Sex-specific fetal weight prediction by ultrasound




To improve sonographic birth-weight prediction by developing fetal gender-specific formulae.


This was a retrospective cross-sectional study. Two gender-specific formulae were produced from the data of 527 patients and the data of a further 349 patients were used to evaluate the formulae. Inclusion criteria were a singleton live fetus, gestational age above 25 weeks, birth weight between 1000 g and 4500 g and fetal biometry within 8 days of delivery. Data retrieval was specifically for the purpose of this study.


To yield the best-fit weight formula for each fetal gender we employed step-wise regression analysis based on fractional polynomials with the biometric parameters biparietal diameter (BPD), head circumference (HC), transverse abdominal diameter (TAD), abdominal circumference (AC) and femur length (FL): estimated fetal weight for girls (g) = − 4035.275 + 1.143 × BPD3 + 1159.878 × AC1/2 + 10.079 × FL3 − 81.277 × FL2 [in cm]; estimated fetal weight for boys (g) = 43576.579 + 1913.853 × log10BPD + 0.01323 × HC3 + 55.532 × AC2 − 13602.664 × AC1/2 − 0.721 × AC3 + 2.31 × FL3 [in cm]. These formulae showed superior results compared with those of conventional weight formulae.


Gender-related fetal weight calculation allows optimized prediction of fetal weight at birth. Copyright © 2004 ISUOG. Published by John Wiley & Sons, Ltd.


Estimation of fetal weight is an integral part of modern obstetrics and as such has been routinely used for more than three decades. The majority of published formulae use some combination of biparietal diameter (BPD), head circumference (HC), transverse abdominal diameter (TAD), abdominal circumference (AC) and femur length (FL) to assess gestational age, evaluate fetal growth and estimate fetal weight1–6. However, none of the standard weight formulae considers fetal sex, despite compelling evidence of gender-specific differences between male and female infants.

The purpose of this study was to develop gender-specific weight formulae and to test them against established methods in an independent evaluation group.


We created two new gender-specific formulae for optimized fetal weight prediction based on the data of 527 predominantly Caucasian women (‘formula-creation’ group), collected during a 4-year period (1994–1997) in a tertiary referral center (the Department of Prenatal Diagnosis and Therapy, University of Bonn). The ultrasound examinations were performed for a variety of reasons and included normal pregnancies as well as women with diabetes and hypertensive disease. Included in this retrospective, cross-sectional study were all subjects who fulfilled the following criteria: a singleton live fetus, gestational age above 25 weeks, birth weight between 1000 g and 4500 g, and fetal biometry within 8 days of delivery. Multiple pregnancies, stillbirths and infants with congenital anomalies were excluded, as were those pregnancies that presented in established labor and those for which information was incomplete or when delivery occurred more than 8 days after the last ultrasound examination. Data retrieval was specifically for the purpose of this study. For cases in which fetal growth or condition had been followed serially only the last examination before delivery was considered. Each fetus was included only once. Measurements were taken by several investigators experienced in fetal biometry, on a variety of ultrasound machines: Voluson 530, 530D and 530 MT (GE, Solingen, Germany), Acuson 128 XP, Aspen and Sequoia 512 (Acuson, Mountain View, CA, USA) and Toshiba SSA-270A (Toshiba, Tokyo, Japan). Gestational age determined from the last menstrual period and confirmed by first- or second-trimester biometry was noted in days. If there was more than a 7-day discrepancy or if the woman was unsure about the date of her last menstrual period, gestational age was based on the crown–rump length obtained in the first trimester.

The BPD measurements were taken from the outer edge of the proximal fetal skull bone to the outer edge of the distal bone. No correction was made for different shapes of the fetal head in non-vertex presentation. The HC was calculated from the measurement of the occipitofrontal diameter and the BPD using the formula: equation image, where d1 and d2 are the two diameters2. The TAD and AC were measured in standard transverse planes at the levels of the stomach and umbilical vein–ductus venosus complex; the AC was calculated by derivation from the measurement of the transverse and anteroposterior diameters using the formula4: π × (d1 + d2)/2. The FL was measured from the proximal end of the greater trochanter to the distal metaphysis. Ultrasound measurements were expressed in cm.

To validate our new gender-specific formulae in the prediction of fetal birth weight, we studied the data of 349 fetuses seen in the same setting as described above between January 1998 and August 1999 (‘formula-evaluation’ group). Birth weight and length were obtained within 1 h of delivery by our nursing staff. Weight calculations with our new formulae were also tested against established equations1–4. Estimated and actual weights were expressed in g.

Statistical analysis

For statistical analysis we used a RS6000 workstation using SAS procedure REG. Weight-specific reference intervals for the estimated fetal weight were constructed according to the method described by Royston and Wright7. Stepwise regression analysis based on fractional polynomials8, 9 was performed with birth weight as the dependent variable, and sonographic measurements (BPD, HC, TAD, AC and FL) as independent parameters to describe the best-fit weight formula for each fetal gender (SPSS® statistical package, version 11.0; SPSS Inc., Chicago, IL, USA). A forwards selection procedure was employed and the cut-off value for selection or removal of covariates was a P-value of 0.05. Polynomial expressions were considered up to the third degree and natural logarithmic powers of the covariates were fitted. In addition, mean error, mean absolute error, mean percentage error and mean absolute percentage error in the formula-evaluation group were calculated for established weight equations and for the new formulae. Absolute and absolute percentage differences from the true birth weight were compared between new and established formulae with Wilcoxon's test. The Bland and Altman limits of agreement method was used to plot the difference between estimated and true birth weights providing a visual assessment of agreement between the two sets of data10, 11.


The clinical data of the patients in the formula-creation and formula-evaluation groups are given in Table 1. There was no significant difference in height or weight between mothers with a female fetus and those with a male fetus. Furthermore, previous obstetric history was very similar in each group (data not shown).

Table 1. Demographic and clinical data of the formula-creation and formula-evaluation study groups
CharacteristicFormula-creation group (n = 527)Formula-evaluation group (n = 349)
  • *

    According to Voigt et al.23. GA, gestational age.

Age (years, mean ± SD [range])30.9 ± 5.0 [18–46]31.4 ± 5.6 [16–44]
Body mass index (kg/m2, mean ± SD)26.3 ± 4.024.4 ± 4.1
Parity (mean ± SD [range])0.79 ± 0.96 [0–6]0.80 ± 0.90 [0–5]
Gestational diabetes (%)4.77.4
Pre-existing diabetes mellitus (%)3.22.3
GA at ultrasound examination (days, mean ± SD [range])259.9 ± 22.8 [182–294]265.1 ± 19.9 [183–302]
Interval between ultrasound examination and delivery (h, mean ± SD [range])78.5 ± 57.9 [0–192]53.7 ± 53.5 [0–192]
Cases (%)
 > 37 weeks61.570.8
 > 34 weeks84.189.1
 > 30 weeks95.197.7
Delivery mode (%)
 Cesarean section60.557.2
 Spontaneous vaginal33.838.3
 Vaginal operative5.74.4
Birth weight (g, mean ± SD [range]))2856 ± 821 [1000–4480]3058 ± 748 [1030–4500]
 < 10th centile (%)*8.76.3
 > 90th centile (%)*3.03.9
Fetal gender: female/male (%)47.4/52.648.4/51.6
Birth length (cm, mean ± SD [range]))48.4 ± 4.5 [34–57]49.1 ± 4.0 [28–58]

The best-fit weight formula for each gender was derived from stepwise polynomial regression analysis:

equation image

In the formula-evaluation group, 9/180 male fetuses (5.0%) and 6/169 female fetuses (3.6%) had a birth weight <1500 g; the equivalent numbers for birth weights >4000 g were 19/180 (10.6%) and 10/169 (5.9%), respectively.

When tested in the independent evaluation group our gender-specific formulae compared favorably with established formulae with regard to accuracy of weight estimation. Our formulae had the lowest mean error (15 ± 266 g), the lowest mean absolute error (203 ± 173 g), the lowest mean percentage error (1.3 ± 8.9%) and the lowest mean absolute percentage error (6.8 ± 5.8%) of all equations studied in the formula-evaluation group (Table 2). Exclusion of women with gestational or pre-existing diabetes from the final analysis did not change results significantly (data not shown). As shown in Table 3, our formulae also had the highest number of calculations within the 10% and the 15% ranges of the actual birth weight. Figures 1 and 2 illustrate the correlation between estimated and actual weights at birth for our new gender-specific formulae. Figure 3 provides the limits of agreement between sonographically derived fetal weight and newborn weight at delivery. Absolute differences and absolute percentage differences of our new weight formulae were significantly different from those of all other equations (P < 0.01, data not shown).

Figure 1.

Correlation between estimated and actual weight at birth for male fetuses using our new formulae, showing the mean (solid line) and 5th and 95th centiles (dashed lines).

Figure 2.

Correlation between estimated and actual weight at birth for female fetuses using our new formulae, showing the mean (solid line) and 5th and 95th centiles (dashed lines).

Figure 3.

Limits of agreement between estimated and true birth weight according to the method used for calculating fetal weight: our new formulae (a) and formulae of Campbell and Wilkin1 (b), Hadlock et al.3 (c), Hansmann et al.2 (d) and Merz et al.4 (e).

Table 2. Comparison of our new formulae with conventional formulae1–4 using the formula-evaluation study group (n = 349; males, n = 180; females, n = 169)
Formula*E (g, mean ± SD)AE (g, mean ± SD)PE (%, mean ± SD)APE (%, mean ± SD)
  • *

    Formula of Campbell and Wilkin1: log(EFW) = − 4.564 + 0.282(AC) − 0.00331(AC)2 [in cm]; formula of Hadlock et al.3: log(EFW) = 1.326 + 0.0107(HC) + 0.0438(AC) + 0.158(FL) − 0.00326(AC × FL) [in cm]; formula of Hansmann et al.2: EFW = − 0.001665958(TAD)3 + 0.4133629(TAD)2 − 0.5580294(TAD) − 0.01231535(BPD)3 + 3.7020000(BPD)2 − 330.18110(BPD) − 0.49371990(GA)3 + 55.958061(GA)2 − 2034.3901(GA) + 32768.19 [in mm]; formula of Merz et al.4: EFW = − 3200.40479 + 157.07186(AC) + 15.90391(BPD)2 [in cm]. AC, abdominal circumference; AE, absolute error (|EFW − birth weight|); APE, absolute percentage error (|EFW − birth weight| × 100/birth weight); BPD, biparietal diameter; E, error (EFW − birth weight); EFW, estimated fetal weight; FL, femur length; GA, gestational age (weeks); HC, head circumference; PE, percentage error ((EFW − birth weight) × 100/birth weight); TAD, transverse abdominal diameter.

Campbell and Wilkin (1975)1− 169 ± 328285 ± 233− 4.9 ± 11.19.5 ± 7.6
Hadlock et al. (1985)355 ± 301232 ± 1991.9 ± 9.87.7 ± 6.3
Hansmann et al. (1978)250 ± 296231 ± 1922.2 ± 10.48.0 ± 7.0
Merz et al. (1988)4− 163 ± 303272 ± 210− 6.2 ± 11.09.5 ± 7.7
Our new formulae
 All15 ± 266203 ± 1731.3 ± 8.96.8 ± 5.8
 Males only11 ± 262206 ± 1611.3 ± 8.97.0 ± 5.5
 Females only− 21 ± 275209 ± 180− 0.1 ± 9.16.9 ± 5.8
Table 3. Number and percentage of estimations within the 10% and 15% ranges of birth weight
Formula≤10% (n (%))≤15% (n (%))
Campbell and Wilkin (1975)1224 (64.2)279 (79.9)
Hadlock et al. (1985)3252 (72.2)309 (88.5)
Hansmann et al. (1978)2252 (72.2)308 (88.3)
Merz et al. (1988)4221 (63.3)273 (78.2)
Our new formulae
 All266 (76.2)317 (90.8)
 Males only132 (73.3)164 (91.1)
 Females only134 (79.3)153 (90.5)


Ultrasound measurement of fetal weight has been used in obstetrics for more than 30 years and a variety of weight formulae with different fetal anthropometric measurements have been described1. There is now good evidence that a variety of factors, such as maternal weight and size, smoking status, parity, ethnic origin and fetal sex, are important regulators of fetal growth and final birth weight12, 13. However, none of the widely used weight formulae considers fetal gender, despite consistent sex differences in BPD, HC and AC, which measure about 2% larger for males14. Previous ultrasound studies found differences in fetal size as early as the first trimester of pregnancy15 and these differences tended to increase with advancing gestation16. At birth, the mean weight of females is lower than that of males17. In fact, examination of time necessary for the female fetus to reach male size showed that this increased from one day at 8–12 weeks to 6 or 7 days at term15. Several hypotheses have been postulated to explain this gender-specific growth pattern. Thomson et al. suggested that sex hormone differences rather than the genetically pre-determined growth potential may be responsible for greater growth of the male fetus18. Others have argued that gender differences in fetal growth rate are due to maternal–fetal antigenic disparity caused by the Y-chromosome19 or are already encoded at conception15. In contrast, in-utero fetal weight differences associated with maternal stature are reported to be apparent early, whereas those due to fetal sex become apparent later20. Nevertheless, there is now convincing evidence that adjusting birth-weight centiles for physiological variables such as fetal sex improves weight prediction and distinction between normal and abnormal pregnancy outcomes. Although nowadays fetal sex can be reliably determined as early as the end of the first trimester21 none of the commonly used antenatal weight formulae considers fetal gender. We therefore developed sex-specific formulae which we then tested against established formulae.

Most of the American-based weight equations include the BPD, the measurement of which differs in the US from current practice in Germany. In Germany, fetal BPD is measured from the leading edges of the skull, whereas in the USA, measurements are taken from the outer edge of the proximal bone to the inner edge of the distal bone. To avoid systematic errors we therefore did not consider American-based formulae other than the Hadlock equation with the parameters HC, AC and FL3. In our study, the vast majority of true birth weights fell within the range of 1500–4000 g; numbers of cases with lower or higher birth weights were too small to allow meaningful conclusions on the accuracy of our formulae at these extremes of fetal weight. Several factors contributed to the relatively high Cesarean section rate: complicated singleton pregnancies were not explicitly excluded; in our department, Cesarean section was, until recently, the preferred delivery route in fetuses <32 weeks' gestation; a significant number of cases booked for elective Cesarean section were included; ultrasound scans had to be performed before active labor and by highly trained personnel, thus excluding many normal cases admitted in labor or outside normal working hours. We are aware that the study population included a significant number of abnormal pregnancies, also evident by the relatively low mean birth weight. However, exclusion of women with gestational or pre-existing diabetes from the final analysis did not change results significantly (data not shown). Furthermore, the intervening fetal growth between ultrasound examination and delivery was not taken into account, which theoretically may have added another source of variance to our findings. The GAP (gestation-adjusted projection) method as described by Mongelli and Gardosi22 might have corrected this presumed systematic error, but we decided not to employ this extrapolation as the GAP method was found to be significantly correlated with true birth weights above 3200 g only22. Mean birth weights in our study populations were well below this limit (Table 1).

The results obtained from our new formulae demonstrate that this approach improves weight prediction by lowering error rates when compared with conventional equations. They will, however, need to be tested in different settings and populations before their widespread use can be recommended.