al., 1959), the calculated density of
brain fat is 1.005 g/ml. This agrees very well with the value of 1.002 g/ml measured by Allen et
al. (1959). However, since the quantity of fat in the nervous system is of the order of 2OOg
(Forbes et al., 1956), the error in using 0.900 g/ml for the density of all body fat is negligible even
for very lean individuals.
The difficulty in applying equation I lies in determining a value for the density of the FFM, and
this uncovers the basic assumption in whole-body densitometry, namely that the FFM has a
known density that does not vary from one individual to another or within one individual over a
period of time. Unlike the water and potassium contents of the FFM, there is no cadaver
evidence on which to base an estimation of the fat-free density; this has never been measured
directly in humans.
The earliest proposed figure was that of Pace and Rathbun (1942) who determined a value of
1.0939 for the specific gravity of the eviscerated guinea pig, leading to an estimation of about
1.090 g/ml for the density of the whole fat-free animal. They subsequently arrived at a prediction
equation for humans (Rathbun and Pace, 1945) utilizing a value of 1.100 glml for the fat-free
density which they attributed to Behnke and which Keys and Brozek (1953) in their
comprehensive review on body fat in adult man, described as "a very rough 'armchair'
9-6
Estimating % Body Fat
computation from old anatomical data". This is still the value most commonly used today, a
testament to the accuracy of Behnke's intuition.
With B being the Fraction of Fat Mass, applying the values of the density of Fat Free Mass (a) =
1.100 g/ml and the density of Fat (b) = 0.900 g/ml to equation 2
B
1
1.1x0.9
0.9
x

D (1.1  0.9) (1.1  0.9)
B
1
x 4.95  4.50
D
It becomes the well-known equation of Siri (1956):
FractionofFatMass 
4.95
 4.50
WholeBodyD ensity
or, if F is %Fat,
% Fat 
495
 450
WholeBodyD ensity
Figure 9-1: Plot of Percentage body fat versus Whole Body Density for the Siri equation (1956)
A plot of this equation is shown in figure 9-1. Typical average body fat in adult males ranges
from 18-24% (1.058-1.044 g/ml
─ ), in adult females from 25-31% (1.042-1.029 g/ml ─ ). The
whole body density ranges are indicated on the plot of the Siri equation with the respective blue
9-7
Estimating % Body Fat
and red bars. The plot projects beyond the range (0.900 - 1.100) for whole body density. Based
upon the assumed densities if the whole body density exceeded 1.1 g/ml then a negative body
fat would be predicted. The occurrence of such values would be a clear indication of violation of
the assumption of constant density for the Fat Free Mass. A review of the literature reveals a
significant number of these anomalous fat estimations. In reality any body fat estimate less than
about 3-4% is almost certainly anomalous since this amount can be regarded as 'essential' fat
(Wilmore, 1983). One cadaver (Forbes et al., 1956) which had the remarkably small amount of
136 g fat in the adipose tissue (0.2% of body weight) had a total of 4.32% body fat indicating
more than 4% to be non-adipose fat. Thus any literature values below about 3% for body fat
estimates will probably indicate a violation of the basic assumption. Such values are not rare. In
a study of 20 elite middle-distance and marathon runners, Pollock et al. (1976) found that 5 had
predicted body fat (from density and Siri’s equation) less than 2%. The values were: 0.2%, 1.2%,
1.3%, 1.5% and 1.8%. The leanest of these, Tuttle, had a total estimated fat content of 120 g,
less than the fat typically found in the brain alone. In addition, this subject displayed measurable
subcutaneous fat since the sum of 7 skinfolds was 31.5mm, an average of 4.5mm per skinfold.
In young males, body densities of 1.102 g/ml (Behnke, 1963) and 1.104 g/ml (Michael and
Katch, 1968) have been measured, corresponding to -0.8% and -1.6% fat respectively.
However, it is for lean mesomorphs
that the most anomalous results
Table 6-1.1. Body fat predictions for 9 professional football
players based upon body density determined via underwater
weighing (Adams et al., 1982).
have been found. In a study of 29
Canadian
professional
football
players, Adams et al. (1982) found
that 12 had predicted fat (from
density) less than 2%. Of these,
eight
were
negative
with
two
subjects estimated at -12% fat, and
a ninth had a fat prediction of zero.
Table
6-1.1
shows
whole-body
ID #
Body Density
(g/ml)
% Fat via Siri’s
equation
22
16
24
2
5
9
26
28
25
1.100
1.101
1.102
1.103
1.103
1.105
1.105
1.129
1.130
0
-0.4
-0.8
-1.2
-1.2
-2.0
-2.0
-11.6
-12.0
Sum of 10
Skinfolds
(mm)
63
74
57
55
97
69
87
64
88
density, predicted fat percentage and the sum of 10 skinfolds for each of these 8 subjects.
These subjects were not without subcutaneous fat, even the densest subject exhibited a mean
skinfold thickness of 8.8mm (subject #25, table 6-1.1). With some assumptions the mass of
subcutaneous adipose tissue can be roughly estimated for this subject:
From height and weight data the subject's surface area (SA) is 2.118m (dubois and dubois,
1916). Using the conservative assumption that the mean thickness of the adipose tissue layer is
one half of the mean of the ten skinfolds, then the volume (V) of subcutaneous adipose tissue
can be estimated:
V = SA x mean skinfold/2
Estimating % Body Fat
9-8
= 2.118x 104 x 0.88/2 ml
= 9.3 litres.
Assuming a density of 0.94 g/ml for adipose tissue, this gives a subcutaneous adipose tissue
mass of 8.76 kg. If 60% of this is fat (again a low estimate), a figure of about 5.25 kg is obtained
for subcutaneous fat. If in addition 'essential' fat is assumed to be 2% of body mass (88.2kg)
then total body fat estimated this way is 7 kg. Given a fat mass of 7 kg, a FFM of 81 .2 kg and a
measured whole body density of 1.130 g/ml this subject has a fat-free density of 1.155 g/ml,
which in reality may be even greater than this.
The work of Werdein and Kyle (1960) shows that even higher fat-free densities are probable. By
measuring body density and body water simultaneously they found fat-free densities of 1.057
g/ml for an osteoporotic subject and 1.189 g/ml for an osteosclerotic subject and stated that "the
cases of abnormal high or low bone density and abnormal hydration are merely the extremes of
a broad spectrum seen in normal subjects". In a similar fashion, Norris et al. (1963) estimated a
value of 1.062 g/ml for the fat-free density of an elderly man, emphasizing the compositional
changes in the FFM with advancing age.
The obvious conclusion from these reports is that the assumed value of 1.100 g/ml for the FF
density does not apply to some subjects. In cases where the FF density is greater than 1.100
g/ml and the subject is very lean, the error in the assumption may be indicated by a negative fat
prediction. For those subjects with FF densities below 1.100 g/ml, the error will not be signalled
by the impossible result of a negative body tat, rather, the resulting overestimates of body fat will
go unnoticed since densitometry is regarded as the criterion method.
In practice, there is a family of curves for the prediction of body fat from whole-body density,
each with its own assumed value for the density of the fat free mass. If a subject has an actual
FF density of 1.15 g/ml (as seems likely for some football players), then a measured whole body
density of 1.08 g/ml will correspond to a fat estimate of 23.3%. But, using the traditional
assumption of 1.100 g/ml, estimated fat is only 8.3%, a considerable error. In general, this error
is given by the vertical distance from the "standard" curve (dffrn = 1.100 g/ml) to the curve
corresponding to the actual value of dffm, measured at the obtained value of whole-body
density. It can be seen that this error increases slightly with the leanness of the subject..
The FFM is a chemical concept without anatomical or physiological basis. It is composed of the
fat-free tissues and fat-free fluids of the body. For its density to be constant requires that both
the following conditions be satisfied simultaneously:
(1)
the proportions of all the fat-free tissues (FF muscle, FF bone, FF skin, FF organs etc.)
must be fixed, and
(2)
the densities of these fat-free components must be constant.
Clearly, this is not possible; the question is not whether the FF density is constant, but how
variable is it?
9-9
Estimating % Body Fat
Densitometry – Volumetry by Water Displacement
Densitometric methods rely on the calculation of density from body weight divided by body
volume.
Body Density = Body Weight / Body Volume
equation 3
Body weight is easily determined by use of a traditional weigh scale. Body volume is a bit trickier
to determine and people have been very ingenious in developing ways to measure it. The
following densitometic methods rely on body volume being determined in different ways. The
first to be considered is body
volumetry using a tank of water
(Figure 9-2). It is as simple as
measuring the volume of water
displaced
by
the
whole
body.
However, this does present some
technical difficulties. The tank used
needs
to
have
the
following
characteristics:

the smallest diameter possible to
maximize
meniscus
rise
upon
immersion

a uniform diameter rigid cylinder to
provide consistent calibration at all
Figure 9-2: Volumetric tank for determination of Body Volume
heights of the tank

subject needs to gets in and out by a removable ladder

fitted with a capillary tube continuous with the water near the base of the tank, mounted on a
board with a linear measurement scale. Meniscus position can be recorded before and after
immersion.

Tank needs to be calibrated to establish the relationship between volume change and
measurement of meniscus excursion in the capillary tube.

thermometer to monitor tank water temperature

preferable to have perspex or toughened glass window part way down to monitor subject and to
help subject with any feelings of claustrophobia
Measuring Body Volume with the Volumetric Tank
1. Fill the tank with water to a level that will allow the level to rise to near the top but not
overflow during immersion.
2. Take the water temperature.
3. Record the measurement of position of the meniscus in the capillary tube.
9-10
Estimating % Body Fat
4. Get subject to climb into the chamber.
5. Measure Residual Volume of the subject while they are submerged in the water.
6. The subject may stand on the bottom of the tank.
7. After getting used to being in the tank get the subject to blow out all of the air in their
lungs and gently immerse themselves totally under the water.
8. Quickly read the new meniscus level after the initially bouncing has stopped (5 or 6
secs).
9. Instruct the subject to come up for air
10. Repeat measurement trials at least 5 times with appropriate rest time in between.
11. Apply calibration data to the test readings to calculate volume of water displaced and
hence volume of the subject.
Calculating Body Density from Volumetric Data
Body density ia calculated using the basic equation 3 shown above
Body Density = Body Weight / Body Volume
Which looks a little more complicated when body volume is corrected for residual volume and an
estimate of entrapped intestinal gas. The equation becomes:
Density 
Where:
Wa
V  ( RV  c)
Wa
equation 4
= Body Weight in Air
V
= Body Volume
RV
= Residual Volume of Lungs
C
= Volume of Entrapped Intestinal Gas
Densitometry – Underwater Weighing (hydrostatic)
Rather than directly measuring the volume of water displaced the volume is measured by
weighing the person freely suspended and totally submerged in water. The subject sits on some
form of seat suspended from a weigh scale. To be fully submerged the subject needs to have a
weight belt to stop them floating. This weight is taken into account in the calibration of the
weighing. Despite an apparently more complicated procedure it is preferred over the volumetric
method for various reasons.

It has been shown to be more reliable in repeat assessments

A larger tank needs to be used to allow the person to freely suspend in the water, which
is a good this in that it is less claustrophobic

It can be carried out in open water like at the side of a swimming pool which dispenses
with the need for a tank at all
9-11
Estimating % Body Fat
Calculating Body Density from Volumetric Data
The equation to calculate the body density from underwater weighing is the same as the one for
volumetry except that the volume of water displaced is calculated using Archimedes Principle.
Archimedes Principle
“The weight of water displaced is equal to the loss of weight of the body in water (weight
in air minus weight in water: Wa - Ww)”
So because
 Wa  Ww 
V 

 dw 
Density 
Wa
V  ( RV  c)
Density 
Wa
 Wa  Ww 

  ( RV  c )
 dw 
equation 4
becomes:
Where:
Wa
equation 5
= Body Weight in Air
Ww
= Body Weight in Water
dw
= Density of Water at specific temperature
RV
= Residual Volume of Lungs
c
= Volume of Entrapped Intestinal Gas
Densitometry - BodPod
The BOD POD technology is fundamentally the same as underwater (hydrostatic) weighing, but
uses air instead of water. The BOD POD measures the volume of air a person's body displaces
while sitting inside a sealed chamber, rather than measuring how much water their body
displaces when dunked in a tank. By using air instead of water, the BOD POD is a more user
friendly methodology as long as claustrophobia is not an issue.
Estimating % Body Fat
9-12
BodPd
The seat is a scale to determine body weight. Once body volume has been determined body
density and then % Body Fat can be estimated in the same way as for volumetry and
underwater weighing. The whole process of measurement and calculation is controlled by the on
board computer.
The BOD POD itself is a dual-chambered, fiberglass plethysmograph that determines body
volume by measuring changes in pressure within a closed chamber. The front, or test chamber,
has a seat that forms a common wall separating it from the rear, or reference chamber.
Total Body Water
If a known amount of a substance that is completely miscible with all body water is introduced
into the body and its concentration is determined in any of the body fluids (e.g. urine), after an
appropriate length of time for equilibration, then the total body water can be determined (Hevesy
and Hofer, 1934). The technique has been refined over the years and tritiated water has become
the substance of choice (Sheng and Huggins, 1979). Two major sources of error exist here:
1) while it is commonly assumed on theoretical grounds that using tritiated water
measures total body water (TBW) to within 2% (Forbes 1962), desiccation studies on
animals show an overestimate of from 4-15% of body mass (Culebras et al., 1976; Foy
and Schneider, 1960; 'I'isavipat et al., 1974).
2) to convert from TBW to percent body fat, it is assumed that the FFM contains a fixed,
known fraction of water, commonly taken to be 0.732 (73.2%). The value of 0.732 was
Estimating % Body Fat
9-13
derived primarily from data on guinea pigs (Rathbun and Pace, 1945). Data from the
eight human dissections are shown in table 4.1. The mean water content of the FFM is
74.91%, but the variance is high (S.D.= 4.95%). Some workers have rejected several
cadavers as "abnormal" and have obtained a mean value closer to the accepted 73.2%
(Forbes and Hursch, 1963). For example, if the cadavers of Moore and Widdowson #1
are omitted on the grounds of "abnormality", the mean water content becomes 72.68%
with a S.D. of 3.18%. With such a small sample it is very difficult to set criteria for
rejection of data. However if the standard formula for fat determination, i.e. mass of
body fat = body mass - 'I'BW/0.732 is applied to these eight cadavers, we arrive at a
mean percent body fat of 11.7% compared with the directly weighed value of 15.0%. It is
important to realize that this is the data that "justified" the constant 0.732 in the
estimation equation; the predictive accuracy for subjects outside this sample can only be
speculated upon.
Considerations such as these led Sheng and Huggins (1979), in their thorough review, to state
that "the use of the equation 100 - %TBW/0.732 for the estimation of fat can at best be a gross
approximation".
Whole-Body Counting
Since the potassium content of fat is negligible, virtually all body potassium is found in the FFM.
Of this naturally-occurring potassium, 0.012% consists of the isotope 40 K which emits gamma
radiation in the 1.46 MeV range. This can be detected under low background conditions using
an appropriately calibrated whole body counter, hence the total potassium content of the body
can be determined (Forbes and Hursch, 1963). If the potassium density of the FFM is constant
and known then the FFM, and thus fat, can be readily calculated (e.g. Cobn and Dobrowski,
1970). The validity of the technique hinges on the accuracy of the assumed potassium
concentration in the FFM. Again, data on this are sparse.
Of the eight whole body chemical analyses, only six included potassium determinations. The
data are shown in Table 4.1. Forbes and Hursch (1963) selected three of these and arrived at a
mean potassium concentration of 68.1 meq/kg FFM, a commonly used value.
9-14
Estimating % Body Fat
However, it is well knownTable
that 1: Water & Potassium content of the FFM, data from 8
dissections
neonatal
concentrations
of
Potassium in
Cadaver
potassium in the FFM are of the
% Water in FFM
FFM
Identification
(mE/kg of FFM)
order of 50 meq/kg (McCance and
Mitchell
77.56%
Widdowson, 1951, Novak, 1974),
Forbes #1
68.44%
66.50
while the age at which adult
Forbes #2
70.13%
66.60
Forbes
#3
74.02%
values obtain, so-called "chemical
Widdowson #1
72.62%
71.10
maturity", remains unclear. Sex
Widdowson #2
73.30%
72.63
Widdowson #3
82.41%
34.78
differences have been observed
Moore
80.83%
27.86
(e.g. Burkinshaw et al., 1971;
Mean
74.91%
56.58
Forbes, 1962; Oberhausen and
Onstead, 1965).
In addition to the progressive loss of lean body mass with age, Pierson et al. (1974) have shown
a decline in the FFM potassium from 72 to 50 meq/kg in males and from 60 to 47 meq/kg in
females over the age range 20-90 years. Also, changes in the potassium content of the FFM
with muscularity have been reported (Womersley et al., 1976; Ferroluzzi et al., 1978), with the
latter workers finding that sex differences were absent in their athletic subjects. They concluded
that variation in the muscle content of the FFM was the major factor in altering the potassium
content of the FFM.
Again as in the case of whole body water, there appears to be inadequate evidence to support
the basic assumption of a constant fraction of potassium in the fat free mass of all subjects.
Doubly Indirect Methods for the Estimation of % Body Fat
The Doubly Indirect methods rely for their validation on their prediction of % body fat values
determined by an Indirect methodology. The following are the more commonly encountered
Doubly Indirect methods

Anthropometric Predictions
o
One of the most common doubly indirect methods is prediction from
anthropometric measures, chiefly skinfolds. They are very sample specific,
hence there are over a hundred of them out there in the scientific literature.

Ultrasound
o
Ultrasound can be used to estimate uncompressed tissue depth at any skinfold
site on the body and therefore can be substituted for skinfolds in the production
of the % body fat prediction equations.

Bioelectrical Impedance Analysis (BIA)
9-15
Estimating % Body Fat
o
The impedance of current flowing through the body relates to the body
composition of the body. It would work best if we were uniform shape and
composition. We are unfortunately not uniform which causes validity issues with
this methodology. However, bio-impedance values in conjunction with height,
weight are used to predict % body fat.

Near-infrared Spectrophotometry (NIR)
o
This is an interesting approach in that it is not estimates of tissue thickness at
the sites that is used but estimates of tissue composition. Specifically the
change in near-infrared light spectrum in light reflected back from the tissue.
The shift in spectrum relates to the water/fat content of the tissue. Estimation of
% body fat is from these reflectance generated scores rather than thickness
estimates.

DEXA – Dual Energy X-Ray Absorptiometry
o
This relies on a whole body scan and generates regional or whole body
estimates of % body fat based upon image density related to calibration
standards.
Process for Development of a Doubly Indirect Methodology
The basic research approach to the development of the Doubly Indirect methods is the same for
all of the Doubly Indirect methods. The basic steps are:
Select a specific subject sample
These methods are very sample specific so it is best to have a very clear definition of who you
expect the method to be applied to and select your sample accordingly. This is important to
document so that your method is not applied to the wrong people. For instance, if you are
working with young south Asian females you must use methods that were developed for such a
subject population.
Determine body density or % fat using an accepted methodology
Once you have the sample selected they need to have their % body fat estimated using an
accepted Indirect methodology. This often underwater weighing but can be any indirect method.
This becomes the criterion % body fat for the individual.
Estimating % Body Fat
9-16
Measure subjects with other technique
The next step is to measure each subject with the new methodology that you are going to
predict their % body fat from. This could be skinfolds, other anthropometry, bio-impedance
measures, any method in fact that you feel relates to body fatness.
Produce regression equations to best predict % fat from new technique
Now you have a set of data with criterion values for % body fat for each subject and the
measurements on them for the new predictive technique. Now you let the computer do the work
and produce the best equation to predict the criterion 5 body fat from the predictor measures.
The best equation will be the one with the lowest Standard Error of Estimate (SEE).
Anthropometric Prediction of % Body Fat
The best example of a Doubly Indirect methodology is the estimation of % Body Fat from
anthropometric measures. Underwater weighing is not a practical field technique for the
assessment of body composition. In search of a practical field technique, weight for height
tables and their indices have been used in the assessment of obesity, however, they are limited
in that not all people who are heavy for their height are obese. You only have to look at a body
builder to see the fallacy of using weight for height indices in the individual assessment of
obesity. Since the early 1940's the field method of choice has been the prediction of percentage
body fat from anthropometric measures. These predictions are based on regression equations
for the prediction of percentage body fat or body density from various anthropometric measures.
Some equations predict percentage body fat directly, while others predict body density initially
and this is then transformed to percentage body fat using an equation such as the Siri equation
(1962). The predictive equations are produced by determining body density on a group of
subjects using underwater weighing or volumetry and carrying out a regression analysis with
numerous anthropometric variables. The result of such an analysis will be a prediction equation
containing the anthropometric variables that best predict body density (or its derivative
percentage body fat) in the given sample. The ability of these equations to predict is indicated by
the correlation coefficient (r) and the standard error of estimate (SEE).
Skinfold measures tend to be the best predictors of body fat, although there are equations that
use height, weight and various girths or bone widths. There are over one hundred equations
available for the prediction of body density (or percentage body fat). This is due to the sample
specific nature of the equations. Equations developed on young females for instance are not
applicable for use on males or older females. There are many factors that can affect the
relationship between body density (or percent body fat) and skinfold or other measures. Sex,
age, race and habitual physical activity level are factors that have been shown to be important in
Estimating % Body Fat
9-17
determining the sample specificity of the equations. Specificity due to these factors is due to the
fact that it is inherently assumed that in the sample upon which the equation was developed the
following factors are constant:
Skinfold Patterning
The pattern of deposition of skinfolds around the body is known to differ from individual to
individual.

Females have characteristic deposition of secondary sexual adipose tissue on the upper
arms, hips and thighs.

With ageing in both sexes there is a shift in dominance from limb to trunk deposition of
adipose tissue
Skinfold Compressibility
Skinfold compressibility varies from site to site due to differences in skin thickness, skin tension
and adipose tissue composition.

Skinfolds in females are more compressible than in males.

Skinfold compressibility decreases with age due to dehydration and changes in elastic
properties of tissues
The ratio of external/internal adipose tissue

The ratio of external/internal adipose tissue declines with ageing.
Fat (lipid) content of adipose tissue

Lipid content of adipose tissue varies from individual to individual due to variations in
adipocyte size and number.
Sample Specificity: It is important in using an equation that it was derived from a sample
containing individuals similar to the subject that is being measured. Such that if a 22 year old
male university student is being measured, an equation should be used where the originating
sample consisted of male university students of an appropriate age range. This is referred to as
sample specificity in that the equation works best on the type of individuals from which it was
derived. The equations by Sloan (1962, 1967) and Yuhasz (Carter 1982) applicable to university
aged subjects have been popular in routine use in North America.
In recent years the use of such predictive equations has been criticised. A judgement of the
ability of a regression equation in individual prediction can be based on the standard error of
estimate (SEE). The SEE of these equations tends to be in the order of 3.7% of body fat. This
can be interpreted as meaning that when the equation is used to predict the body fat of an
individual, the prediction approximately 2 out of 3 (actually 68.26%) times is within plus or minus
3.7% of body fat of the right answer. Thus, if a prediction of 15% is made then the confidence in
prediction is that in 2 out of 3 occasions the body fat is actually between 11.3 - 18.7% body fat.
9-18
Estimating % Body Fat
Obviously the usefulness of a methodology carrying this degree of error is limited in individual
assessments.
Such is the disillusionment with the use of such equations that a former editor of the American
Journal of Physical Anthropology is unequivocal about the prediction of percentage body fat from
anthropometry:
"At present it seems that human biologists are better off to continue to use
anthropometry itself, rather than attempt to make estimates of whole body composition
from available equations. Even if such equations could provide useful estimates for
mean parameters for samples, it seems clear that they are not reliable for individual
prediction." Johnston, F.E., Human Biology, 54:211-245, 1982.
SLOAN (1962,1967) : This is one of the earliest well accepted set of equations. The equations
predict body density and then the Siri equation (1962) is used to transform this density to a
percentage of body fat. These equations were developed on samples of university students from
the U.S.A.
FEMALES 17-25 years of age
Density = 1.0764 - 0.00081(Iliac Crest Skinfold) - 0.00088(Triceps Skinfold)
SEE = 0.0082 gm/ml
MALES 18-26 years of age
Density = 1.1043 - 0.001327(Front Thigh Skinfold) - 0.001310(Subscapular Skinfold)
SEE = 0.0082 gm/ml
Siri equation (1962):
%fat = ((4.95/Density) - 4.5) x 100
YUHASZ: These equations derived on Canadian university males and females use the sum of
six skinfold measurements (S6SF). Where S6SF = Sum of Triceps, Subscapular, Supraspinale,
Abdominal, Front Thigh and Medial Calf skinfolds. These sex specific equations predict
percentage body fat without the intermediary of body density.
MALES
% fat = 0.1051(S6SF) + 2.585
FEMALES
% fat = 0.1548(S6SF) + 3.580
Sloan, A.W., J.J. Burt, C.S. Blyth. Estimation of body fat in young women. J. Appl.
Physiol. 17:967-970, 1962.
Sloan, A.W. Estimation of body fat in young men. J. Appl. Physiol. 23:311-315, 1967.
Yuhasz, M.S. Physical Fitness Appraisal. London, University of Western Ontario,
London, Ontario, 1982.