Estimate body surface area from height and weight with Mosteller, Du Bois, Haycock, Gehan and George, and Boyd equations. Compare all five results in square metres, square centimetres and square feet without sending your measurements anywhere.
- Five published formulas
- Metric and US units
- Formula-by-formula steps
- No data sent by the tool
Body Surface Area Calculator
Choose a headline formula, then enter height and weight. The tool keeps each formula result separate, reports the spread, and shows the exact converted measurements used in every calculation.
Using 170 cm and 70 kg
Five-formula comparison
Selected: MostellerBar lengths compare the five equations for the same measurements. They are not a healthy-range scale.
Formula results
| Formula | BSA | Difference from selected | Substituted equation |
|---|---|---|---|
| Mosteller | 1.8181 m² | Selected formula | sqrt((170 × 70) / 3600) |
| Du Bois & Du Bois | 1.8097 m² | −0.46% | 0.007184 × 1700.725 × 700.425 |
| Haycock | 1.8257 m² | +0.42% | 0.024265 × 1700.3964 × 700.5378 |
| Gehan & George | 1.8313 m² | +0.72% | 0.0235 × 1700.42246 × 700.51456 |
| Boyd | 1.8347 m² | +0.91% | Boyd equation using 70,000 g |
Measurement and result details
| Measure | Result | Meaning |
|---|---|---|
| Converted height | 170 cm | Height used by all five formulas |
| Converted weight | 70 kg | Weight used by four formulas |
| Boyd weight | 70,000 g | Boyd uses weight in grams in its original form |
| Formula range | 1.8097 to 1.8347 m² | Lowest to highest estimate, not an error interval |
| Relative spread | 1.37% | Range divided by the five-formula average |
Calculation steps
- Use height 170 cm and weight 70 kg.
- Multiply height by weight: 170 × 70 = 11,900.
- Divide by 3,600: 11,900 ÷ 3,600 = 3.305556.
- Take the square root: √3.305556 = 1.818119 m².
- Round only the displayed result: 1.8181 m².
Recent calculations
Results stay in this page session. Nothing is sent by this calculator.
How to Use This Body Surface Area Calculator
- Select the formula you want as the headline result. Mosteller is the default because its square-root form is easy to audit.
- Choose metric or US units. In metric mode, enter centimetres and kilograms. In US mode, enter feet, additional inches and pounds.
- Select “Calculate Body Surface Area.” The tool converts the measurements with exact unit factors before applying every formula.
- Review the selected result in square metres, square centimetres and square feet. Compare it with the other four estimates.
- Read the formula spread and substituted steps. If a clinical form or protocol names one equation, use that equation rather than an average.
Measure height or recumbent length and weight as accurately as the situation allows. Do not enter 5.10 for 5 feet 10 inches. Use 5 in the feet field and 10 in the inches field. The calculator keeps full precision internally and rounds only the values displayed on the page.
What Is Body Surface Area?
Body surface area, shortened to BSA, is an estimate of the total external area of a person’s body. It is expressed as an area, usually square metres, because the result represents a two-dimensional surface rather than body mass or volume. Directly measuring every contour of the skin is difficult, so published equations estimate BSA from measurements that are easier to collect.
BSA appears in clinical research and healthcare because some physiological measurements scale with body size. It is used to index values such as cardiac output and appears in some medicine protocols and renal or metabolic comparisons. Those uses require professional context. A calculator result alone does not determine treatment, dose, diagnosis or risk.
Body Surface Area Formulas Compared
All five formulas on this page return square metres when height is in centimetres and weight is in kilograms, except the original Boyd form, which uses weight in grams. The equations use different coefficients and exponents because they were developed from different samples and measurement methods.
| Formula | Equation | Practical note |
|---|---|---|
| Mosteller | BSA = √[(height cm × weight kg) ÷ 3600] | Simple square-root equation and a useful transparent default. |
| Du Bois & Du Bois | BSA = 0.007184 × height0.725 × weight0.425 | Historic 1916 equation that remains widely referenced. |
| Haycock | BSA = 0.024265 × height0.3964 × weight0.5378 | Published as validated across infants, children and adults. |
| Gehan & George | BSA = 0.0235 × height0.42246 × weight0.51456 | Derived from height and weight data across a broad size range. |
| Boyd | BSA = 0.0003207 × height0.3 × weight g(0.7285 − 0.0188 log10 weight g) | Uses grams and a weight-dependent exponent, so unit handling matters. |
Mosteller formula
The Mosteller equation is the default headline method on this page. It multiplies height in centimetres by weight in kilograms, divides by 3,600 and takes the square root.
Its main advantage is transparency. You can reproduce the calculation with a basic square-root function. Simplicity does not make it the mandatory formula for every use. A hospital, study or clinical protocol may specify another equation.
Du Bois and Du Bois formula
The Du Bois equation was published in 1916 and became a long-standing reference. It raises height and weight to fixed powers. Later work has revisited its performance because the original development sample was small and modern populations include body sizes that were poorly represented at the time.
Haycock formula
Haycock, Schwartz and Wisotsky developed their geometric equation using subjects ranging from infants to adults. This makes it an important comparison when paediatric measurements are involved. It still remains an estimate, and paediatric care must follow the formula and rounding policy chosen by the treating service.
Gehan and George formula
Gehan and George published another power equation based on height and weight. For many ordinary adult inputs, its answer sits close to the Mosteller result. Agreement at one size does not mean the equations remain identical across all heights and weights.
Boyd formula
The Boyd equation is the easiest one to enter incorrectly because its original form expects grams rather than kilograms and changes the weight exponent through a base-10 logarithm. This calculator converts kilograms to grams before applying it. It shows the gram value in the result details so you can audit the input.
Worked Body Surface Area Example
Suppose a person is 170 cm tall and weighs 70 kg. Using the Mosteller formula:
- Multiply height and weight: 170 × 70 = 11,900.
- Divide by 3,600: 11,900 ÷ 3,600 = 3.3055556.
- Take the square root: √3.3055556 = 1.818119.
- Display the estimate as 1.8181 m², or about 18,181 cm² and 19.570 ft².
The other formulas give nearby but non-identical values. The comparison is useful because it exposes the equation choice instead of presenting one estimate as a directly measured fact.
Why BSA Formulas Give Different Results
A formula fits a mathematical relationship to measurements from a particular group. Sample size, age range, body proportions, measurement technique and statistical method all affect its coefficients. The formulas also respond differently as height and weight move toward unusual combinations.
The calculator reports two comparison figures:
- Formula range is the lowest through highest result among the five equations.
- Relative spread is the high-low difference divided by the average of all five results, expressed as a percentage.
This spread is not a confidence interval or measurement-error estimate. It shows only how much these five equations disagree for the entered height and weight. When the result affects care, the named protocol and professional judgement matter more than choosing the middle value.
BSA Compared with BMI and Body Weight
| Measure | Uses | Does not show |
|---|---|---|
| Body surface area | Estimated external area from height and weight; indexing some physiological values. | Body-fat percentage, skin condition, burn percentage or treatment need. |
| Body mass index | Adult weight-for-height screening and population comparisons. | Direct body composition, muscle distribution or individual diagnosis. |
| Body weight | Total mass measured on a scale. | Height-adjusted size, tissue composition or external area. |
Two people can share the same BMI but have different BSA values because their absolute heights and weights differ. BSA and BMI answer different mathematical questions, so one should not be treated as a substitute for the other.
Adults, Children and Infants
This calculator accepts a broad technical range so it can demonstrate formulas across adult, child and infant measurements. It does not ask for age or sex because none of the five displayed equations includes those variables. That does not mean age and population are irrelevant. It means the mathematical inputs are limited to height and weight.
For an infant, clinicians may use recumbent length rather than standing height. Small errors become more important when the measurements are small. Use a calibrated paediatric scale and an appropriate length board when accuracy matters. Haycock’s paper explicitly included infants, children and adults, but the correct clinical equation still depends on the applicable service, guideline and purpose.
Do not use this educational calculator to choose or verify a paediatric medicine dose. Dosing requires the correct medicine, indication, route, concentration, maximum limit, organ function, current measurements and an authorised protocol.
Clinical Uses and Safety Limits
Indexing physiological measurements
Some clinical values are divided by BSA to compare a measurement with body size. Cardiac index, for example, relates cardiac output to body surface area. A commonly used historical reference area of 1.73 m² also appears in some normalised kidney measurements. That reference is a convention for indexing, not an ideal BSA for an individual.
Medication protocols
Some medicines and treatment protocols refer to an amount per square metre. The BSA number is only one part of that process. Formula selection, dose caps, rounding, laboratory results, organ function, prior treatment and protocol-specific adjustments can change the final order. This page intentionally does not multiply BSA by a medicine amount.
Burn area is a different measure
Total body surface area burned, often written as TBSA%, describes the percentage of the body affected by burns. It is assessed with burn-specific methods such as age-adjusted charts and clinical examination. A height-and-weight BSA equation does not locate a burn, grade its depth or calculate resuscitation fluid. Seek emergency care for serious burns.
Extremes of height or weight
Equation differences may grow at unusual combinations of height and weight. Research comparing formulas has reported close overall agreement in many groups while also finding systematic differences at some extremes. Check the measurements, inspect the five-formula spread and follow the equation specified for the intended use.
How to Improve Measurement Quality
- Measure standing height without shoes when standing measurement is appropriate.
- Use recumbent length and paediatric equipment for infants when trained to do so.
- Place a scale on a firm, level surface and check its calibration.
- Use a recent weight if the result is being discussed with a health professional.
- Enter the full precision you have. Let the calculator round the output.
- Confirm the unit system before calculating, especially grams versus kilograms in the Boyd formula.
Common BSA Calculator Mistakes
- Entering metres in a field that expects centimetres.
- Entering pounds in the kilogram field or kilograms in the pound field.
- Typing 5.10 feet to mean 5 feet 10 inches.
- Applying the Boyd gram formula directly to kilograms.
- Rounding height and weight before exponent or square-root calculations.
- Averaging formulas when a specific protocol names one formula.
- Treating 1.73 m² as a universal healthy target.
- Using BSA as a medicine-dose calculator or a burn-percentage assessment.
Calculation Method and Review Sources
The Mosteller equation was checked against the original 1987 publication indexed by PubMed. The historic Du Bois equation was checked against the 1916 paper record. The Haycock population scope and formula were reviewed against the Journal of Pediatrics record, while Gehan and George were checked against their 1970 publication record.
The formula-comparison limits were reviewed against peer-reviewed discussions of differences between common BSA equations and a nine-formula evaluation. General uses and cautions were cross-checked with the NCBI Bookshelf overview of body surface area. Unit conversion uses exactly 2.54 cm per inch and 0.45359237 kg per pound.
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Frequently Asked Questions
What is body surface area?
Body surface area is an estimate of the total external area of a person's body. It is usually reported in square metres and estimated from height and weight because direct skin-area measurement is difficult.
How do I calculate BSA with the Mosteller formula?
Multiply height in centimetres by weight in kilograms, divide by 3,600 and take the square root. For 170 cm and 70 kg, the result is about 1.8181 square metres.
Which BSA formula is most accurate?
No one equation is best for every population and purpose. Mosteller is simple, while Du Bois, Haycock, Gehan and George, and Boyd use different fitted relationships. Use the formula named by the relevant professional protocol.
Why does the calculator not ask for age or sex?
The five equations on this page use height and weight only. Age, sex, body shape and population still affect interpretation, but they are not variables in these formulas.
Can this BSA calculator be used for children and infants?
It can compare mathematical estimates across a broad size range, and the Haycock equation was validated in infants, children and adults. Do not use this educational result to calculate paediatric medicine doses or replace clinical measurement.
Is body surface area the same as BMI?
No. BSA estimates external area in square metres. BMI divides weight by height squared for weight-status screening. Two people with the same BMI can have different BSA values.
Can I use this result to calculate a medication dose?
No. Medication dosing requires an authorised protocol, the correct formula, current clinical information, dose limits and professional verification. This calculator intentionally does not provide medicine-dose calculations.
Is BSA the same as total body surface area burned?
No. BSA estimates total external body area from height and weight. TBSA% estimates the percentage affected by burns using burn-specific assessment methods. This tool does not assess burns or fluid needs.
Why do the five formulas give different results?
They were built from different samples, measurements and statistical models. Their exponents respond differently to changes in height and weight, so disagreement can increase for some body sizes.
Why is BSA measured in square metres?
BSA represents area rather than mass or length. Square metres are the conventional clinical unit, while this calculator also converts the selected result to square centimetres and square feet.
Health and Calculation Disclaimer
This calculator provides educational body surface area estimates only. It does not directly measure skin area, diagnose a condition, assess burns or determine medication, chemotherapy or fluid doses. Use the formula, measurements, rounding rules and limits required by the responsible clinician or protocol.