BSA formula (Mosteller): how to calculate body surface area

Body surface area (BSA) by the Mosteller formula is the square root of (height in cm × weight in kg ÷ 3600). For someone 170 cm tall who weighs 70 kg, BSA is 1.8181 m².

Not a medical device. Not a diagnosis or dosing recommendation.

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What is body surface area (BSA)?

Body surface area (BSA) is reported in square metres (m²). The Mosteller formula calculates it from height and weight.

Physiologic measurements are indexed by dividing the absolute value by BSA: cardiac index is cardiac output divided by BSA, and stroke index is stroke volume divided by BSA.[1]

Several BSA equations have been published, and they can give noticeably different results for the same height and weight, especially at extremes of body weight.[2] This page covers the Mosteller formula.

The Mosteller BSA formula

BSA_m2 = sqrt((height_cm * weight_kg) / 3600)

In words: BSA is the square root of (height in cm × weight in kg ÷ 3600).

What each part means

How the formula works

The formula has three steps:

1. Multiply height in centimetres by weight in kilograms.
2. Divide that product by 3600.
3. Take the square root.

The division happens inside the square root. If you take the square root first and then divide, the answer will be far too small.

Mosteller published this version in 1987 as a simplified calculation of body surface area. It uses just multiplication, division and a square root, so any basic calculator can do it.

Units and conversions

The constant 3600 assumes centimetres and kilograms. If your measurements are in inches or pounds, convert them first:

• 1 in = 2.54 cm, so multiply inches by 2.54.
• 1 lb = 0.45359237 kg, so multiply pounds by 0.45359237.

Height and weight should be entered as a consistent pair: centimetres with kilograms, or inches with pounds.

Conversion table

Computed from the conversion factors above and rounded to 2 decimal places.

How to calculate BSA: worked example

Metric example: 170 cm, 70 kg

1. Multiply height by weight: 170 × 70 = 11,900
2. Divide by 3600: 11,900 ÷ 3600 = 3.3056
3. Take the square root: √3.3056 = 1.8181 m²

The result is rounded to 4 decimal places.

BSA reference table (Mosteller)

These values are computed directly from the Mosteller formula, square root of (height in cm × weight in kg ÷ 3600), and rounded to 4 decimal places, as Magent's calculator reports. They show how BSA changes with height and weight. They are not targets or reference ranges.

To read it, find the row for height and the column for weight. The 170 cm, 70 kg cell matches the worked example above.

History of the Mosteller formula

The formula comes from a one-page article by R. D. Mosteller, Simplified calculation of body-surface area, published in the New England Journal of Medicine in 1987 (volume 317, issue 17, page 1098). As the title says, the aim was a simpler way to calculate body surface area. The whole calculation fits in one square root.

When it's used

BSA is used to index physiologic measurements to body size, for example cardiac index (cardiac output ÷ BSA) and stroke index (stroke volume ÷ BSA).[1]

Where it's used

Indexed values such as cardiac index come up in haemodynamic monitoring. Published work notes that minimally invasive monitors encourage looking at cardiac output and stroke volume in real time, and discusses the BSA-indexed versions of those values alongside them.[1]

Who uses it

Cardiac and stroke indices are routinely used to communicate the adequacy of circulation, especially by cardiac anaesthesiologists.[2]

When BSA is used, and its limits

BSA is used to index measurements such as cardiac output and stroke volume to body size.[1]

Published work notes that very large BSA values, as in severe obesity, can distort indexed values such as cardiac index.[1] Different BSA equations also diverge most at these extremes.[2]

This page calculates BSA and nothing else. It doesn't say what any BSA value means for an individual person or what to do with it. Clinical decisions that use BSA belong to a qualified clinician who knows the patient.

How BSA differs from related calculators

• BMI also uses height and weight, but it gives body-mass index, not a surface area. Published work notes that BSA and BMI are not interchangeable and don't always move together. A short, heavy person and a tall, thin person can differ in one and not the other.[1]
• Devine IBW estimates ideal body weight from height and sex, plus an adjusted body weight that uses actual weight. It gives a weight in kilograms, not a surface area.

Glossary

• Body surface area (BSA): a body-size value in m², calculated here from height and weight.
• Mosteller formula: the 1987 BSA equation, square root of (height in cm × weight in kg ÷ 3600).
• m² (square metre): the unit BSA is reported in.
• Indexing: dividing a measurement by BSA so it is expressed per m².
• Cardiac index: cardiac output divided by BSA.

Common mistakes

• Using inches and pounds with 3600. The constant 3600 belongs with centimetres and kilograms. Convert imperial measurements before you calculate by hand.
• Moving the division outside the square root. Divide by 3600 first, then take the square root.
• Rounding too early. Keep full precision through the steps and round once at the end. Magent's calculator reports 4 decimal places.
• Entering values outside the accepted range. Heights outside 50–250 cm (20–98 in) and weights outside 1–500 kg (2–1100 lb) are rejected, not estimated. Check for a typo or a unit mix-up.
• Mixing equations. A BSA from another equation won't exactly match the Mosteller result, so compare like with like.

Source

Mosteller RD. Simplified calculation of body-surface area. N Engl J Med. 1987;317(17):1098. DOI: 10.1056/NEJM198710223171717

Further reading

1. Adler AC, Nathanson BH, Raghunathan K, McGee WT. Misleading indexed hemodynamic parameters: the clinical importance of discordant BMI and BSA at extremes of weight. Crit Care. 2012;16(6):471.
2. Adler AC, Nathanson BH, Raghunathan K, McGee WT. Effects of body surface area-indexed calculations in the morbidly obese: a mathematical analysis. J Cardiothorac Vasc Anesth. 2013;27(6):1140-1144.

Frequently asked questions

How do you calculate BSA?

With the Mosteller formula:

1. Multiply height in cm by weight in kg.
2. Divide by 3600.
3. Take the square root.

For 170 cm and 70 kg: 170 × 70 = 11,900, then 11,900 ÷ 3600 = 3.3056, and the square root is 1.8181 m².

How can I calculate body surface area from height and weight?

Put height in centimetres and weight in kilograms, then use the square root of (height in cm × weight in kg ÷ 3600). If you have inches or pounds, convert first (inches × 2.54, pounds × 0.45359237).

What is a good BSA level?

There isn't a "good" or "bad" BSA. It's a size value that rises with height and weight, so it varies naturally between people. This page doesn't give a normal range; what a value means depends on clinical context.

Can I use the BSA formula with inches and pounds?

Yes, but convert first. The constant 3600 belongs with centimetres and kilograms, so multiply inches by 2.54 and pounds by 0.45359237, then use the formula as usual.

Are there BSA formula examples?

The worked example above (170 cm, 70 kg → 1.8181 m²) goes step by step. The reference table gives Mosteller BSA for heights from 150 to 190 cm and weights from 50 to 100 kg.

Is the Mosteller formula the same as the Du Bois formula?

No. They are different published BSA equations, and they can give different results for the same person.[2] This page and Magent's calculator use the Mosteller formula.

Related

• Body size calculators
• BMI: body-mass index from height and weight
• Devine IBW: ideal body weight from height and sex
• All calculator explainers