# Surface Area of the Human Body

TR Smith is a product designer and former teacher who uses math in her work every day.

A person can accurately calculate the total volume of his body by submerging himself in a tank of water and measuring how much water is displaced. But measuring surface area is much trickier. There is no simple physical experiment, such as submerging yourself in a tank, that lets you equate the surface area of your skin to the area of another measurable object.

A time-consuming, but accurate method is to cover your body in small equally sized pieces of paper, then multiply the area of one piece of paper by the number it takes to cover you.

Or, you can use a simplified estimation formula for body surface area. Several such formulas have been developed by medical researchers to calculate the approximate number of square meters of skin on a human. These equations were developed in the context of finding the correct dosages for certain medications. All of them are estimates computed from your weight in kilograms and your height in centimeters. The body surface area equations have the form

BSA = a * (W^b) * (H^c)

where W and H are the height and weight of the individual, and a, b, and c are some constants that depend on the particular formula.

## Mosteller Formula

The Mosteller formula for BSA is one of the most commonly used equations for estimating surface area in humans. The equation is

BSA = (1/60) * (W^0.5) * (H^0.5)

where W is the weight in kilograms, H is the height in centimeters, and BSA is the body surface area in square meters. The constants a, b, and c from the general formula are in this case a = 1/60, b = 0.5, and c = 0.5. Since the exponents on W and H are both 1/2, the formula can be written in the equivalent form

BSA = sqrt(WH)/60

The simplicity of this formulation -- the square root of the product of W and H divided by 60 -- has made it one of the most popular equations for estimating BSA. (See also properties of exponents and properties of square roots.)

## DuBois & DuBois Formula

This next formula was devised by the married research couple DuBois and is probably the most widely used formula for estimating BSA, since it provides slightly more accurate results over the Mosteller formula. The DuBois formula is

BSA = 0.007184 * (W^0.425) * (H^0.725)

Again, height is measured in cm, weight in kg, and the output is in square meters.

Post-it note mural of Marilyn Monroe.

## Example 1

Approximately how many Post-it notes will it take to cover a man's body if he weighs 66 kg and is 175 cm tall? Using the Mosteller formula, his body surface area is approximately

sqrt(66*175)/60 = 1.791182 sq. meters

And using the DuBois formula his BSA is approximately

0.007184 * (66^0.425) * (175^0.725)
= 1.802499 sq. meters.

A post it note is 7.6 cm by 7.6 cm, with a total area of 57.76 cm squared, or equivalently 0.005776 square meters. Divide the BSA by this number and you get the approximate number of Post-it notes needed to cover the man.

1.791182/0.005776 ≈ 311 rounded up to next integer

1.802499/0.005776 = 313 rounded up to next integer.

So it will take between 311 and 313 Post-it notes.

## Example 2

In the example above, the DuBois equation gave a higher estimate than the Mosteller equation. However, this is not always the case; it depends on the relative values of the height and weight. For example, suppose a woman weighs 85 kg and has a height of 150 cm. Using the Mosteller formula her bodily surface area is approximately

sqrt(85*150)/60 = 1.881932 sq. meters

and using the DuBois formula her BSA is estimated to be

0.007184 * (85^0.425) * (150^0.725)
= 1.79488 sq. meters

So in this example, the Mosteller formula provides a higher estimate.

## BSA Estimation Table (Mosteller Formula)

Use this table to estimate your body surface area. Find the row that corresponds to your weight in kg and the column that corresponds to your height in cm. The value in the table is your approximate BSA in square meters based on the Mosteller formula. If your weight and/or height is between two numbers, you can interpolate between the table entries find your approximate BSA.

145
150
155
160
165
170
175
180
185
45
1.35
1.37
1.39
1.41
1.44
1.46
1.48
1.50
1.52
50
1.42
1.44
1.47
1.49
1.51
1.54
1.56
1.58
1.60
55
1.49
1.51
1.54
1.56
1.59
1.61
1.64
1.66
1.68
60
1.55
1.58
1.61
1.63
1.66
1.68
1.71
1.73
1.76
65
1.62
1.65
1.67
1.70
1.73
1.75
1.78
1.80
1.83
70
1.68
1.71
1.74
1.76
1.79
1.82
1.84
1.87
1.90
75
1.74
1.77
1.80
1.83
1.85
1.88
1.91
1.94
1.96
80
1.80
1.83
1.86
1.89
1.91
1.94
1.97
2.00
2.03
85
1.85
1.88
1.91
1.94
1.97
2.00
2.03
2.06
2.09
90
1.90
1.94
1.97
2.00
2.03
2.06
2.09
2.12
2.15
95
1.96
1.99
2.02
2.05
2.09
2.12
2.15
2.18
2.21
100
2.01
2.04
2.07
2.11
2.14
2.17
2.20
2.24
2.27

Example of how to interpolate between measurements:

Suppose a man's weight is 83 kg and his height is 177 cm. We look at the point in the table between the rows labeled 80 and 85, and between the columns labeled 175 and 180. The four cells in the table around this point have the values 1.97, 2.00, 2.03, and 2.06 square meters. Their average is 2.15 square meters.

If you plug W = 83 and H = 177 directly into the Mosteller formula, you get BSA = sqrt(85*177)/160 = 2.04 square meters.

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• CWanamaker 2 years ago from Arizona

This is so cool! Very interesting to read. Thanks!