JGERLL C APP111 IYSIOLO, Vol. 21, No. 1 uno 066

Determination of human body volumefrom height and weight'

JULIUS SENDROY, JR. AND HAROLD A. COLLISONDivision of Chemistry, US Naval Medical Research Institute,National Naval Medical Center, Bethesda, Maryland

SENDROY, JuIus, Ja., AND HAROLD A. COLLISON. Dete- surface area, derived from known weight and height byiniion of human body volume from height and weight. J. Appl. simple location of a point on a chart (3o) or nomogram

Physiol. 21(i): 167-i72. t966.-A previously developed (32); this is then followed by a calculation of the volumemethod of graphical determination of human body volume according to equation z. A further simplification, wherebyfrom measurements of height and weight has been extended for volume may be obtained by direct reading from a chartutilization from a limited range to one spanning the develop- with weight and height as coordinates, would be morement of the male and female form from infant to adult. Equa- desirable. Moreover, in developing such a relationship,tims best suited to express the relations of weight and heightto show body volume and surface area over the periods of the it seemed advantageous to extend the previously re-life span for WIH - 0.04-0., 0.1-0.2, and o.2-o.8, were found stricted range of body size, age, and sex to be covered. W

to be, respectively, for males: V/S = 57.26 (W/H) 0 'e0 + Obviously, linear relationships, however satisfactory, LO)0.254, V/S = 50.6 (WIH)"'", and V/S = 60.20 (WH)0'-6; apply only to a limited population. Equation i wasand for females V/S - 6o.36 (W/H)o 'a" + 0.254, V/S - 5t.1 derived from a group of 78 young, normal males of a(WIH) ° '0 , and V/S - 62.90 (W/H)Q' m . A statistical evalua- relatively restricted range of body parameters (27). Ation and comparison with results of almost igoo physical meas- more general relationship, applicable to humansurenents taken from the literature indicate that this approach throughout growth and development from birth toprovides results acceptable for most clinical purposes, and is maturity, would provide a more satisfactory and con-much more convenient and rapid than other, conventional voemethods of arriving at indices of body composition (volume, venient basis forbodyvolume estimates. The results ofspecific gravity, density, and body fat). The method permits the efforts toward the attainment of that objective are |*simultaneous determination of human body surface area as described in the following.previously described. 0

CONSTRUCTION OF CHART FOR VALUES OF

body composition; body density; body fat; body surface area; VOLUME FROM W RIGHT AND HEIGHTanthropometric measurements; human body composition; The basic diagram of Sendroy and Cecchini (Fig. I of 0body development and growth (31)) for values of V/S plotted against W/H was ex-

panded to cover a wider range of body sizes. As manyindividual values as possible for directly measured

Fparameters of body V (or density)' and W and H,FROM VALUES in the literature for humati body weight through the range of infants to adults, of both sexes, were(W), height (H), surface area (S), and volume (V) gathered from the literature. From W and H, cor-obtained by direct physical measurement, several responding values for S were obtained from the enlargedempirical equations for the estimation of body volume diagram of Sendroy and Cecchini (Fig. 3 of (30)).for a limited range of male adults in terms of weight The data were then processed by means of an IBM '9and height alone, have been derived and tested in this t620 computer to determine the relationship of V/S tolaboratory (29, 31). The most acceptable relationship WIM for the several groups of studies composed of 737

found, in respect to reliability and convenience in use, individual subjects.' The equations best fitting the data

was that expressed by 'sofar a possibie, alt original data given in terns of specific

V - S (51.44 W/H + 15.3) (r) gravity were converted to body density (with a correction for lungresidual volume (7)) in accordance with principles discused by

where V, S, W, and H are in liters, square meters, Keys and Broek (2 t, p. *68) and by the use of average respira-kilograms, and centimeters, respectively (31). tory pace relationships (2) P. 34, 35, 38, 39, (23).

The use of this equation requires a prior estimate of 8 The source rerec of the measurements used (all of living-.subjects with the exception of three*) we indicated by numerals

Received for publication 2 9 Jute 1965. in parenthesu, and refer to the data shown in Table s t (t) Table'Thi study wa suppoied by the Bureau of Medicine and t; (3)*; (5) Tables 4 and 9; (8), (9) Table I; (is) Tables 13, 14,

Sugery, Navy Department, Research Task MR oo5 eo.ool .0t. and t6; (ii) Table I, p. 35; (I5) Tabls 4 and 9; (i6) Table i;

167

x68 SENDROY AND COLLISON

Lia m and m', drawn on a log-log plot, were con-F nected by an interpolated straight line. as were lines f

and f. These interpolated lines, represented by equations44

V/S = 50.6 (W/H)04'86 for males, and (6)

4 v/S - 51.1 (W/H).', for females (7)

were then used to connect m and m' and f and f', respec-tively, to form the completed lines M and F in Fig. 1.6

A diagram showing the relationship of isovolumeW values to weight and height, corresponding to that forsurface area by Sendroy and Cecchini (30), was thenprepared as follows. On the surface area chart withweight on the abscissa scale and height on the ordinate

,,R if 0h1 sk 97 03 R h II WN R (Fig. 3 of (30)), iso-W/H lines were drawn. Over a

Fo. i. Diagram for the relationship of VI to W/H for nude range of assumed -physiological values for volume for• (M) and female (F) humans, based on physically measured values each of progressive increments of such values of V,

of weight, height, and volume taken from sources indicated in several appropriate values of W/H were taken. Thefootnote 2, and the calculation of surface area according to Sendroy corresponding value for S for each of these was cal-and Cecchini (30). culated from the V/S value found from equation 2, 4,

or 6 (line M, Fig. i). Each of these values for S waswere found to be of the form V/S - A(W/H)b. Deter- then located on the corresponding value for W/H on themination of the contents of these gave: for 446 adult men surface area chart, to obtain a point for the givenand adolescent boys, ranging in W/H from o.2 to o.8, value for V. Then, by joining these points for V values,

isovolume lines were drawn on the chart already markedV/S = 6o.2o (W/H)6.562 (*) with isoarea lines, as shown in Fig. 2 of this paper.

For the sake of simplicity and convenience in use, theand for 1 13 adult women and adolescent girls, in the graph shown in Fig. 2 is directly applicable for estima-same range, tions solely of males. However, body volumes of females

from H and W values are obtained by corrections indi-V/S - 62.9o (W/H)O.6,, () cated at the head of each isovolume line. Thus, for a fe-

male weighing 70 kg and i8o cm tall, the V is found toOther data for 84 male infants in range of W/H from be 67.7 instead of 66.o liters.6 Values for infants and chil-0.04 to o. i gave an equation dren (to W/H values of o.2) are obtained from the insert

of Fig. 2 with tabular indication for the conversion ofVIS -. 57.26 (W/H).1"4 + 0.254 (4) male to female values.

Obviously, Fig. 2 also serves for the estimation of bodyand for 94 female infants in the same range, surface area from height and weight, to the extent that

it duplicates the diagram of Sendroy and CecchiniV/S = 60.36 (W/H)"."'" + 0.254 (5) (Fig. 3 of (30)). Since publication size does not allow the

measure of accuracy and convenience desirable for

A chart of coordinates of V/S and WIH was prepared &A plot of the large number of points representing individualon a large (2 x 3 ft) piece of i o x i o to % in. cross-section measurements, 737 in all, was actually made. Although possibly

desirable for visual assessment of the scattering of the data aboutpaper. Plots of lines n and in', and f and f', representing the computed lines, its reproduction in Fig. i would be impracticalequations s and 4, and 3 and 5, respectively, were made. and possibly misleading, in view of the repetitive overlapping ofThis obviously left a break in what otherwise would be many of the data. A more adequate evaluation indicative of thethe best line representing the relationships among these reliability of the basic data used is afforded by the statisticalbody parameters from the prenatal to the adult state of treatment which follows in the text. Data on other individuals

comprising 696 males and 428 females were also found in the litera.development. Unfortunately, no data have been found tare (io, 12, 13, 24-6, 28, 35-38) but in the form only of averageavailable for physically measured values of body volume values of height, weight, and specific gravity or density for a groupfor children (for W/H values in the range of o. i-o.2).4 of subjects. The plot of such average values as point units, althoughThe gap in question was filled in the following manner. in close proximity to the lines of Fig. t, would likewise be unsatis-factory in that they would fail to serve as indicators in number

and extent, of the nature of the scattering about the lines M and(il) Tables i and 2; (2o) Table II; (27) Appendix; (34) Appen. F, of the points representing the individual measurements made.dix; (37) Table 1; (39) Table i; (4o ) Table 49. ' The point for 7o kg and j8o cm is located at about o.6 of the

4This is probably owing to the fact that the understanding and distance from the 6o liter line to the 70 liter line. With corrections,cooperation necessary for such experiments are difficult to obtain in a female of these dimensions is calculated as (70 + 1.9) - (6o +subjects between the ages of 2 and io years. 1.5) - 10.4, of which o.6, or 6.2 added to 6a.5, becomes 67.7.

DETERMINATION OF HUMAN BODY VOLUME 169

0 2o 40 SO so 100 120 140 160 The assessment of the reliability of the results obtained2GO : *" . 20 by calculation is affected not only by the aberrations of250- 250 individuals from the average of other members of their

240 '. ., '.240230_ 7 2 \ 230 particular group. There is, in addition, an added varia-

230 . .2 tion encountered in this study of subjects over a lifetime

220 220 span, in a continuing change in shape and body pro-21o0 -KW A5 \ 210 portions from the newborn to the oldster (Fig. I). s

200 o 1 0 2 200 Imposed upon these limitations, or running concomi-

I .-0 \ 190 tantly with them, are those of the possible errors involvedISO - 3IS

O in the values obtained by actual measurement, especially170. . 170 on the part of earlier or inexperienced workers.

ISOse SO The foregoing comments are amply confirmed and

15o ' 150 illustrated by the data of Table I. The values for male

40 -l 140 adults show a range of body volumes from 19 to 126i3o liters. However, the statistical evaluation of the entire140 *0 10 40S

120 group of 446 adult individuals compares favorably with10 .. that of most of the io separate studies comprising the

whole. With especial reference to the work of OssermanO.. et al. (27), it is apparent that the general equation 2 forSo 0adult males applies almost equally well as does the

O 20 linear one (equation r), previously based solely on the0[ 40 05 measured data of these particular 78 individuals (see

60o \ , ° Table I of (30). Damon and Goldman (14) used a50 Z0 01 similar but much smaller group of 13 males in a test of

20 40 60 8o I 4 : : o, 94 .S ,, io formulas for the prediction of total fat from bodyW IW I 3 1 - measurements. If one calculates from the mean W, H,K , lc o ?0Pi006 10 1 o 0 1 0 and body fat (F) of their Table , the body volume from

io. 2. Diagram for the calculation of human body volume the best of these equations found by them (14) for bodyfrom measurements of height and weight. Values for V (solidlines) are for male subjects, with a correction shown to be added fat (F = (4.0439/density) - 3.6266), based on Grande'sfor females. (Insert is used for low range of infants from birth to work cited by Brozek in a comment attached to a paperattainment of volume of about 7 liters). This diagram may also be by Behnke ((6), p. 128) the value of 66.o liters is likewiseused for the estimation of body surface area (dashed lines) as de- in good agreement with that of 66.3 liters obtained by theveloped by Sendroy and Cecchini (30). use of our equation 2.

On the other hand, one may compare two groups ofpractical use, Fig. 2 should be reproduced on an enlarged extremes of variation from the average standard error ofscale7 for determining surface area and/or volume, estimate of volume for male adults referred to measured

values, namely, that of Behnke's (5) 17 subjects con-RSULTS AND DISCUSSION sisting in part of weight lifters and others of a wide range

Table I shows a statistical treatment of results for of body builds (sEE = 4- .97 liter), with the 13 of Damon

human body volume as found by a method of direct and Goldman (14) (sEE = :o.74 liter). The -test (Main-

physical measurement (weighing in water, helium, or land (22), page 169) indicates that the standard error of

air displacement, etc.) compared with volumes obtained the coefficient of variation (here, sEE X ioo/mean) is

by the use of the diagram of Fig. 2. I-n effect, Table I significantly different for these two groups (P < o.oi).

shows the results of applying equations 2-5 derived by On the other hand, the set of experiments (5) showing

computer processing of measured data for human sub- the greatest deviation (sEz = 4-1.97 liter) from that of

jects, to the calculation of the individual V values of the the whole group (sEE = + i.o6 liter) shows no significant

subjects of the various studies comprising the whole. difference from the latter for the standard error of the

The relationship of empirical expressions representa- coefficient of variation (P > o. Io).

tive of human anatomical and geometrical configurations From the foregoing, one may conclude that for the

has been discussed in previous publications (29, 3 1). The estimation of body volume of adults varying from 19 to

difficulties and limitations of applying equations to 326 liters, 95 % of the results calculated by means of the

populations other than those from which the basic data present method will be within 3.5 % of the "true"

were derived have also been made apparent, and pointedout by others (5, 14, 33). s These lines may be regarded as reflections of the growth andout bohr(development of the "average" human body in terms of the indi-

I For maximum convenience and accuracy in reading large- cated corporeal dimensions. The obvious break where W/H isScale grid diagrams, the indicated coordinate scale marks may be approximately o.a, in what would otherwise be smooth curvesjoined by the desired numbeT of lines drawn m the chart, corresponds to the cessation of "normal" development at the endSince accurate reproduction of such charts may present a problem point entering upon adolescence, beyond which increase in bodyto many users, enlarged copka of Fig. 9 will be made available size and shape follows a somewhat altered course. These cosidera.upon request to the authors. tio are discused at length in a previous paper ((3o) p. to).

J 70 SENDROY AND COLLISON

TABLz i. Human body voume V, from height and uiht charts eomared* with direct physical mesureentNo. Rn SubJ l Vane F ad (1a),

Ref n al to/ ad Sea litrs MD, litets MD.R lier tanrs us, %5Allen et &1. 5 M 4o-t (53) 0.57 -0.15 *o.76 *1 .4

5 Behnke 17 54-115 (79) 1.63 -0.10 "1 .97 =i"2.58.9 Behnke ct al. 31 49-t15 (74) 1.37 +1.4 * 1.74 4-2.3

12 Brozek et al. 20 71-126 (9o ) 1.29 -1.39 -k-1.5834 Damon and Goldman 13 5-79 (66) o.56 +o.56 *0.74 :3.315 Durnin and Taylor 10 51-73 (61) 0.49 +0.27 +0.72 *3.227 Osserman et al. 78 49-100 (71) 0.72 +0.14 *0-.90 _.334 von Dobln 35 47-83 (65) 0.63 +0.19 A-0.84 -4-1.337 Welham and Behnke 25 71-111 (85) 1.51 +1.47 : 1.68 :§:2.040 Zook 162 19-74 (43) o.62 -0.01 o.8o =1.9

Mean of male adults 446 (59.7) 0.8o -0.01 *-.o6 *H.8

i Allen et al. 26 F 37-65 (48) 0.44 -0.17 =E0.52 *1.318 Goldman et al. 31 56-100 (74) 3.07 -0.58 :k:3.47 4-2.038 Goldman et al. 12 51-78 (66) 0.75 -0.68 4-0.86 *-.334 von Dobeln 35 48-76 (6o) o.62 +0.54 +0.77 *-.339 Young et al. 9 58-96 (73) .05 +1.00 +1.25 -*-13.7

Mean of female adults 113 (62.4) 0.75 -0.02 *bi.oo :.6

3 Barnum 3 M 2.4-2.7 (2.5) o.o6 -0.003 :o.o8 -4-3.2

16 Friis-Hansen 14 2.5-4.0 (3.3) 0.09 -0.08 *0. I "4-3-420 Kastner 67 2.o-6.8 (3.8) 0.17 +0.02 *o.26 -*-6.7

Mean of male infants 84 (3.63) o. 16 +0.003 +0.23 :*=6,3

16 Friis-Hansen 15 F 2.7-3.7 (3.2) o.o8 -0,03 *o.3 "I-3"42o Kastner 79 2.2-6.5 (3.5) 0.13 +0.03 ::o. 18 t:5.1

Mean of female infants 94 (3.45) 0.13 +0.007 :-0.17 :L-4.9

MD = Arithmetical mean of individual deviations of calculated from measured V. MDa = Algebraic mean of such deviations.szz - Standard error of estimate t VZDt/N - where N - number of subjects for the group. The percentage se = sEz X3oo/mean V, for the group.

measured value. Very nearly the same considerations Table i for adult dimensions. Comparison of the stand-and conclusions in the foregoing hold true for the values ard error of the mean measured volume for femalesfor adult females ranging in body volume from 47 to (62.4 liters) and males (59.7 liters) leads to a standardioo liters, error of difference between the two sets of data of :-0.49

.In the case of infants ranging from 2 to about 7 liters liter, which is more than five times the difference inin body volume, a standard error of estimate of about their means. Volume measurements for adult females4-0.20 liter represents a 5-6 % variation from the "true" are quite significantly higher than for males of the samemeasured value, for 95% of the calculated values.9 By height and weight by from 2 to 3.3 %, from one end ofdirect physical measurements of 29 infants less than 24 the range of volumes to the other (15 to 150 liters).hr of age, Friis-Hansen (16) obtained an average body These differences are also reflected in, and indicated by,density of .030, SD of -0.030. The use of our Fig. 2 the corrections to values found by Fig. 2, to be applied to(insert) predicts an average of 1.045 SD of -o.oi 7. values for females.

It is well known that the female has a thicker layer of Although the values of measurements of corporealadiposity tissue with resultant lower body density and density have long been established in physiological andincreased volume as compared with the male of the same clinical observations and investigations, interest in theheight and weight. Brozek's reports (io, i i) on the relationship of density to the fat content of the body hasvariation of experimentally determined body specific increased tremendously during the last two decades (8).gravity and fat content of males and females at different The military aspects of the subject have been particularlyages is satisfactorily borne out by the curves of Fig. x considered and well studied by Behnke (4). Despite theand the subsequent discussion. The quantitative signifi- essential limitations of biological variation and humancance of the difference in calculated from measured error, and the resultant variation in the number andvalues of V between the samples over the entire range variety of relationships proposed by many workers (6,of body sizes and shapes is represented by the data of 12, 14, 21, 24, 33), with an awareness that the present

proposed calculation of body volume is not intended forI It should be noted that Kastner's studies (2o), upon which the more exacting demands of research activities, one may test

the relationships for infants here developed are predominantly its value under less rigorous requirements.based, were one of the earliest in the field and were done on sub.jects almost all of whom were clinically not normal but patho- As examples, a normal adult male and female of heightlogical. 170 cm and weight 74.5 kg, Fig. 2 shows V values of 70

DETERMINATION OF HUMAN BODY VOLUME 171

and 7.9 liters, with values of D = t.o643 and 1.0362, CONCLUSION

respectively. By calculation according to Grande'sequation, F = (4o439/D) - 3.6266, body fat of the The importance and significance of measurements of

male and female will be 17.3 % and 27.6 %, respectively, human body volume, density, or fat have been simply and

values only a little higher than most of those in the clearly discussed by many workers, who have beenliterature. Thus, a difference of o.ox density unit, or I concerned with the pitfalls, difficulties, errors, and vari-

liter of body volume, represents a difference of 3.7 % or ations in their evaluations, especially by densitometry.

5.47% of body fat, respectively. Since the standard Under the conditions prevailing, one may conclude that

errors of estimate of density measurements will be the graphical method here presented is the simplest

4-o.oi9 and -4-o.oi3 units for males and females, respec- available for the prediction of human body volume,

tively, the estimate of body fat will compare with those and is useful and adequate for most practical and

obtained by standard methods for body density, the clinical purposes.

szz values of which are -o.oo8 units. In other words,the error in estimating body fat by the proposed use of The authors are indebted to Mr. Carlis Taylor of the Data

tof Fig. 2 may be up to twice that incurred in Systems Division, National Naval Medical Center, and to Dr.the chartJohn W. Wrench, Jr., of the Applied Mathematics Laboratory,the use of current classical methods of estimating that David Taylor Model Basin, for the machine data processing of

portion of total body composition.10 the measured and calculated values used in this work.

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* , 72 SENDROY AND COLLISON

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