Estimating fat mass indirectly

Up to now, various methods for analysing body composition and, more specifically, for estimating the percentage of fat mass have been dealt with. Indirect methods for calculating it, i.e. those that presuppose a preliminary calculation aimed at estimating body density, will be dealt with here.

Indice

1 Estimating body density
- 1.1 The formula of Durnin and Womersley
- 1.2 The Jackson and Pollock formula
  - 1.2.1 Preliminary skin fold detection
  - 1.2.2 The equation
2 Estimating fat mass by knowing body density
3 Siri’s formula
4 The Brozek formula

Estimating body density

Two formulas can be used to obtain an approximate measure of body density: the first is that of Durnin and Womersley, while the second is that of Jackson and Pollock

The formula of Durnin and Womersley

Only for subjects between the ages of 20 and 29, Durnin and Womersley suggest the possibility of calculating body density using the following equation:

$D\;=\;c\;-\;m\;\times\;logS$

D is the body density, c and m are constants that vary according to gender and age, while logS is the logarithm in base 10 of the sum of the bicipital, tricipital, subscapular and suprailiac skin folds (for details on how to find them, see the section on somatotype and the appendix on plicometry for estimating the percentage of fat mass). As far as the constants are concerned, their value is as follows:

Constant	Men	Women
C	1,1307	0,0603
M	1,1398	0,0738

The Jackson and Pollock formula

Jackson and Pollock classified the total population according to gender and athleticism. They therefore provide a formula for male athletes, one for female athletes and two designed for a generic population of individuals. Of the latter, like those for athletes, one is for men, while the other is for women. The authors report that the formulas for athletic individuals are only suitable for those between the ages of 18 and 29, so anyone over the age of 29 should use the alternative for the generic population (which, on the other hand, is suitable for those between the ages of 18 and 61).

Preliminary skin fold detection

For calculation purposes, the preliminary measurement of certain skinfolds is required. Since body fat tends to be distributed differently in men and women, the skinfolds whose measurement is required also differ according to gender. Specifically, for men the measurement of the pectoral, abdominal and crural (i.e. thigh) folds is required, whereas for women the measurement of the triceps, suprailiac and crural folds is required. In addition to these measurements, the formulae for male and female athletes require additional ones. In particular, for athletes the supra-iliac, subscapular and tricipital folds are also required, while for female athletes the abdominal fold must also be taken. Please refer to the text for indications on the location of the tricipital, supra- and subscapular folds. Concerning the pectoral, crural and abdominal folds, the first should be taken diagonally between the axilla and the nipple, the second should be taken vertically, centrally between the inguinal fold and the kneecap, and finally the abdominal fold should be taken about 2 cm laterally from the umbilicus. Some authors suggest taking it horizontally, while others prefer a vertical survey. The use of the plicometer is the same as in the section on the somatotype.

The equation

Finally, we come to the formulas. The equation for estimating body density for generic male individuals is:

$D\;=\;1,10938\;-\;0,0008267\;\times\;(pp\;+\;pa\;+\;pc)\;+\;0,0000016\;\times\;(pp\;+\;pa\;+\;pc)^2\;-\;0,0002574\;\times\;E$

Where D = body density; pp = pectoral plica; pa = abdominal plica; pc = crural plica and E = age. The equivalent formula for women is:

$D\;=\;1,10994921\;-\;0,0009929\;times\;(pt\;+\;psi\;+\;pc)\;+\;0,0000023\;\times\;(pt\;+\;psi\;+\;pc)^2\;-\;0,0001392\;\times\;E$

Where D = body density; pt = tricipital plica; psi = supriliac plica; pc = crural plica and E = age.

Again, the formula for male athletes is:

$D\;=\;1,112\;-\;0,00043499\;\times\;(pp\;+\;pa\;+\;pc\;+\;psi\;+\;pss\;+\;pt)\;+\;0,00000055\;\times\;(pp\;+\;pa\;+\;pc\;+\;psi\;+\;pss\;+\;pt)^2\;-\;0,00028826\;\times\;E$

Where D = body density; pp = pectoral plica; pa = abdominal plica; pc = crural plica; psi = suprailiac plica; pss = subscapular plica; pt = tricipital plica and E = age.

Finally, the formula for female athletes is:

$D\;=\;1,096095\;-\;0,0006952\;\times\;(pt\;+\;psi\;+\;pc\;+\;pa)\;+\;0,0000011\;\times\;(pt\;+\;psi\;+\;pc\;+\;pa)^2\;-\;0,0000714\;\times\;E$

Where D = body density; pt = tricipital plica; psi = supriliac plica; pc = crural plica; pa = abdominal plica and E = age.

Estimating fat mass by knowing body density

Once body density has been calculated, it is possible to use this data to estimate the percentage of body fat by entering it into other formulae. In this case, these are the Siri equation and the Brozek equation.

Siri’s formula

Siri’s (1956) formula for estimating the percentage of fat mass is as follows:

$\%FM\;=\;(\frac{4,95}{D}\;-\;4,5)\;\times\;100$

Where %FM is the percentage of fat mass and D is the body density.

The Brozek formula

Brozek ‘s (1963) formula is set out below:

$\%FM\;=\;(\frac{4,57}{D}\;-\;4,142)\;\times\;100$

Where %FM is the percentage of fat mass and D is the body density.