Mosteller formula

The square root applies to the entire height-times-weight quantity after division by 3,600. This calculator converts inches to centimeters by multiplying by exactly 2.54 and pounds to kilograms by multiplying by 0.45359237. It retains full internal precision and rounds only displayed results.

An equivalent form uses height in meters: √[(height in meters × weight in kg) ÷ 36]. Mixing 3,600 with meters or 36 with centimeters creates a tenfold error inside the square root and a major error in BSA.

Worked 170 cm and 70 kg example

The default U.S. entries convert to essentially 170.00 centimeters and 70.00 kilograms. Multiplying gives 11,900 cm·kg. Dividing by 3,600 gives 3.305555…. Taking the square root gives 1.818118…, displayed as 1.818 m² or 1.82 m² when two-decimal rounding is required.

Using the same height and weight in the Du Bois equation gives approximately 1.8097 m². Mosteller is about 0.0084 m² higher, a difference of roughly 0.46% relative to Du Bois. The formulas are close for this example but are not mathematically identical.

Dividing Mosteller BSA by 70 kg gives about 0.0260 m²/kg. That descriptive ratio is not a dosing recommendation and should not be substituted for a protocol’s body-size scalar.

Why the Mosteller equation became popular

R. D. Mosteller published the simplified calculation in a 1987 New England Journal of Medicine letter. Its square-root structure was easy to remember and practical on a pocket calculator, reducing dependence on printed nomograms.

A small usability study later found formula calculation faster than a nomogram and observed fewer serious calculation errors in its test sheets. Simplicity does not make the estimate a direct measurement, but a transparent formula can make arithmetic easier to audit.

Today, electronic health records and pharmacy systems can calculate BSA automatically. Automation still requires verification: an old weight, inches entered as centimeters, pounds entered as kilograms, a copied result from another patient, or an incorrect formula setting can silently propagate.

Where BSA appears in clinical work

BSA is not automatically superior to weight, lean body mass, kidney function, pharmacokinetic monitoring, or fixed dosing. The best size descriptor depends on the outcome and evidence. Some uses persist by convention even when individual drug clearance does not scale perfectly with surface area.

Why formulas disagree

Mosteller, Du Bois, Haycock, Gehan and George, Boyd, and other equations were developed from different samples, measurement approaches, age ranges, and mathematical forms. The Du Bois equation is 0.007184 × height(cm)0.725 × weight(kg)0.425. Haycock used different exponents after geometric measurements in infants, children, and adults.

At ordinary adult sizes, formulas often agree closely. Differences can widen at very low or high height and weight. A 2006 adult comparison found strong correlations among formulas but systematic differences, including in obesity. Correlation does not mean identical answers for an individual.

A 2016 analysis warned that many available formulas create ambiguity across body sizes. More recent three-dimensional scanning research continues to study prediction. The existence of newer equations does not authorize replacing the one named in a validated protocol.

Infants and children need extra measurement care

For a child who cannot stand, measure recumbent length according to the clinical procedure. A diaper, blanket, cast, medical equipment, movement, and an unzeroed scale can materially affect a small child’s weight. Premature infants and rapidly growing children may need very recent measurements.

Different pediatric services may prefer Mosteller, Haycock, or another formula. Haycock’s derivation included premature infants through adults and found that older Du Bois estimates increasingly underestimated surface area below 0.7 m². This calculator displays Mosteller because that is the requested method; it does not claim universal pediatric superiority.

Pediatric medication arithmetic should use institution-approved tools, independent verification when required, maximum-dose checks, concentration checks, and current weight. Never use a parent-estimated weight for a high-risk dose when a measured value is available.

Extremes of body size and changing fluid status

Edema, ascites, pregnancy, amputation, severe obesity, cachexia, dehydration, and rapid fluid shifts can make current weight a poor proxy for the physiological quantity a protocol intends. The formula will still return a mathematically valid number, but applicability and dosing weight require clinical judgment.

Some chemotherapy protocols historically capped BSA at 2.0 m², while modern recommendations may favor full weight-based dosing in certain settings. Whether a cap applies is drug-, disease-, intent-, and protocol-specific. This calculator does not impose or recommend a cap.

If actual, ideal, lean, dry, or adjusted weight is required, calculate or obtain it under the governing method and document the choice. Do not silently substitute one weight for another. Repeat weight after a clinically important change and preserve the date and scale source.

BSA is not percent total body surface area burned

Mosteller estimates the total exterior surface area in square meters from height and weight. Burn care often describes the percentage of total body surface area affected using age-adjusted charts or the Rule of Nines. Those are different quantities.

A Mosteller result of 1.82 m² does not mean an 18.2% burn, and entering a burn percentage into either height or weight is meaningless. Burn extent, depth, location, inhalation injury, age, and timing require urgent professional assessment. Fluid-resuscitation formulas have separate inputs and rules and must not be improvised from this BSA estimate.

Call emergency services for a serious burn, electrical or chemical exposure, inhalation concern, circumferential burn, significant face/hand/genital/joint involvement, or any severe symptom. Do not delay care to calculate surface area.

Rounding and audit trail

Keep height and weight at the precision justified by the measuring devices. Convert units with exact factors, calculate BSA without intermediate rounding, then round only as the receiving protocol directs. Rounding height, weight, BSA, and a later dose at every step can compound differences.

A transparent record should contain patient identifiers in the clinical system, measurement date and time, height or length, weight, original units, converted values, formula name, unrounded BSA, displayed BSA, protocol, and verifier. This public calculator should not be used to store protected health information.

If an electronic result disagrees, compare source units, formula, date, and rounding before deciding one system is wrong. Recalculate independently with an approved tool and escalate unexplained discrepancies to a pharmacist, clinician, or informatics team.

A safe calculation workflow

BSA calculation checklist

1. Confirm the correct patient.
2. Use current measured height or length.
3. Use current measured weight.
4. Record the original units.
5. Convert inches by 2.54.
6. Convert pounds by 0.45359237.
7. Multiply centimeters by kilograms.
8. Divide the full product by 3,600.
9. Take the square root last.
10. Keep unrounded internal precision.
11. Name the Mosteller formula.
12. Check whether the protocol specifies another formula.
13. Do not infer a drug dose here.
14. Document verification and date.

It does not calculate medication costs, medical deductions, insurance coverage, treatment eligibility, or body surface area.

Frequently asked questions

References

• Mosteller, Simplified calculation of body-surface area
• NCBI Bookshelf, Body Surface Area
• Comparison of BSA formulas in normal-weight, overweight, and obese adults
• Haycock et al., geometric height-weight formula in infants, children, and adults
• Body surface area formulae: an alarming ambiguity
• FDA guidance on weight- or BSA-based dose banding