Volume 24, Issue 7 p. 775-780
Original Paper
Free Access

A new formula for calculating weight in the fetus of ≤ 1600 g

R. L. Schild

Corresponding Author

R. L. Schild

Department of Obstetrics and Fetal Medicine, Centre for Obstetrics and Gynaecology, Germany

Frauenklinik der Universität, Universitätsstraße 21–23, 91054 Erlangen, GermanySearch for more papers by this author
K. Fell

K. Fell

Department of Obstetrics and Fetal Medicine, Centre for Obstetrics and Gynaecology, Germany

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R. Fimmers

R. Fimmers

Institute for Medical Statistics, University Hospital Bonn, Germany

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U. Gembruch

U. Gembruch

Department of Obstetrics and Fetal Medicine, Centre for Obstetrics and Gynaecology, Germany

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M. Hansmann

M. Hansmann

Department of Obstetrics and Fetal Medicine, Centre for Obstetrics and Gynaecology, Germany

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First published: 08 October 2004
Citations: 25



To develop and test a new formula for estimating weight in the fetus of ≤ 1600 g.


A formula for sonographic estimation of fetal weight was produced retrospectively from 84 singleton fetuses with a birth weight of ≤ 1600 g, examined sonographically within 1 week before delivery. Exclusion criteria were multiple pregnancy, intrauterine death and major structural or chromosomal anomalies. The new formula was then compared prospectively in an evaluation group of fetuses (n = 87) with six currently available equations for estimating weight in the preterm fetus.


Stepwise regression analysis with gestational age (in days) and fetal biometric parameters was employed to yield the best-fit formula for predicting fetal weight at birth. The new formula (estimated fetal weight = 5381.193 + 150.324 × head circumference + 2.069 × femur length3 + 0.0232 × abdo- minal circumference3—6235.478 × log(head circumference)) proved to be superior to established equations. The lowest mean ± SD absolute error was 66.2 ± 59 g and the lowest mean absolute percentage error was 7.1 ± 5.9% SD when studied prospectively in the evaluation group. With the new formula, 48.3% of estimates fell within ±5% of the actual weight at birth, 73.6% fell within ±10%, 90.8% fell within ±15% and 95.4% fell within ±20%.


Our new formula is relatively easy to use and needs no adjustment to weight centiles or to fetal lie. It allows reliable weight estimation in the fetus ≤ 1600 g. Copyright © 2004 ISUOG. Published by John Wiley & Sons, Ltd.


The majority of currently available fetal weight formulae were first described 20–30 years ago at a time when a very small fetus was often considered to be previable. As a consequence, the number of such cases included in formula descriptions remained low1. This fact may partly explain why many formulae fail to estimate the weight of small fetuses in a reliable manner. In contrast, recent advances in neonatal medicine have lowered the threshold of survival to a gestational age of approximately 24 weeks and to a birth weight of approximately 500 g. As neonatal risk of morbidity and mortality are highest in the lowest weight range, diagnostic assessment of the small fetus should be as precise as possible2. The purpose of our study, therefore, was to develop a new weight formula for fetuses with a birth weight ≤ 1600 g and to test this formula in an independent evaluation group against established methods.


Based on the data of 171 predominantly Caucasian women, collected during a 14-year period (1990–2003) in the Department of Obstetrics and Fetal Medicine, University of Bonn and for whom a complete set of data was available, a new formula for optimized fetal weight prediction in the small fetus was generated and tested. Data in the formula-finding group were retrieved retrospectively (1990–1998, n = 84); data in the evaluation group were collected prospectively (1999–2003, n = 87). Ultrasound examinations were performed for a variety of reasons including both normal pregnancies and women with diabetes, hypertension, fetal growth restriction and other pregnancy complications. Inclusion criteria for the retrospective and prospective groups, respectively, were a singleton live fetus at delivery or at the time of study entry, actual birth weight or estimated birth weight of ≤ 1600 g. Multiple pregnancies, intrauterine fetal death at presentation and infants with major structural or chromosomal anomalies were excluded, as were those pregnancies with incomplete information, i.e. those lacking fetal biometric measurements obtained within 7 days preceding delivery, or those in which delivery occurred more than 7 days after the last ultrasound examination. Data retrieval was specifically for the purpose of this study. In cases where fetal growth or condition had been followed serially, the last examination before delivery was considered. Each fetus was included only once.

Measurements were taken by several trained investigators 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 given in days. If there was any uncertainty about the true gestational age it was based on crown–rump length obtained in the first trimester. Biparietal diameter (BPD) measurements were taken from the outer edge of the fetal proximal skull bone to the outer edge of the distal bone. No correction was made for different shapes of the fetal head in non-vertex presentations. The head circumference (HC) was calculated from measurements of the occipitofrontal diameter (OFD) and the BPD using the formula 2.325 × (d12 + d22)1/2, where d1 and d2 were the two diameters3. The fetal abdominal transverse diameter (ATD) and circumference (AC) were measured in standard transverse planes at the levels 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 following Merz et al.4. The femur length (FL) was measured from the proximal end of the greater trochanter to the distal metaphysis.

We generated our formula from the formula-finding group, collected between 1990 and 1998, with an actual fetal weight at delivery of ≤ 1600 g, and studied retrospectively (n = 84). To validate our new formula we used the formula-evaluation group, seen between 1999 and 2003 in the same setting, with an estimated fetal weight (EFW) of ≤ 1600 g, and studied prospectively (n = 87). Weight calculation with our new formula was also tested against established equations1, 5-8. Patients gave their verbal consent to this part of the study. In our department fetal weight determination is routinely applied in the diagnostic work-up of a small fetus. Ethical approval was therefore not sought. Birth weight and length were obtained within 1 h of delivery by our nursing staff.

Statistical analysis

For statistical analysis we used a RS6000 workstation using SAS (version 6.12, SAS Institute Inc., Cary, NC, USA) procedure REG. Stepwise regression analysis was performed with birth weight as the dependent variable, and sonographic parameters (BPD, OFD, HC, ATD, AC and FL) and gestational age (in days) as independent parameters. The squares, cubes and natural logarithms of these variables were also included in the modeling process. Criteria for inclusion and exclusion of ultrasound parameters in the regression analysis were P-values of <0.05 and ≥0.1, respectively. To facilitate comparison between the tested formulae, mean absolute and mean absolute percentage errors in the evaluation group were calculated. For absolute and absolute percentage differences from the true birth weight between new and established formulae, Wilcoxon's test was used. Bland and Altman's 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 data9.


The clinical data of our study patients and their infants are given in Table 1, separated into formula-finding and evaluation groups. We used stepwise regression analysis from which the best-fit weight formula was derived: EFW = 5381.193 + 150.324 × HC + 2.069 × FL3 + 0.0232 × (AC)3 − 6235.478 × log(HC). When tested in the independent evaluation group our new formula compared favorably with established formulae specifically generated for small fetuses. Our formula had the lowest mean ± SD absolute error (66.2 ± 59 g) and the lowest mean absolute percentage error (7.1 ± 5.9%) (Table 2). As shown in Table 3, 48.3% of estimates with our newly generated formula fell within ±5% of the actual weight at birth, 73.6% fell within ±10%, 90.8% fell within ±15% and 95.4% fell within ±20%. Figure 1 illustrates the correlation between formula-derived and actual weights at birth for the evaluation group. With the exception of the Scott formula, absolute differences and absolute percentage differences of our new weight formula were significantly different from all other equations (P < 0.05, data not shown). Finally, Figure 2 provides the limits of agreement between sonographically derived fetal weight and actual neonatal weight at delivery.

Details are in the caption following the image

Correlation between estimated and actual weights at birth for the evaluation group (n = 87). The dashed lines represent the 5th and 95th centiles.

Details are in the caption following the image

Limits of agreement between estimated and actual birth weights according to the formula used for calculating fetal weight in the evaluation group (n = 87): a) our formula, b) Hadlock formula1, c) Scott formula7, d) Weiner formula A8, e) Weiner formula B8, f) Mielke formula I5 and g) Mielke formula II6. The straight lines represent the mean, and the dashed lines the upper and lower 2 SD.

Table 1. Demographic and clinical data of the formula-finding and the evaluation study groups
Characteristic Formula-finding group (n = 84) Evaluation group (n = 87)
GA at ultrasound (weeks) 28.8 ± 3.1 [20.6–36.9] 28.3 ± 3.5 [18.6–36.4]
Parity 0.8 ± 1.1 [0–4] 0.8 ± 1.4 [0–10]
Birth weight (g) 997 ± 329 [350–1580] 960 ± 345 [345–1580]
Birth weight centiles12
 Percentage < 10th centile 40.5 41.4
 Percentage > 90th centile 1.2 0
Percentage of cases with GA at US:
 <24 + 0 weeks 7.2 6.9
 24 + 0 to 30 + 0 weeks 57.9 60.7
 ≥30 + 0 weeks 34.9 32.4
Percentage of cases with birth weight:
 <500 g 3.5 6.9
 500–1000 g 51.7 49.4
 ≥1000 g 48.2 43.7
Fetal gender (female : male) 42.2 : 57.8 47.1 : 52.9
Birth length (cm) 36.4 ± 4.2 [26–45] 34.6 ± 4.5 [25–44]
  • Data are expressed as n, %, mean ± SD and/or [range]. GA, gestational age; US, ultrasound examination.
Table 2. Evaluation group (n = 87): comparison of error rates between our new formula and previously published weight formulae
Reference Formula Absolute error (g, mean ± SD) Absolute percentage error (mean ± SD)
Hadlock et al.1 log(EFW) = 1.5662 − 0.0108(HC) + 0.0468(AC) + 0.171(FL) + 0.00034(HC)2 − 0.003685(AC × FL) 82 ± 67 9.2 ± 7.1
Scott et al.7 log(EFW) = 0.66 × log(HC) + 1.04 × log(AC) + 0.985 × log(FL) 70 ± 58 8.0 ± 6.8
Weiner et al.8 A log(EFW) = 1.6961 + 0.02253(HC) + 0.01645(AC) + 0.06439(FL) 83 ± 69 8.8 ± 6.2
Weiner et al.8 B log(EFW) = 1.6575 + 0.04035(HC) + 0.01285(AC) 98 ± 83 10.3 ± 7.5
Mielke et al.5 I log(EFW) = 3.06751 + 0.017677(BPD) + 0.000412(ATD)2 + 0.040611(FL) − 0.000000006027957(BPD2 × ATD2) − 0.000005086(ATD2 × FL) 85 ± 74 9.7 ± 8.8
Mielke et al.6 II log(EFW) = 3.071723 + 0.025139(BPD) + 0.00036(ATD)2 + 0.030545(FL) − 0.00000001938224(BPD2 × ATD2) − 0.000002893(ATD2 × FL) 86 ± 77 9.7 ± 8.7
Our formula EFW = 5381.193 + 150.324 × (HC) + 2.069 × (FL)3 + 0.0232 × (AC)3 − 6235.478 × log(HC) 66 ± 59 7.1 ± 5.9
  • Mean absolute error = |EFW − BW| and mean absolute percentage error = |(EFW − BW) × 100/BW|. AC, abdominal circumference; ATD, abdominal transverse diameter; BPD, biparietal diameter; BW, birth weight; EFW, estimated fetal weight; FL, femur length; HC, head circumference.
Table 3. Evaluation group (n = 87): estimated vs. actual birth weight
Reference Percentage of cases with estimated vs. actual birth weight within:
± 5% ± 10% ± 15% ± 20%
Hadlock et al.1 35.6 57.5 85.1 92
Scott et al.7 46 70.1 88.5 92
Weiner et al.8 A 31 66.7 80.5 96.6
Weiner et al.8 B 26.4 55.2 74.7 89.7
Mielke et al.5 I 39.1 59.8 80.5 89.7
Mielke et al.6 II 35.6 62.1 80.5 90.8
Our formula 48.3 73.6 90.8 95.4


The majority of commonly used weight formulae were derived from fetuses of appropriate size close to term, with small numbers in the ≤ 1600 g range1, 3. However, these formulae are still widely used in predicting weight of the small fetus despite evidence that no single formula can provide reliable estimations across the whole fetal weight range5. Only few weight formulae were designed specifically for the small fetus remote from term. Theoretically, these formulae can improve weight prediction by accounting for the altered head–abdomen ratio and for the growth restriction often found in these fetuses7.

Weinberger et al.10 evaluated several formulae in 41 fetuses weighing 500–2000 g and designed a new formula using BPD and AC. In 85.3% of cases the estimated weight fell within ±15% of the birth weight. The authors, however, did not test the validity of their new formula in an independent evaluation group. In a retrospective study, Medchill et al.2 compared the actual birth weight of 76 extremely low birth-weight neonates (500–1000 g) with estimations derived from 20 published formulae. None of the tested formulae estimated fetal weight significantly more accurately compared with any other. Using Rose's formula, the maximum weight underestimate and overestimate were 95g and 159g, respectively. Similarly, 73% of estimated weights fell within 10% of the final weight and 89% of calculations fell within ±100 g of the birth weight2. Weiner et al.8 developed a weight formula for the preterm fetus, including head, abdomen and FL measurements. The results of the new formula compared favorably with those of the formulae of Hadlock et al.1 and Shepard et al.11. Scott et al.7 performed the largest such study to date including 142 cases with a fetal weight of < 1000 g. The newly generated best-fit formula included the parameters HC, AC and FL. For the purpose of improving accuracy of the fit, three cases were later excluded for being overly influential. Subsequently, the newly postulated formula was prospectively evaluated using data from 27 fetuses with a birth weight between 420 g and 1080 g. The Scott formula achieved the lowest mean percentage error when compared with 10 currently available formulae. Mielke et al.5 described a new weight formula for infants delivered before 30 weeks of gestation, weighing between 400 g and 1680 g. The data of 73 cases were used to develop a new best-fit formula, with the parameters BPD, ATD and FL. In cases of non-vertex fetal lie, BPD measurements were corrected using standard HC charts. Separate coefficients for different weight percentile groups further improved the accuracy of weight prediction. However, the design of this study may be criticized for failing to exclude multiple pregnancies. The same authors undertook another study6 to test the accuracy of their previously described formulae in a group of 62 premature infants of < 30 weeks' gestation with a weight of ≤ 1400 g. With the combined data of the two studies the authors then calculated new coefficients for their different formulae. Using separate sets of coefficients fetal weight prediction could be further improved. The latter findings, however, await prospective evaluation in an independent sample of patients.

The present study focused on fetal weight prediction in the very small fetus, and contains one of the largest published series of such estimates for this group. The newly generated formula was prospectively tested in an independent evaluation group. Our results demonstrate that the new formula allows reliable weight prediction in the very small fetus, ≤ 1600 g in weight, irrespective of the weight percentile or the gestational age. When compared with already published formulae used for weight calculation in the small fetus, our new formula had the lowest mean absolute error (66.2 ± 59 g) and the lowest mean absolute percentage error (7.1 ± 5.9%). Of all measurements, 48.3% fell within ±5% of the birth weight, 73.6% within 10%, 90.8% within 15% and 95.4% within 20%. Our formula is easy to use as no further adjustments to weight centiles or to non-vertex presentations5, 6 have to be made. Although included in the stepwise regression analysis, gestational age did not contribute significantly to our best-fit formula and was therefore omitted. This in turn may facilitate weight calculation in all those pregnancies remote from term for which exact pregnancy dating is not available.