Body Surface Area Formula Explained with Examples

Open any oncology protocol or paediatric drug chart and you will see doses written as mg per m2. The m2 comes from a body surface area formula. But there is not one formula; there are several, and each was built from a different group of people.

This guide explains the main formulas in plain words, shows the maths, and works through Indian examples in cm and kg. By the end you will know why Mosteller is so popular, when DuBois or Haycock may be used, and how little the answers differ for most people.

You can test each formula yourself with the body surface area calculator. As always, this is educational content. It is not medical advice, and doses must be decided by a qualified doctor.

Why Are There Several BSA Formulas?

Nobody can easily measure the full skin area of a living person. Early researchers did it the hard way, by coating bodies in paper or wax moulds and measuring the area. They then looked for a pattern linking surface area to height and weight.

DuBois and DuBois did this in 1916 with only nine subjects, and it is still widely quoted. Later studies used larger groups and better methods, giving us Haycock in 1978 for children and Gehan and George in 1970 from cancer patients. Mosteller came in 1987 as a simple shortcut that gave nearly the same answers.

Because each group of subjects was different, each formula has a slightly different shape. None of the original samples were mainly Indian, so all are approximations when used for Indian patients. That is one reason hospitals choose one formula and use it consistently.

The Mosteller Formula

Mosteller is the easiest to remember. In words: multiply height in cm by weight in kg, divide by 3600, then take the square root. In short form, BSA equals sqrt((H times W) divided by 3600).

It needs only one square root, so you can do it on a basic phone calculator. Many calculators, electronic records and Indian hospital worksheets default to it. Its main strength is simplicity, and its accuracy is close to the more complex formulas for typical body sizes.

The DuBois and DuBois Formula

DuBois is the oldest. It reads: BSA equals 0.007184 times weight to the power 0.425 times height to the power 0.725, with weight in kg and height in cm. Powers like 0.425 need a scientific calculator or a spreadsheet.

DuBois is still used in many textbooks, cardiac studies and older protocols. For an average adult it gives almost the same answer as Mosteller. Its sample was tiny, so researchers often treat it as a historical standard more than a perfect one.

The Haycock Formula

Haycock was built with children in mind, from newborns to adults. It reads: BSA equals 0.024265 times weight to the power 0.5378 times height to the power 0.3964. The powers differ from DuBois because growth in a child follows a different pattern.

Paediatric teams often favour Haycock for infants and small children. If you see a child dose worked out in a paediatric ward, this formula may be behind it, although Mosteller is also common there.

The Gehan and George Formula

Gehan and George used a larger sample of children and adults, many of them patients. The formula is: BSA equals 0.0235 times weight to the power 0.51456 times height to the power 0.42246. It was developed for paediatric oncology dosing.

Today it appears in some research papers and pharmacy tools. Like the others, it gives close results for ordinary body sizes. Here is a summary of all four.

Formula	Year	Expression (W in kg, H in cm)	Typical use
Mosteller	1987	sqrt(H times W divided by 3600)	General, adults and children
DuBois	1916	0.007184 times W^0.425 times H^0.725	Textbooks, older protocols
Haycock	1978	0.024265 times W^0.5378 times H^0.3964	Infants and children
Gehan and George	1970	0.0235 times W^0.51456 times H^0.42246	Paediatric oncology research

Expert insight: For a person of average build, the four formulas usually land within a few hundredths of a square metre of each other. What matters most in practice is that one hospital or one protocol uses the same formula every time.

Worked Example 1: An Adult in Hyderabad

Suresh is 170 cm tall and weighs 70 kg. Let us compare Mosteller and DuBois.

Mosteller: 170 times 70 is 11,900. Divided by 3600 gives 3.3056. The square root is 1.818, so BSA is 1.82 m2.

DuBois: 70 to the power 0.425 is about 6.08, and 170 to the power 0.725 is about 41.4. Multiply 0.007184 by 6.08 by 41.4 and you get about 1.81 m2. The two answers differ by just 0.01.

Haycock gives about 1.83 and Gehan-George also about 1.83. All four sit between 1.81 and 1.83 m2, a spread of about one per cent.

Worked Example 2: A Slim Woman in Guwahati

Rina is 150 cm tall and weighs 45 kg. This is a small build, common among Indian women, so it is a useful test.

Mosteller: 150 times 45 is 6,750. Divided by 3600 gives 1.875. The square root is 1.369, so BSA is 1.37 m2.

DuBois: 45 to the power 0.425 is about 5.04, and 150 to the power 0.725 is about 37.7. Then 0.007184 times 5.04 times 37.7 gives about 1.37 m2. Here both formulas match to two decimals.

Worked Example 3: A Young Child in Jaipur

Meera is three years old, 100 cm tall and weighs 15 kg. Children are where the formulas can split a little more.

Mosteller: 100 times 15 is 1,500. Divided by 3600 gives 0.4167. The square root is 0.6455, so BSA is 0.65 m2.

Haycock gives about 0.65 m2 and DuBois gives about 0.64 m2. If a drug is dosed at 100 mg per m2, then 0.65 gives 65 mg and 0.64 gives 64 mg, a gap of only 1 mg. For very strong drugs even that small gap is checked carefully, which is why protocols name one formula.

Which Formula Is Used in India?

There is no single national rule that every hospital follows. Large cancer centres and government hospitals usually follow their own treatment protocols, and these name the formula or the software they use. Mosteller is very common in electronic worksheets and mobile tools because it is simple. DuBois still appears in older charts and textbooks.

For a patient, the practical point is simple. If a hospital worked out your BSA, ask which formula it used before comparing your number with another source. Two correct numbers from two formulas can differ in the second decimal place and still both be right. I have not cited any specific hospital policy here, because protocols change and should be confirmed with the treating team.

Benefits of Knowing the Formulas

• Clarity: You can see why two sources show slightly different BSA values.
• Cross-checking: A quick Mosteller calculation can catch a typing error in a chart.
• Learning value: Students of nursing, pharmacy and medicine use these formulas in exams.
• Confidence: Families can ask better questions during treatment.

Challenges and Limitations

Every formula rests on old samples that were small and not Indian. Studies in other countries have found that the formulas can over or under-estimate surface area at the extremes of height and weight. For Indian adults of small stature, the differences are usually modest, but they are not zero.

Another limit is that none of the formulas account for body composition. Two people with the same height and weight get the same BSA, even if one has much more muscle and the other more fat. Clinical teams know this and treat BSA as a guide inside a wider plan.

Finally, powers such as 0.725 are hard to compute by hand. This is why a tool or spreadsheet is the safer way to run DuBois, Haycock or Gehan-George, while Mosteller can be done on any phone.

Common Mistakes to Avoid

• Mixing units: All four formulas here expect cm and kg. Feet, inches or pounds give wrong values.
• Mixing formulas: Do not compare one hospital’s Mosteller value with another’s DuBois value and call it an error.
• Dropping a power: Writing weight to the power 0.425 as weight times 0.425 gives nonsense.
• Rounding early: Round only at the very end of the calculation.
• Copying constants wrongly: A mistyped 0.007184 will shift every answer. Check each digit.
• Treating BSA as a diagnosis: It is a size measure, not a health score.

Best Practices

• Pick one formula and keep to it for the same purpose.
• Use a tool or spreadsheet for the formulas with powers.
• Keep height and weight current, since both feed directly into the result.
• Check the answer against a typical range: about 0.5 to 1.2 for children and 1.4 to 2.1 for most adults.
• Use our BMI calculator alongside BSA to see both height-weight views.
• Look at the body fat calculator if you want to understand body composition, which BSA ignores.

Educational Note

This page describes maths for learning. It is not medical advice. Drug doses are set by licensed doctors using hospital protocols, and no value on this page should be used to start, stop or change any medicine.

Conclusion

Body surface area formulas all try to answer the same question: how large is the body’s skin area, given height and weight? Mosteller gives a quick answer with one square root, while DuBois, Haycock and Gehan-George use powers and were built on different groups of people.

For most Indian adults and children, the answers agree within a few hundredths of a square metre. Choose one formula, stay consistent, and let doctors make dosing decisions. A reliable calculator takes the strain out of the powers.

FAQs

Which BSA formula is the most accurate?

No single formula is best for everyone. Studies show they agree closely for average builds and differ more at extremes of height and weight. Clinicians usually pick one formula and use it consistently.

Why is Mosteller so popular?

It is easy to remember and needs only one square root. Its results are close to the more complex formulas for most people, so it suits phones, worksheets and busy wards.

Is DuBois still used?

Yes. It appears in many textbooks and older protocols, even though it was built from a very small sample in 1916.

Which formula suits children?

Haycock is often chosen for infants and children, though Mosteller is also widely used in paediatric settings. The treating team decides which one applies.

Do the formulas give very different answers?

For an adult of 170 cm and 70 kg, they range from 1.81 to 1.83 m2. The gap widens slightly for very small children or very large adults.

Can I use these results to decide a medicine dose?

No. This article is educational only. A doctor or pharmacist must set every dose using current protocols.