Paper  Simple formulae for estimating the age and size of human embryos
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Arey LB. Simple formulae for estimating the age and size of human embryos. (1925) Anat. Rec. 30(4): 290  294.
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This historic 1925 paper by Arey describes arithmetical formulae for estimating human embryo age.

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Simple Formulae for Estimating the Age and Size of Human Embryos
Leslie B. Arey
Department of Anatomy, Northwestern University Medical School
There are several formulae of use in computing the age and size of human embryos. Some are complicated (Henry and Bastien, ’04; Scammon, ’21); most are limited to the determination of the age or size from one particular type of data; none cover both age and size, utilizing crownrump or crownheel measures.
In 1923, Scammon and Calkins published empirical formulae for calculating the age and size of fetuses between three and ten months in terms of crownheel values. Further simpliﬁcation produced the following equations:
2 Age=( + 1.49 )
OH = 3o\/X§e“— 44.7
These formulae aressaid to be correct between limiting deviations of —— 2.97 and —2.66 per cent. It appears that the total body lengths used were derived by interpolation with the view of correcting for a difference of ten days between the menstrual and actual age; since, however, this correction had already been made by Mall (’10), whose data were employed, the accuracy of the results are correspondingly impaired.
Noback (’22) has also shown how to derive crownrump or crownheel size from the complementary data:
3 CR « 3 CH = T‘2 2 CH 3 CR ——— + 3 F 1 Eontribution Iio. 110. — 289
It is evident that besides exact formulae for the accurate calculation of fetal age and size there is need also of simpler ones that give reasonable approximations, quickly estimated. It is often necessary while reading, viewing specimens, or considering cases to translate age into size, or the reverse, and since some workers employ only crownrump or crownheel measurements, while others use both, multiplicities are introduced for which provision must be made. The formulaproblem thereby resolves itself into a fulﬁlling of the following conditions:
1. The formulae should be simple and easily remembered.
2. They should be solvable by mental computation.
3. They should be reasonably accurate.
4. They should utilize both CH and CR size data.
A familiar rule is that of Hasse (’7 5), which states that for the ﬁrst ﬁve fetal months the total length in centimeters ‘equals the square of the month, whereas in the last ﬁve months it equals the month multiplied by ﬁve. As seen from the appended tabulation (table 1), this rule conforms to the requirements of simplicity and reasonable accuracy and is easily remembered. On the contrary, it has the disadvantages of ﬁtting only CH data and of requiring a preliminary computation in estimating age to determine whether division by ﬁve or the extraction of square root is necessary.
A comparable table can be prepared for crownrump values (table 2). Similar criticisms apply to it as to Hasse’s rule. In this instance crownrump size in centimeters is derived by multiplying the ﬁrst three fetal months by 0.5, 1.5, and 2.5, respectively, and the remaining seven months by 3.5.
Attempts to construct age formulae which fulﬁll all of the four conditions previously enumerated have resulted in the following rules:
Standing height (in cm.)'>( 0.2 zage (in months) Sitting height (in cm.) X 0.3 zage (in months)
For embryos less than 10 cm. long, that is, those of the ﬁrst three months, the values thus obtained are too small, since in such early embryos the growth curve is of a different contour. This discrepancy, however, can be corrected with fair success by adding one month to the results gained by direct multiplication; obviously, there will be a certain incongruity in the results bordering the correction point thus arbitrarily set at 10 cm. These values, with the actual and percentage deviation from normal, are collected in the subjoined tabulations (tables 3 and 4).
AGE AND SIZE FORMULAE FOR HUMAN EMBRYOS 29]
TABLE 1 Estvlmaﬁon of fetal age and size based on crownheel lengths (Hesse)
ESTIMATED BODY 3
STANDARD BODY DEVIATION OF :PERCEl\'TAGE DEVIATION
it  LE.\'G'I‘H LENGTH ES'I‘IMA’l‘E I or ESTIMATE — ~»»———»—.»—il—»»?—. —. 1.. ._E'_.._.....___.__.____.._..____ mos. cm. em. l
1 x1: 1 1 0 0.2" »—0.75 ——300.02 2 x2: 1 4 3.0 i ——1.0 7 —— 33.3 3><‘:: 9 i 9.3 0.3 i — 3.2 4 ><4= 16 ; 13.0 4 1 442.0 E —» 11.1 5 ><5= 1 25 3 25.0 ! 0.0 { 0.0 6><5= ; 30 31.5 —1.5 ‘_ — 4.3 7x5: 1 35 f 37.1 ——2.1 5 — 5.7 3><5= 40 3 42.5 f —2.5 ' — 5.9 9><5= ; 45 f 47.0 i —2.0 ; — 4.3 101><5= { 50 1. 50.0 I 0.0 E 0.0 I‘ Sum 12.7 t 73.3
5 Mean 1 1.3 g 7.3
1 The actual fetal age at full term is 270 days, or 9.6 months; the corresponding estimated size is 48 cm., which is less correct than that recorded.
”Although the actual error is low, the percentage error is high and unrepresentetive. For this reason it is omitted from the sum a11d mean for the column.
TABLE 2 Esttmration of fetal age and size based on crowwmmp lengths
ESTIMATED BODY STANDARD BODY DEVIATION OF EPERCENTAGE DEVIATION
ll LENGTH LENGTH . ESTIMATE OF‘ l~1STIMA'l‘E mos. Cm. cm. ‘g
1 ><0.5= l 0.5 ! 0.25 t —0.25 4400.02
2 ><1.5= 3.0 2.5 F ——0.5 E « 20.0
3 ><2.5= E 7.5 6.8 ; ——0.7 1 ——. 10.3
4 ><3.5= “ 14.0 12.1 i ——1.9 i —— 15.7
5><3.5: 1 17.5 1 16.7 ~—0.3 6 —— 4.8
6 X35: 1 21.0 ; 21.0 0.0 7 0.0
7 ><3.5= 1 24.5 1 24.5 ' 0.0 0.0
3><3.5= 9 23.0 ! 23.4 0.4 — 1.4
9><3.5= I 31.5 31.6 ' —0.1 —~ 0.3
10'><3.5= 5 35.0 g 33.6 % +1.4 + 4.2
Sum 3 6.1 56.7 Mean E 0.6 5.7 ‘If the real age of 9.6 months at full term were used, the estimated value would be 33.7 cm., which agrees closely with the standard size of 33.6 cm. 3 Omitted from calculation of the sum and mean for the column. (See footnote 2, table 1).
It is at least of passing interest to point out that rather accurate results may be obtained for the last ﬁve lunar months by replacing 0.2 and 0.3 as the multiplying factor by 0.19 and 0.29. The ﬁgures thus obtained are collected in tables 5 and 6.
In a similar fashion, adherence to the four fundamental
stipulations was attempted in educing rules which calculate size from age:
Age (in months) —:~ 0.2 2 standing height (in cm.) Age (in months) —% 0.3 'zsitting height (in cm.)
Again the results are out of line for embryos of the ﬁrst
three months, but reasonable correction is obtained when
4 cm. are subtracted from the values obtained directly by division. These determinations are assembled in tables 7 and 8.
As before, quite exact values are obtainable for the last ﬁve lunar months if 0.19 and 0.29 replace 0.2 and 0.3 as divisors (tables 9 and 10).
Those who are interested in mnemonic aids will perceive that all four formulae deal only with the digits, one, two, three, four, and their numerical sum which is ten. The use
lasoatxzasA
10
of the appropriate multiplying and dividing factors, 0.2 and 0.3, is apparent in each case, for obviously the higher factor (0.3) always accompanies the shorter fetal length (CR), and 293
AGE— AND SIZE FORMULAE FOR HUMAN EMBRYOS
Vice Versa. The digit 1 must be the correction for age and 4 for length—the reverse is patently absurd. Embryos less than 10 cm. long, or three months old, are the ones for which
TABLE 3
Estimation of fetal age from crownheel length
S§$’§‘3£.E” ESTIMATED AGE CORRECT AGE ”E§s'$ﬁii3¥E°F PE“°"5‘}T‘;7§$’.?.§¥’n‘T‘°" cm. 5 months months 0.25>(0.2= .05——121.05 1.0 +0.05 —— 5.0 3.0 X0.2= .60——1=1.6 2.0 ~—0.40 —20.0 9.8 ><0.2= l.96——1=2.96 3.0 —0.04 — 1.3 18.0 X0.2= 3.60 4.0 —0.40 —10.0 25.0 ><0.2= 5.00 5.0 0.00 0.0 31.5 ><0.2——— 6.30 6.0 ——0.30 —— 5.0 37.0 )(0.2*—" 7.40 7.0 ~—~0.40 —— 5.7 42.5 >(0.2= 8.50 8.0 ——0.50  6.3 47.0 )(0.2= 9.40 9.0 ——0.40 —— 4.4 50.0 ><0.2= 10.00 10.01 0.00 0.0 8 Sum 2.35 57.7 Mean 0.29 5.8 1 Exact fullterm age is 9.6 lunar months. TABLE 4 Estimation of fetal age from crownrump length siiﬁgfgn ESTIMATED AGE connncr AGE DEE‘g,I,‘:'§{I£'£'E°F 1frl:;\:r§:.}f§{?§§:gF cm. months months 0.25>(0.3= .075+~1=1.075 1.0 —— .075 H 7.5 2.5 )<0.3= .75 ——1:1.75 _ 2.0 — .25 ——12.5 6.8 )<0.3= 2.04 ~l=3.04 3 0 —~ .04 1.3 12.1 ><0.3= E 3.63 = 4.0 — .37 H. 9.3 16.7 >(0.3='——‘" I 5.01 1 5.0 —— .01 ~~ 0.2 21.0 ><0.3= ! 6.30 E 6.0 —— .30 M 5.0 24.5 ><0.3: ! 7.35 . 7 0 —~ .35 4 5.0 28.4 ><0.3= } 8.52 7 3.0 —— .52 H 3.5 31.6 >(0.3= 9.48 9.0 —* .48 ~— 5.3 33.6 ><0.3= [ 10.08 I 10.01 — .08 —— 5.0 1 Sum 2.43 53.6 Mean 0.25 5.4
‘ Exact fullterm age is 9.6 lunar months. 294 LESLIE B. AREY
corrections are made. With these numbers (1, 2, 3, 4, 10) once in mind, it is easy to reconstruct the formulae at any time by using them as common sense dictates.
TABLE 5 Exact calculation of later fetal age from crownheel length
y
__ i __ ,___1 __ _ ._ __________________.___ i I cm. E months months I 31.5><0.19= 5.99 6.00 —0.01 ~—0.2 37.0><0.19= 7.03 7.00 ——0.03 I ——0.4 42.5><0.19== l 8.08 8.00 ——0.08 I ——~1.0 47.0><0.19= l 8.93 9.00 i —0.07 5 0.8 50.0><0.19.= E 9.50 9.64 l —«0.14 1 1.4 ' Sum 0.33 l 3.8 f Mean l 0.07 l 0.3 ._ __ _ __ _.i _. _ _.._ l .. _.._..._._. ___.._._ _._.m T _..__....__ —. __. TABLE 6 Exact calculation of later fetal age from crownramp length Sigigﬁfb ESTIMATED AGE cosnncr AGE DE:J_,:$;r:8’,”;E°F iPERC%’;,T‘;g1'?I;’IE¥;‘TI0N l  _ ._m. . ..__n____.__. _ _ _ cm. I months i months 21.0><0.29= E 6.09 6.00 ~—0.09 I ——1.5 24.5><0.29= ' 7.12 ! 7.00 ——0.12 ——1.7 23.4><0.29= 8.24 8.00 0 ——0.24 ——3.0 31.6><0.29= 9.16 ‘ 9.00 —~0.16 l ——1.8 33.6><0.29= 9.74 , 9.64 E +0.10 ——1.0 1 Sum 0.71 ! 9.0 I Mean 1' 0.14 1.8
Summary
Formulae for estimating the age and size of human embryos and fetuses have been developed which are simple, reasonably accurate, and utilize both crown—~rump and crown—heel data:
Standing height (cm.) )( 0.2 =age (months) Sitting height (cm.) X 0.3 =age (months) (For embryos less than 10 cm., add one month) Age (months) ~:— 0.2 = standing height (cm.) Age (months) —e— 0.. = sitting height (cm.) (For embryos of ﬁrst three months, subtract 4 cm.) AGE— AND SIZE FORMULAE FOR HUMAN EMBRYOS 295
TABLE 7 Estimation of fetal size in c7'0wn—heel measure
ESTIMATED BODY STANDARD BODY DEVIATION OF PERCEN.'I'A.GEDF.VIATION 1 LENGTH LENGTH ESTIMATE OF ESTIMATE 4 mos. C37?. 1 cm.
10.2:: 5.04.0: 1 .25 1  0.75 1 300.02 20.2: 10040: 6 3.0  3.00 100.02 30.2: 15.04.0211 9.8 1  1.20 1  12.2 40.2: 20.0 18.0 1  2.0 1  11.1 50.2: 25.0 25.0 1 0.0 l 0.0 60.2: 130.0 31.5 i  1.5 1  4.8 70.2:: 335.0 37.1 E  2.1 1  5.7 80.2:  40.0 42.5 E  2.5 1  5.9 90.2: 45.0 47.0 7 1  2.0 1 — 4.3 1010.2: 50.0 50.0 0.0 1 0.0 1 Sum 15.1 1 44.0
’ _Mean 1 1.5 1 4.4
i
‘If the exact age of 9.64 months at full term were used, the estimated size would be 48 cm.
“Omitted from the calculation of the sum and mean for the column. (See footnote 2, table 1).
TABLE 8 Estimation of fetal size in e7'0w42rump measure
ESTIMATED BODY STXNDARD BODY DEVIATION OF PERCENTAGE DEVIATION
I ll LENGTH I LENGTH ¥ ESTIMATE 1 OF ESTIMATE mos. cm. ! cm. ‘I : 10.3: 1 3.34:0.71 0.25 1 0.95 1 380.02 20.3: '0.74: 2.71 2.5 1 0.2 1  8.0 30.3: 10.0 : 6.01 6.8 1 0.8 1  11.8 40.3: 3133 1 12.1 1 1.1  9.1 50.3: 107 13.7 1 0.0 1 0.0 60.3: 200 1 21.0 1 1.0 1  4.8 70.3: 233 1 24.5 1 1.2 ;  4.9 30.3: 1267 1 28.4 1 1.7 3  6.0 9031300 1 31.6 I 1.8 1  5.1 10103: 333 1 33.3 1 0.3 1 ~— 0.9 E Sum I 8.9 50.6 '1 Mean E 0.89 5.1 i I
‘If the exact age of 9.6 months at full term were used, the estimated size Would be 32 cm.
‘Omitted from the calculation of the sum and mean for the column. (See footnote 2, table 1). 296 LESLIE B. ABEY
TABLE 9 Exact calculation of later fetal size 4121, crownheel measure
ESTIMATED BODY STANDARD BODY DEVIATION OF PERCENTAGE DEVIATION LENGTH LENGTH ESTIMATE OF ESTIMATE
M08. I cm. cm. i 0.00+0.19= . 31.6 31.5 +0.1 +0.3 7.00+0.19= 33.3 1 37.1 0.3 ’ —~0.3 3.00+0.19= 42.1 1 42.5 I 40.4 0.9 9.00+0.19= . 47.4 1 47.0 +0.4 440.9 93440.19: i 50.7 1 50.0 +0.7 5 ——1.4
i Sum 0.19 4.2
 Mean 0.04 0.9
l 1. 1 _ _
TABLE 10
Exact calculation of later fetal size in crownrump measure
I . l ESTIMATED BODY STANDARD BODY I DEVIATION OF iPF.RCENTAGE DEVIATION 1 LENGTH LENGTH l ESTIMATE OF ESTIMATE mos. cm. cm. 0.00+0.29= ; 20.7 . 21.0 1 40.3 _ 2.9 7.00 : 0.29: 24.1 24.5 —0.4 —— 1.3 3.00 : 0.29: 27.0 ' 23.4 , —0.3 , H 2.3 9.00+0.29= 31.0 1 31.6 E 0.3 1 — 1.9 9.64+0.29= 33.2 1 33.3 0.4 — 1.2 { Sum . 2.5 10.4 3 Mean 0.5 2.1
Literature Cited=
HASSE 1875 Ent.bindungs~Ansta1t. Jahresbericht pro 1875. Charité Annalen, Jahrg. 2, S. 668696.
HENRI, 0., AND BASTIEN, L. 1904 Sur la croissance de l’h0mn1e et sur la croissance des étres vivants en général. Compt. Rend. Acad. Sc., T. 139, pp. 811814.
MALL, F. P. 1910 Determination of the age of human embryos and fetuses. Chapter 8 in Keibel and Mall ’s Manual of Human Embryology. J. B. Lippineott 00., Philadelphia.
NOBACK, G. J. 1922 Simple methods of correlating crownrump and crownheel lengths of the human fetus. Anat. Ree., vol. 23, pp. 241244.
SCAMMON, R. E. 1921 On the weight increments of premature infants as compared with those of fetuses of the same gestation age and those of fullterm children. Proc. Soc. Exp. Biol. and Med., vol. 19, pp. 133136.
SCAMMON, R. E., AND CALKINS, L. A. 1923 Simple empirical formulae for expressing the lineal growth of the human fetus. Proc. Soc. Exp. Biol. and Med., vol. 20, pp. 353356.
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