Macrosomia: a new formula for optimized fetal weight estimation



This article is corrected by:

  1. Errata: Errata Volume 37, Issue 2, 254, Article first published online: 24 January 2011



To develop and test a specific formula for estimating weight in the macrosomic fetus.


Ultrasound estimations of fetal weight were carried out within 1 week of delivery in 424 singleton fetuses with a birth weight of ≥ 4000 g. Exclusion criteria were multiple pregnancy, intrauterine death and major structural or chromosomal anomalies. Stepwise regression modeling was used to derive a prediction formula with birth weight as the dependent variable and maternal booking weight and fetal biometric measurements as independent parameters. After a new formula for estimated fetal weight (EFW) had been developed in a formula-finding group (n = 284), it was compared with commonly used weight equations (evaluation group, n = 140).


The new formula (logeEFW = 7.6377445039 + 0.0002951035 × maternal weight + 0.0003949464 × head circumference + 0.0005241529 × abdominal circumference + 0.0048698624 × femur length) proved to be superior to established equations, with the smallest mean error (mean ± SD, −10 ± 202 g), the smallest mean percentage error (mean ± SD, −0.03 ± 4.6%) and the lowest mean absolute percentage error (3.69 (range, 0.05–13.57)%) when studied in the evaluation group. With the new formula, 77.9% of estimates fell within ± 5% of the actual weight at birth, 97.1% within ± 10%, and 100% within ± 15% and ± 20%.


The new formula allows better weight estimation in the macrosomic fetus. Copyright © 2009 ISUOG. Published by John Wiley & Sons, Ltd.


The incidence of fetal macrosomia and its associated risks for mother and child have increased continuously in recent years1, 2. Typical risks include a prolonged second stage of labor, serious maternal trauma after vaginal and surgical delivery, increased postpartum hemorrhage, and shoulder dystocia with brachial plexus paralysis and/or clavicular fracture3, 4. Relative to all births, the risk of shoulder dystocia is 0.2%. With a birth weight (BW) of 4000–4500 g and above 4500 g, the risk increases to 5% and 30%, respectively5–7. Therefore, recognition of macrosomic fetuses as such is not the only matter of interest. To ensure that the obstetric management associated with the lowest possible risk can be chosen, prenatal weight estimation needs to be as accurate as possible. The American College of Obstetricians and Gynecologists' guidelines recommend elective Cesarean sections above an estimated fetal weight (EFW) of 5000 g in pregnant women without diabetes, and above 4500 g in pregnant women with diabetes8.

Available methods of fetal weight estimation include measurement of the symphysis–fundus distance, maternal biometry parameters such as height and weight, and various formulae based on fetal ultrasonography9, 10. Commonly used weight formulae are associated with very large deviations when used in the macrosomic fetus. This is partly because these formulae were derived from heterogeneous groups (Hadlock et al.11: n = 167, 600–4680 g; Warsof et al.12: n = 85, 174–4760 g; Campbell and Wilkin13: n = 140, weight range not given; Merz et al.14: n = 196, 610–4520 g) and were not specifically designed for assessing fetal weight at the upper end of the weight scale. In addition, none of the established formulae takes maternal biometry parameters into account. Against this background, the aim of the present study was to develop a specific formula for estimating weight of the macrosomic fetus taking fetal biometry and maternal weight into account, and to test this new formula in a large independent group.


A new formula for optimized prediction of fetal weight in the macrosomic fetus was generated on the basis of data for 424 predominantly Caucasian women for whom a complete set of data was available. All data were consecutive and were collected retrospectively over a 4-year period (2003–2006). Two-thirds of the cases were randomized into the formula-finding group (n = 284) and the others into the evaluation group (n = 140). As this was a retrospective study, weight estimations using the new formula had no impact on clinical management in the evaluation group. Our local ethics committee guidelines did not require written consent as fetal biometry was performed routinely on admission for delivery and data were extracted anonymously for the purpose of the study.

Inclusion criteria for the formula-finding and evaluation groups were a singleton live newborn and complete fetal biometry within 7 days of delivery. Multiple pregnancies, intrauterine fetal death at presentation and infants with major structural or chromosomal anomalies were excluded, as were pregnancies for which there was incomplete information, an actual BW below 4000 g, or in which delivery occurred more than 7 days after the last ultrasound examination.

For cases in which serial follow-up examinations had been carried out to assess fetal growth or condition, only the last examination before delivery was considered. Each fetus was included only once. Measurements were performed by several trained investigators (N.C.H., J.S., B.M., M.S., R.L.S.) using the Voluson Expert system (GE Medical Systems, Solingen, Germany), Elegra, Sonoline G60 and Sienna systems (Siemens AG Medical Solutions, Erlangen, Germany), and Xario and Nemio systems (Toshiba Medical Systems, Neuss, Germany). Gestational age was based on fetal crown–rump length obtained in the first trimester15.

Biparietal diameter (BPD) measurements were made from the outer edge of the proximal fetal skull bone to the outer edge of the distal bone, as is routine practice in Germany. No correction was made for different shapes of the fetal head in non-vertex presentations. The head circumference (HC) was calculated from measurement of the occipitofrontal diameter (OFD) and the BPD using the formula 2.325 × (d12 + d22)1/2, where d1 and d2 were the two diameters16. The transverse diameter (ATD), abdominal anterior–posterior diameter (ASD) and circumference of the fetal abdomen (AC) were measured in standard transverse planes at the level of the stomach and umbilical vein–ductus venosus complex. The circumference was calculated by derivation from the measurement of the transverse and anteroposterior diameters using the formula π × (d1 + d2)/2. Femur length (FL) was measured from the proximal end of the greater trochanter to the distal metaphysis17.

All cases meeting the inclusion criteria were included in the final statistical analysis. Maternal weight was measured in kilograms at the booking visit. Ultrasound measurements were expressed in centimeters and fetal weight in grams. BW and length were recorded within 1 h of delivery by the nursing staff.

Statistical analysis

The Statistical Package for the Social Sciences version 13.0 (SPSS, Inc., Chicago, IL, USA) and the R Package for Statistical Computing, version 2.7.018 were used for randomization of each case to one of the two groups and for further statistical analysis.

Differences in demographic and clinical variables between the formula-finding group and the evaluation group were compared using Wilcoxon's test at a significance level of 5% (normal Q-Q plots indicated that continuous variables were non-normally distributed). The distribution of fetal gender was compared by using the chi-square test.

Stepwise regression modeling19 was used to derive a prediction formula with BW as the dependent variable and sonographic parameters (BPD, OFD, HC, AC, ATD, ASD, FL) and maternal booking weight as independent variables. Because distribution of BW was right skewed, linear models (assuming a normally distributed outcome) proved to be inadequate. Instead, generalized linear models with a log-transformed gamma-distributed outcome were considered19. In the course of the modeling process, Akaike's information criterion was used for variable selection. Pearson and deviance residuals were used for checking model assumptions. Scatter plots between sonographic parameters and BW were used to assess the adequacy of variable transformations. In order to detect the presence of severe multicollinearity, variance inflation factors were computed.

For evaluation, the new formula was compared with seven widely accepted weight formulae (Hadlock et al.11, Merz et al.14, Warsof et al.12, Campbell and Wilkin13; Table 1). These formulae have been described in detail previously and have been found favorable in estimating weight in macrosomic fetuses20, 21. Accuracy of EFW was assessed by calculating the percentage error (PE; (EFW − BW)/BW × 100) and the absolute percentage error (APE; (|EFW − BW|)/BW × 100). Differences between the established weight equations and the new formula were compared using Wilcoxon's test for APE values and the paired t-test for mean PE values, at a significance level of 5%. As a total of seven different comparisons were made between the new formula and the traditional equations, a Bonferroni adjustment22 was carried out and P ≤ 0.007 was regarded as significant. The SDs of PEs of different models were compared using Pitman's test for correlated variance23, 24. At a significance level of 1% and with a sample size of more than 100, R ≥ 0.254 was significant. This test served to assess significant differences between the new equation and traditional formulae with regard to relative errors.

Table 1. The new formula and seven regression formulae for estimating fetal weight used in the evaluation group
FormulaRegression equation
  1. AC, abdominal circumference; BPD, biparietal diameter; EFW, estimated fetal weight; FL, femur length; HC, head circumference.

Hadlock I11Log10 EFW = 1.3596 −0.00386 AC × FL + 0.0064 HC + 0.00061 BPD × AC + 0.0424 AC + 0.174 FL
Hadlock II11Log10 EFW = 1.304 + 0.05281 AC + 0.1938 FL −0.004 AC × FL
Hadlock III11Log10 EFW = 1.335 −0.0034 AC × FL + 0.0316 BPD + 0.0457 AC + 0.1623 FL
Hadlock IV11Log10 EFW = 1.326 −0.00326 AC × FL + 0.0107 HC + 0.0438 AC + 0.158 FL
Warsof12Log10 EFW = −1.599 + 0.144 BPD + 0.032 AC −0.111 (BPD2× AC)/1000
Campell13Loge EFW = −4.564 + 0.282 AC −0.00331 AC2
Merz14EFW = −3200.40479 + 157.07186 AC + 15.90391 BPD2
New formulaLoge EFW = 7.6377445039 + 0.0002951035 maternal weight + 0.0003949464 HC + 0.0005241529 AC + 0.0048698624 FL

Percentages of fetal weight estimations falling within discrepancy levels of ± 5%, ± 10%, ± 15% and ± 20% of the actual BW were also calculated for each formula. Differences between the new formula and commonly used methods were compared by McNemar's test. Bonferroni adjustments22 were also made, and P ≤ 0.007 was regarded as significant.

In addition, we derived a simple rule for determining whether fetal macrosomia is present or not, i.e. whether a child has a BW ≥ 4000 g. The objective of this rule was to determine whether the newly derived formula should be applied or not. The rule was derived by performing a receiver–operating characteristics (ROC) curve analysis on 3019 singleton pregnancies between 2003 and 2006 at our hospital (including the 424 macrosomic cases in this study and 2595 non-macrosomic fetuses). The children's BWs ranged from 3000 g to 5050 g. Fetal AC was used as a predictor variable for the outcome < 4000 g or ≥ 4000 g. Youden's index (defined as sensitivity + specificity −1)25 was computed for determining the AC threshold of the optimal prediction rule. In addition, the area under the ROC curve, as well as likelihood ratios and odds ratios, were computed for evaluating the prediction rule for fetal macrosomia.


Clinical data of our study patients and their infants are presented in Table 2, specified by formula-finding and evaluation group. There were no significant differences between the groups. Diabetes was present in 37 patients (gestational diabetes, n = 30; pre-existing Type 1 diabetes, n = 6; pre-existing Type 2 diabetes, n = 1). Eight and 29 of the diabetic cases belonged to the formula-finding and evaluation groups, respectively.

Table 2. Demographic and clinical parameters studied in the formula-finding and evaluation groups
ParameterFormula-finding group (n = 284)Evaluation group (n = 140)P*
  • Data are median (range) or n.

  • *

    All comparisons, except for gender, were carried out by Wilcoxon's test. The chi-square test was used to compare distribution of gender.

Maternal age (years)32 (18–46)32 (15–41)0.415
Body mass index at booking visit (kg/m2)24.5 (16.8–47.2)23.9 (18.3–42.5)0.228
Body weight at booking visit (kg)70.0 (43–128)70.0 (49–120)0.567
Parity2 (1–5)2 (1–5)0.540
Gestational age at delivery (days)282 (254–295)283 (267–295)0.314
Interval between ultrasound and delivery (days)1 (0–7)1 (0–7)0.571
Fetal gender (female/male)92/19245/950.856
Birth weight (g)4170 (4000–5050)4200 (4000–4900)0.305

Scatter plots between the independent variables OFD, ATD, ASD, AC, HC, BPD, FL, maternal booking weight and the dependent variable BW indicated only slight deviations from linearity. Consequently, the independent variables were left untransformed in the process of finding a prediction formula. Owing to high correlations between OFD, ATD, ASD, HC and AC, variance inflation factors for BPD, OFD, HC, ASD, ATD and AC became > 10, indicating severe multicollinearity. After removing OFD, ATD and ASD from the list of independent variables, variance inflation factors were < 10 for all remaining variables. Therefore, OFD, ATD and ASD were not used in the course of the formula-finding process. Stepwise regression modeling resulted in the following prediction formula for EFW: Loge EFW = 7.6377445039 + 0.0002951035 × maternal weight + 0.0003949464 × HC + 0.0005241529 × AC + 0.0048698624 × FL.

A residual analysis of the prediction model did not reveal significant violations of the model assumptions. When tested in an independent evaluation group, the new formula had a mean ± SD error of −10 ± 202 g and a mean ± SD PE of −0.03 ± 4.60, with no significant bias apparent compared to zero (paired t-test; data not shown). The mean APE was 3.69. With the new formula, 77.9% of the estimates fell within ± 5% of the actual weight at birth, 97.1% within ± 10%, and 100% within ± 15% and ± 20% (Table 3). These results were highly significant compared with all other weight equations. Stepwise generalized linear modeling with interaction terms between the independent variables did not result in smaller prediction errors.

Table 3. Percentage of cases in the evaluation group (n = 140) falling within discrepancy levels of ± 5%, ± 10%, ± 15% and ± 20% of the true birth weight using different regression formulae
Formula ± 5%P* ± 10%P* ± 15%P* ± 20%P*
  • *

    P-values were calculated using McNemar's test. After Bonferroni adjustment, P ≤ 0.007 was considered significant.

Hadlock I1128.6< 0.00162.1< 0.00182.9< 0.00194.30.008
Hadlock II1122.1< 0.00157.9< 0.00177.9< 0.00187.9< 0.001
Hadlock III1131.4< 0.00163.6< 0.00183.6< 0.00193.60.004
Hadlock IV1124.3< 0.00154.3< 0.00178.6< 0.00193.60.004
Warsof1230.0< 0.00157.1< 0.00174.3< 0.00190.7< 0.001
Campbell1310.0< 0.00130.0< 0.00164.3< 0.00183.6< 0.001
Merz1446.4< 0.00171.4< 0.00191.4< 0.0011001
New formula77.997.1100100

Table 4 shows the mean PEs with SDs for all formulae in the evaluation group. The new weight formula had a significantly lower tendency to underestimate fetal weight than did the other formulae. As an indicator of random errors, the SD of the new equation was significantly lower than that of all other evaluated methods.

Table 4. Mean ± SD of the percentage error (PE) for each regression formula in the evaluation group (n = 140)
FormulaPE (mean ± SD)P*R
  • *

    Mean values for the PE were compared between the new formula and widely used equations using the paired t-test. After Bonferroni adjustment, P ≤ 0.007 was considered significant.

  • The SDs of PEs of different models were compared using Pitman's test for correlated variance, with R ≥ 0.254 considered significant.

Hadlock I11−6.49 ± 7.91< 0.0010.621
Hadlock II11−8.44 ± 8.17< 0.0010.626
Hadlock III11−5.41 ± 7.91< 0.0010.619
Hadlock IV11−8.73 ± 7.59< 0.0010.602
Warsof12−6.54 ± 9.37< 0.0010.676
Campbell13−13.39 ± 6.01< 0.0010.432
Merz14−3.93 ± 6.63< 0.0010.522
New formula−0.03 ± 4.60

The APEs are shown as mean values and ranges in Table 5. The lowest mean APE was found for the new formula. These results were significantly different from those for the other equations tested.

Table 5. Mean and range of the absolute percentage error (APE) for each regression formula in the evaluation group (n = 140)
FormulaAPE mean (range)P*
  • *

    APEs were compared using Wilcoxon's test. With Bonferroni adjustment, P ≤ 0.007 was considered significant.

Hadlock I119.09 (0.13–26.58)< 0.001
Hadlock II1110.33 (0.22–30.54)< 0.001
Hadlock III118.50 (0–25.09)< 0.001
Hadlock IV1110.35 (0.25–29.69)< 0.001
Warsof129.82 (0.05–29.33)< 0.001
Campbell1313.45 (0.70–31.10)< 0.001
Merz146.88 (0.06–19.14)< 0.001
New formula3.69 (0.05–13.57)

To achieve a better prediction of fetal macrosomia we performed a ROC analysis on 3019 newborns weighing between 3000 g and 5050 g. The AC was used as a predictor variable for fetal macrosomia26, 27. The best cut-off value with respect to Youden's index was 35.1 cm. When tested in our evaluation group, the sensitivity and specificity for detecting macrosomia at birth were 75% and 73%, respectively, with a positive predictive value of 32% and a negative predictive value of 94% (prevalence of fetal macrosomia, 14%). The corresponding odds ratio obtained from the evaluation group was 2.10 (95% CI, 1.87–2.33). Positive and negative likelihood ratios were 2.78 and 0.34, respectively. The area under the ROC curve was 0.803, indicating a moderate to good ability of the AC to predict fetal macrosomia.

Eventually, the new formula was tested retrospectively on fetuses with a BW of 3500 g to 3999 g, regardless of the AC, who were delivered at our department during the evaluation period (July 2004 to December 2006) and for whom the same inclusion and exclusion criteria applied (n = 719). In this group the mean ± PE was 10.27 ± 4.15, and the mean APE was 10.28.


With rising rates of macrosomia, accurate estimation of fetal weight is important. However, weight in these fetuses is often underestimated, leading indirectly to prolonged delivery with trauma to the mother and/or infant28–31. For this reason, various improved methods of weight assessment in suspected fetal macrosomia have been developed and investigated.

Abramowicz et al. included the ‘cheek-to-cheek’ diameter (CCD), an indicator of the subcutaneous tissue mass, into traditional weight estimation formulae and achieved a better weight prediction in the macrosomic fetus. The difference between the actual and estimated BW was less than 10% in 95.5% of cases, and this difference would have been achieved in only 72.7% of cases if the CCD had not been included9. Although this measurement was performed by transvaginal ultrasonography, it should be noted that this method is more difficult when the infant's head has already descended lower near to term.

Han et al. added soft-tissue thickness of the fetal thigh to conventional biometry, achieving a reliable identification of macrosomia (sensitivity, 91%; specificity, 94%)32.

Matsumoto et al.33, Santolaya-Forgas et al.34 and Petrikovsky et al.35 used three-dimensional qualitative sonographic evaluation of fetal soft tissue, the sonographically measured fetal subcutaneous tissue/FL ratio, and the sonographically measured abdominal subcutaneous tissue thickness, respectively, and achieved improved weight assessment in macrosomic fetuses. Matsumoto and colleagues examined 52 fetuses between the 29th and 41st week of gestation, and determined a fetal nutrition score by measuring subcutaneous fatty tissue at three sites in the body (face, ribs and buttocks). This score was found to be useful for early prediction of extreme fetal growth patterns, as in macrosomia33. Santolaya-Forgas et al. compared measurement accuracy of the fetal AC, EFW and fetal subcutaneous tissue/FL ratio in predicting large-for-gestational age fetuses. They found that the fetal subcutaneous tissue/FL ratio was a parameter independent of gestational age and able to provide greater sensitivity in identifying large-for-gestational age fetuses than AC measurements34. Petrikovsky et al. measured subcutaneous tissue diameter in the abdominal area and found it significantly different between normal and macrosomic fetuses (7.0 mm vs. 12.4 mm; P < 0.0001)35.

By contrast, measurements of the transcerebellar diameter/AC ratio36, subcutaneous fatty tissue in the abdominal area37, upper arm soft-tissue diameter38, and the subcutaneous fatty tissue/FL ratio39 did not lead to optimized diagnosis of fetal macrosomia.

Other groups of researchers have investigated the influence of maternal parameters such as maternal height and weight, parity and ethnic background. None of these additional parameters led to improved fetal weight estimation40. However, taking maternal parameters into account did prove to be helpful in recognizing pregnancies in which there was a tendency for fetal macrosomia to occur41. Nahum et al. studied a group of 262 patients, and developed a new formula including gestational age, parity, fetal sex, and maternal height and weight. The absolute mean error of the new formula was 267 g, and the APE 7.6%. The sensitivity for predicting macrosomia was 80%41.

Combs et al. compared the accuracy of 31 formulae in predicting weight of macrosomic fetuses in women with diabetes (n = 165)42. The formula published by Ott et al. produced the best results43. Sensitivity and positive predictive value for identifying macrosomia (estimated weight, ≥ 4000 g) were 45% and 81%, respectively. Twenty-eight of the formulae tested were able to predict macrosomia better than measurement of AC alone. However, none of the formulae was superior to others in assessing weight in fetal macrosomia42.

When comparing fetal weight equations, some authors derived model coefficients for commonly used formulae from multiple regression analysis of their own data. In this manner, potential bias in comparing estimation errors for two different study populations could be minimized44. We did not choose this procedure, as in our hospital commonly used formulae for fetal weight estimation are used in their originally published form without customized adjustments.

The new formula only includes fetal parameters that are used routinely in biometry, and does not require any special technical facilities such as three-dimensional sonography. The formula presented in this study was specifically developed and evaluated in a large group of macrosomic fetuses. Compared with other formulae, the new formula demonstrated the smallest mean error, the smallest mean PE and the lowest mean APE when tested in the independent evaluation group. For proper application of our new formula the AC could be taken into account. Using an AC of 35.1 cm as a cut-off, the AC had a sensitivity and specificity of 75% and 73%, respectively, for correctly assuming a true BW of ≥ 4000 g.