log10(g) = 1.3596 − 0.00386·AC·FL + 0.0064·HC + 0.00061·BPD·AC + 0.0424·AC + 0.174·FL
2959 g
6 lb 8.4 oz
log10(g) = 3.47111
How it works
Estimated fetal weight is a regression from ultrasound lengths, not a scale reading. This page applies the four equations in Table II of Hadlock and colleagues, American Journal of Obstetrics and Gynecology, 1985. Lengths are centimeters. The output is grams, then the nearest gram converted to pounds and ounces. The four-parameter equation, using biparietal diameter, head circumference, abdominal circumference, and femur length, is the one shown first. The other three run only from the measurements they need. There is no gestational-age percentile and no “normal for this week” band.
Each equation produces log10 of the weight in grams. The weight is 10 raised to that power. With BPD, HC, AC, and FL all in centimeters: log10(g) = 1.3596 − 0.00386·AC·FL + 0.0064·HC + 0.00061·BPD·AC + 0.0424·AC + 0.174·FL. Head circumference, abdominal circumference, and femur length: log10(g) = 1.326 − 0.00326·AC·FL + 0.0107·HC + 0.0438·AC + 0.158·FL. Biparietal diameter, abdominal circumference, and femur length: log10(g) = 1.335 − 0.0034·AC·FL + 0.0316·BPD + 0.0457·AC + 0.1623·FL. Abdominal circumference and femur length: log10(g) = 1.304 + 0.05281·AC + 0.1938·FL − 0.004·AC·FL. A millimeter entry is divided by 10 before these equations see it.
One sample, term by term
Take BPD 9.0 cm, HC 32.0 cm, AC 33.0 cm, and FL 7.0 cm. Then AC·FL = 231 and BPD·AC = 297. The four-parameter log is 1.3596 − 0.00386×231 + 0.0064×32 + 0.00061×297 + 0.0424×33 + 0.174×7. That is 1.3596 − 0.89166 + 0.2048 + 0.18117 + 1.3992 + 1.218 = 3.47111. Ten to that power is 2958.76 g, which rounds to 2959 g. The same gram count is 6 lb 8.4 oz: divide 2959 by 28.349523125 g per ounce, keep whole pounds, and round the leftover ounces to one decimal. Sixteen ounces would carry into the next pound. They do not here.
The same lengths give 2929 g from HC+AC+FL, 3007 g from BPD+AC+FL, and 3015 g from AC+FL. The spread is about 86 g, under 3 percent of 2959 g. Hadlock’s 1985 prospective check reported about 7.5 percent as one standard deviation for the better head, body, and femur models. A reported standard deviation is not a promise for the next scan. A 2 mm error in abdominal circumference moves the product terms, not just the linear ones, so the gram count moves by more than a casual look at the equation suggests.
What was removed, and what this is not
An earlier version of this page mixed a Shepard-style equation with Hadlock coefficients that put biparietal diameter in the head-circumference slot and dropped the BPD×AC term. Those expressions are not the 1985 table, so they are gone. Shepard 1982 is a different paper and is not calculated here. Gestational-week “normal ranges” that were not tied to a published chart are gone as well. If you need a percentile, use the chart your clinic actually uses.
Ultrasound reports often print millimeters. Nine centimeters typed as 90 in the centimeter fields produces a weight that is not a plausible third-trimester fetus. Switch the unit to mm, or divide by 10 yourself. The page warns when a centimeter value sits outside a broad late-pregnancy span (BPD 4–11, HC 15–40, AC 15–40, FL 3–9). That warning is a unit check, not a diagnosis of growth restriction or macrosomia.
Notice
This is arithmetic from a 1985 regression, not a medical device, not a diagnosis, and not a substitute for the ultrasound report or the obstetrician who ordered it. Measurement error of a few millimeters changes the gram count. Do not use this page to decide on induction, mode of delivery, admission, or medication. If the scan worries you, call the clinician who has the images.
Worked examples
Input: BPD 9.0 cm, HC 32.0 cm, AC 33.0 cm, FL 7.0 cm
Output: Four-parameter log10 = 3.47111, 2959 g, 6 lb 8.4 oz
Input: The same lengths, HC+AC+FL only
Output: 2929 g
Input: The same lengths entered as millimeters: 90, 320, 330, 70
Output: The same 2959 g, because each value is divided by 10 before the equation
Limits
- Pounds and ounces are computed from the gram count after it is rounded to the nearest gram. The unrounded four-parameter result is 2958.76 g.
- One ounce is 28.349523125 g, from the international pound of 0.45359237 kg.
- The equations were fit on a particular sample. They do not know presentation, oligohydramnios, or whether the calipers were placed on the outer bone.
Common mistakes
- Entering millimeters into the centimeter fields. 90 cm is not a biparietal diameter.
- Averaging the four equations and treating the average as a fifth Hadlock model. The page shows each equation. The four-parameter result is the headline number.
- Using the gram count to choose a route of delivery. The paper’s own scatter is wider than the gap between 2959 g and 3007 g.
Questions
Why do the four equations disagree?▾
Is 7.5 percent the error I should quote?▾
Can I leave head circumference blank?▾
Sources
- Hadlock FP, Harrist RB, Sharman RS, Deter RL, Park SK. Estimation of fetal weight with the use of head, body, and femur measurements—a prospective study. Am J Obstet Gynecol. 1985;151(3):333-337. Table II supplies the four equations used here. The abstract reports about 1 SD = 7.5% for the better models in that series.
- LOINC 11732-5 records the same four-parameter equation: log10(g) = 1.3596 − 0.00386·AC·FL + 0.0064·HC + 0.00061·BPD·AC + 0.174·FL + 0.0424·AC, with lengths in centimeters.