Hadlock refers to a set of mathematical formulas, developed by radiologist Frank P. Hadlock in the 1980s and early 1990s, that use ultrasound measurements of a baby’s body to estimate fetal weight, gestational age, and growth percentile. When your provider mentions “Hadlock” or your ultrasound report lists it, it means the machine is using one of these specific equations to translate raw measurements of your baby’s head, belly, and thigh bone into a weight estimate or a position on a growth chart. Despite being decades old, the Hadlock formulas remain the most widely used fetal assessment tools in the United States and much of the world, though the science around them is more nuanced than most patients realize.
What the Formulas Actually Measure
During a routine prenatal ultrasound, the sonographer captures several standardized measurements of your baby. The ones that feed into Hadlock calculations are the biparietal diameter (the width of the skull from one side to the other), the head circumference, the abdominal circumference (measured around the baby’s belly at the level of the liver), and the femur length (the thigh bone).1Scientific Reports. New reference values for ultrasound fetal biometry in Japanese population and comparison with other studies These four numbers are the raw ingredients. Hadlock published several variations of his formula, each using a different combination of these measurements. Some use all four; others use three or even two.
The reason multiple versions exist is practical. Sometimes the sonographer cannot get a clean image of the baby’s head because of its position in the uterus. In those cases, a formula that relies on the abdomen and femur instead can still produce a reasonable estimate. A multicenter study of preterm babies with abnormal blood-flow patterns found that the Hadlock formulas using either four or three measurements performed best among eleven tested weight-estimation equations.2PubMed Central. Analysis of the Performance of 11 Formulae for Fetal Weight Estimation in Preterm Fetuses with Abnormal Doppler Velocimetry – A Retrospective Multicenter Study Another study found that the Hadlock formula combining head circumference, abdominal circumference, and femur length had the lowest random error across all weight groups, at about 7.7%.3PubMed Central. Estimating fetal weight for best clinical outcome
Estimated Fetal Weight and What the Number Means
The most common reason you will see “Hadlock” on a report is in the context of estimated fetal weight. The formula takes your baby’s measurements and plugs them into a regression equation that converts centimeters into grams. That estimated weight is then compared against a reference chart to produce a percentile, telling you where your baby falls relative to other babies at the same gestational age.
A percentile of 50 means the estimated weight sits right at the median. A percentile below the 10th raises the possibility of fetal growth restriction, while one above the 90th may flag macrosomia (a larger-than-average baby). These thresholds matter because they can change how your pregnancy is managed. In a study comparing the Hadlock growth standard to the INTERGROWTH-21st standard near term, Hadlock percentiles were better at picking up both small-for-gestational-age and large-for-gestational-age babies, with sensitivities of about 59% and 71% respectively when screening was set at 90% specificity.4PubMed. Comparison of estimated fetal weight percentiles near term for predicting extremes of birthweight percentile
Keep in mind that the estimated weight is just that: an estimate. The average error across all weight ranges is small, roughly 2% to 3%, but the spread around that average can be significant.5PubMed Central. Percent error of ultrasound examination to estimate fetal weight at term in different categories of birth weight with focus on maternal diabetes and obesity A weight estimate is a best guess from a two-dimensional image of a three-dimensional baby who is constantly moving.
How Accurate Is It, Really?
The accuracy of any Hadlock formula depends on several factors, and the picture is more honest than the clean numbers on a report might suggest. One large study looking at term pregnancies found that the overall average error was about 2.4%, but the range was wide. For babies in the mid-range (around 3,000 to 3,250 grams), the estimates were tightest. The further a baby’s weight deviated from average in either direction, the larger the error. Very small babies tended to have their weight overestimated by about 5%, while very large babies were underestimated by roughly 12%.6PubMed Central. Percent error of ultrasound examination to estimate fetal weight at term in different categories of birth weight with focus on maternal diabetes and obesity That asymmetry matters because the clinical decisions at stake are biggest for babies at those extremes.
Whether the formula includes head circumference also affects accuracy. When researchers compared Hadlock formulas with and without head circumference, the version that included it (known as Hadlock I, or H1) had a lower average error of about 1.9%, while the version without it (H2) came in at about 3.2%. The version with head circumference also predicted actual birth weight within 15% more often: roughly 93% of the time versus 90%.7PubMed. Estimation of fetal weight using Hadlock’s formulas: Is head circumference an essential parameter? That difference sounds small, but for the individual baby who falls in that gap, it can mean the difference between a flagged scan and a reassuring one.
At very early gestational ages, accuracy drops further. Among infants born in the periviable period (roughly 23 to 26 weeks), one study found the average error rose to about 10%, and only half of estimates landed within 10% of the actual birth weight. About 16% of estimates were off by more than 20%.8PubMed. The accuracy of sonographic fetal weight in very preterm infants (≤32 weeks) At these gestational ages, even small absolute errors in grams translate into large percentage errors, and the clinical stakes for delivery decisions are extremely high.
Hadlock for Gestational Age Dating
Beyond weight, Hadlock formulas can also estimate how far along a pregnancy is based on the baby’s measurements. This is most relevant in the second and third trimesters, when the earlier and more precise method of dating (first-trimester crown-rump length) is no longer available or was not performed. Hadlock published a gestational-age formula in 1984 that remained widely used for decades. More recent work has refined this approach. A newer formula developed from a large international dataset estimated gestational age within about seven days in the second trimester and within about 17 days in the third trimester, outperforming the original Hadlock formula, which had errors of about 11 and 20 days in the same windows.9PubMed Central. Estimating Gestational Age From Ultrasound Fetal Biometrics
Independent work from China similarly found that population-specific formulas outperformed the Hadlock equation for gestational age determination in the second and third trimesters.10Clinical and Experimental Obstetrics & Gynecology. Gestational age estimation from ultrasound fetal biometrics in China A validation study in a U.S. population reached a similar conclusion, finding that a newer formula produced smaller average errors than the Hadlock regression across all gestational-age ranges tested.11PubMed. Estimating Gestational Age from Ultrasound: External Validation of the NICHD Formula with Comparison to the Hadlock Regression This does not mean the Hadlock gestational-age formula is unreliable, but it does mean your provider may be using an updated version, and either way, later-trimester dating is inherently less precise than first-trimester dating.
Why Your Baby’s Head Shape Matters
One of the measurements in the Hadlock formula, the biparietal diameter, assumes a roughly oval skull shape. But babies’ heads vary. Some are more elongated (dolichocephalic) and others more round (brachycephalic). When the skull shape falls outside the normal range, the biparietal diameter can over- or underestimate the true head size for a given gestational age. Research has shown that a cephalic index more than one standard deviation from the mean may significantly alter what the biparietal diameter suggests about gestational age, and in those cases, head circumference is a more reliable substitute.12PubMed. Estimating fetal age: effect of head shape on BPD This is one reason experienced sonographers check both head width and head circumference rather than relying on a single number. If the baby is in a breech position, the head can be compressed into an elongated shape, making the biparietal diameter artificially narrow and throwing off weight or age estimates that depend on it.
Population Differences and the Ethnicity Question
The Hadlock formulas were originally developed using data from a predominantly white, middle-class American population. A legitimate question is whether they apply equally to babies of different ethnic backgrounds, body sizes, and nutritional environments. The answer is complicated and actively debated.
Data from India, for example, found that while femur length and biparietal diameter tracked the Hadlock curves reasonably well, head circumference and abdominal circumference for Indian fetuses tended to fall in the lower ranges of the Western-derived charts.13PubMed Central. Fetal ultrasound parameters: Reference values for a local perspective That does not necessarily mean those babies are growth-restricted; it may reflect normal variation. Japan uses its own Shinozuka formula for similar reasons.14Scientific Reports. New reference values for ultrasound fetal biometry in Japanese population and comparison with other studies
A study in the United Kingdom illustrated the stakes clearly. When the Hadlock standard was applied, South Asian babies were classified as small-for-gestational-age at more than double the rate of British European babies (about 26% versus 12%). Using a customized standard that adjusts for maternal ethnicity and body size, those rates converged to roughly 14% for both groups.15PubMed. Stillbirth risk and smallness for gestational age according to Hadlock, INTERGROWTH-21st, WHO, and GROW fetal weight standards The implication is that a universal chart can over-diagnose growth problems in some populations and potentially miss them in others.
And yet, when tested head-to-head against race-specific growth standards for predicting actual neonatal illness, the Hadlock standard outperformed or matched them. A U.S. study found that Hadlock had a higher sensitivity for detecting small-for-gestational-age babies and a smaller discrepancy between ultrasound percentile and birth-weight percentile compared to the NICHD race- and ethnicity-specific standard.16PubMed. Comparing the Hadlock fetal growth standard to the Eunice Kennedy Shriver National Institute of Child Health and Human Development racial/ethnic standard for the prediction of neonatal morbidity and small for gestational age Similarly, a study comparing race-customized charts to Hadlock for detecting fetal growth restriction found that Hadlock actually caught more cases of growth restriction among babies born to Black individuals than the race-adjusted standard did.17PubMed Central. Impact of race-based customization on detection of fetal growth restriction The worry is that customizing thresholds for ethnicity might normalize small size that is actually pathologic, effectively lowering the bar and letting some at-risk babies slip through. This remains one of the most active debates in obstetric research.
The Hadlock 1991 Growth Chart and a Hidden Discrepancy
If you have ever seen your baby’s weight plotted on a growth curve, there is a good chance it was the Hadlock 1991 reference. This is the most widely used population reference standard for fetal growth assessment in the United States. But a 2025 study uncovered something surprising: the table of values published in the original 1991 paper does not match the mathematical equation in the same paper.18American Journal of Obstetrics & Gynecology. Discrepancies in the Hadlock 1991 fetal weight standard and their clinical implications The table, which many software systems use to look up percentile values, tends to underdiagnose growth restriction compared to the equation itself. In practical terms, if your provider’s ultrasound machine uses the table version rather than the equation, some babies who should be flagged as potentially growth-restricted might not be. The researchers suggested that clinicians who want higher detection rates for growth restriction should use the equation directly rather than interpolating from the table. Whether this discrepancy has led to real missed diagnoses at scale is not yet established, but the fact that it went unnoticed for over three decades illustrates how deeply embedded these formulas are in clinical practice and how rarely their foundations are re-examined.
Amniotic Fluid, Maternal Size, and Other Complicating Factors
Patients often wonder whether their own body size affects the accuracy of the ultrasound estimate. A study that specifically examined this question found that maternal body mass index did not significantly affect the accuracy of sonographic weight estimation using Hadlock formulas.19PubMed. Effect of Maternal Body Mass Index and Amniotic Fluid Index on the Accuracy of Sonographic Estimation of Fetal Weight in Late Gestation The image quality might be worse in women with higher BMI, making it harder for the sonographer to get precise measurements, but once those measurements are obtained, the formula itself is not inherently biased by maternal size.
Amniotic fluid volume, on the other hand, does matter. The same study found that low amniotic fluid (oligohydramnios) was associated with nearly 80% higher odds of a substantial estimation error, and the direction of that error was systematic: low fluid tended to make the estimate too high, while excess fluid tended to make it too low.20PubMed. Effect of Maternal Body Mass Index and Amniotic Fluid Index on the Accuracy of Sonographic Estimation of Fetal Weight in Late Gestation If your provider notes abnormal fluid levels alongside a weight estimate, it is worth understanding that the weight number may be less reliable than usual.
How the Estimate Affects Your Care
A fetal weight estimate is not just a number on a printout. It can directly change the decisions made about your delivery. When a baby is estimated to weigh 4,000 grams or more (about 8 pounds 13 ounces), the chance of being diagnosed with labor abnormalities and the likelihood of cesarean delivery both increase, even when the baby turns out to weigh less than that after birth. Research has shown that the simple act of performing a late-pregnancy weight estimate is itself an independent risk factor for cesarean delivery, and when the estimate crosses 4,000 grams, cesarean rates rise by up to 2.5 times regardless of actual birth weight.21PubMed Central. Disadvantages of a weight estimation formula for macrosomic fetuses: the Hart formula from a clinical perspective This creates a real tension: providers need to identify genuinely large babies to manage shoulder dystocia risk and other complications, but overestimation can push patients toward interventions they may not have needed.
On the other end of the spectrum, a baby flagged as small-for-gestational-age may prompt increased surveillance, possible induction of labor, or both. The accuracy of the Hadlock percentile in identifying babies who will actually be small at birth is good but far from perfect, so there will always be cases where a baby is flagged but turns out to be normally grown, and cases where a truly small baby is missed.
Hadlock in Twin Pregnancies
If you are carrying twins, your provider is probably still using a Hadlock formula for weight estimates, but with some additional considerations. A study of twin pregnancies found that the Hadlock formulas incorporating abdominal circumference, head circumference, and femur length were the most accurate, with median percentage errors under 1%. The Hadlock formulas tended to overestimate rather than underestimate birth weight in twins, which is the safer direction for error when the concern is detecting growth restriction.22PubMed Central. Accuracy of ultrasound estimation of fetal weight in twin pregnancy For detecting size discordance between twins (where one is significantly smaller than the other), the Hadlock 2 formula had strong predictive accuracy.23PubMed. Ultrasound estimation of birth weight in twin pregnancy: comparison of biometry algorithms in the STORK multiple pregnancy cohort
When a Baby Has a Structural Abnormality
Abdominal wall defects such as omphalocele or gastroschisis complicate weight estimation because the baby’s organs are partially outside the body, distorting the abdominal circumference measurement that Hadlock formulas rely on. Even so, in a comparison of formulas for babies with these conditions, the Hadlock formula still had the highest precision, with a random error of about 11%, and was most accurate at predicting intrauterine growth restriction, catching 91% of cases.24PubMed. Estimation of fetal weight in fetuses with abdominal wall defects: comparison of 2 recent sonographic formulas to the Hadlock formula The error is larger than in babies without anomalies, but the formula still outperformed newer alternatives designed specifically for this situation.
AI-Assisted Ultrasound and the Future of Fetal Measurement
One of the biggest sources of variability in Hadlock-based estimates is not the formula itself but the human doing the measuring. Getting the right cross-section of the baby’s head, placing calipers at exactly the right landmarks, and capturing the abdomen at the correct anatomical level all require training and attention. Recent work has applied deep learning to automate these measurements. A study published in Nature Communications demonstrated an end-to-end system that automatically identifies the correct ultrasound frames and measures biparietal diameter, head circumference, abdominal circumference, and femur length, then feeds those measurements into the Hadlock formula.25Nature Communications. Fetal biometry and amniotic fluid volume assessment end-to-end automation using Deep Learning The promise is not a new formula but more consistent inputs into the existing one. If the measurements themselves become more reproducible, the estimates that flow from them should become more reliable without needing to change the underlying math.