References and formulas used by the Body Surface Area Calculator.

## The Body Surface Area formula.

Below are the body surface area formula by Dr’s Mosteller, DuBois and DuBois, Haycock and Boyd.

### The Mosteller formula^{1}

BSA (me.g. BSA = SQRT( (cm*kg)/3600 )^{2}) = SQRT( [Height(cm) x Weight(kg) ]/ 3600 )or in inches and pounds:

BSA (m^{2}) = SQRT( [Height(in) x Weight(lbs)]/ 3131 )

### The DuBois and DuBois formula^{2}

BSA (m^{2}) = 0.20247 x Height(m)^{0.725}x Weight(kg)^{0.425}A variation of DuBois and DuBois

^{15}that gives virtually identical results is:

BSA (m^{2}) = 0.007184 x Height(cm)^{0.725}x Weight(kg)^{0.425}

This chart shows 33 adult cancer patients, comparing their BSA calculated with the methods of Mosteller and DuBois. The patients were pre-sorted into ascending order of BSA. The data points are so close to each other, the lines overlap each other.

### The Haycock formula^{3}

BSA (m^{2}) = 0.024265 x Height(cm)^{0.3964}x Weight(kg)^{0.5378}

### The Gehan and George formula^{4}

BSA (m^{2}) = 0.0235 x Height(cm)^{0.42246}x Weight(kg)^{0.51456}

### The Boyd formula^{5}

BSA (m^{2}) = 0.0003207 x Height(cm)^{0.3 }x Weight(grams)^{(0.7285 – ( 0.0188 x LOG(grams) )}

The Mosteller formula is recommended^{6}. To learn more about the issues and differences in BSA formulas, read the BSA standards report by Thanh Vu B.Sc(pharm). It explains why the Mosteller formula was adopted for use by the Pharmacy and Therapeutics Committee of the Cross Cancer Institute, Edmonton, Alberta, Canada.

### Lean Body Weight formula & Ideal Body Weight formula

Lean Body Weight (men) = (1.10 x Weight(kg)) – 128 ( Weight^{2}/(100 x Height(m))^{2})

Lean Body Weight (women) = (1.07 x Weight(kg)) – 148 ( Weight^{2}/(100 x Height(m))^{2})

click here for more information about Lean Body Weight, or lean body mass.

Ideal Body Weight (men) = 50 + 2.3 ( Height(in) – 60 ) ( Devine formula)

Ideal Body Weight (women) = 45.5 + 2.3 ( Height(in) – 60 ) (Robinson formula)

click here for more information about Ideal Weight formulas.

### Formula for Body Mass Index.

Body Mass Index = Weight(kg) / Height(m)^{2}

### Definitions of "overweight".

A Body Mass Index between 25 and 29.9 is "overweight", greater than or equal to 30 is "obese^{"7}. However, some very muscular people can have high Body Mass Indexes and in adolescents, BMIs frequently result in overestimation of fatness. A better classification^{8} of "overweight" is given in this table below. These numbers are used in the BSA calculator.

Women | Men | |
---|---|---|

underweight | <19.1 | <20.7 |

ideal weight | 19.1-25.8 | 20.7-26.4 |

marginally overweight | 25.8-27.3 | 26.4-27.8 |

overweight | 27.3-32.3 | 27.8-31.1 |

very overweight or obese | >32.3 | >31.1 |

### Weight Percentile, and Height Percentile, compared to the population.

An adult whose weight is at the 50^{th} percentile, is at the average weight of the population. An adult at the 90^{th} percentile is quite heavy.

For calculating percentiles, the oldest version of the calculator used weight data from a study^{9} of 3992 consecutive adult cancer patients who underwent CT scanning. That study did not stratify males versus females, and it did not include pediatrics. By using the variance distribution from that study, and then adjusting the means to 79.4kg for males and 64.5kg for females, it was able to estimate the weight percentile. The height data came from a study^{10} of 600 randomly selected cancer patients. That study also did not stratify males versus females, and it did not include pediatrics. By using the variance distribution from that study, and then adjusting the means to 69 inches for males and 64 inches for females, the older calculator was able to estimate the height percentile.

The next version of the calculator used better data. Pediatric data was derived from standard pediatric growth charts, based on American 1979 data^{13}. Adult data for median height and weight came from Canadian 1997 data^{11}. The variances for height and weight and the weight for height data comes from Canadian 1971 data^{12}. Americans tend to be a little taller and heavier than Canadians.

The most recent version of the calculator has switched to using exclusively American data from the NHANES III survey^{14} of 1988 to 1994. This data is used for the height and weight percentiles algorithm. It incorporates both adults and children’s data of heights and weights, the median (average) values and the variances (the range of fatness – thinness). Keep this in mind, that American’s tend to be taller and heavier than many other nationalities.

#### References

- Mosteller RD: Simplified Calculation of Body Surface Area.
*N Engl J Med*1987 Oct 22;317(17):1098 (letter) - DuBois D; DuBois EF: A formula to estimate the approximate surface area if height and weight be known.
*Arch Int Med*1916 17:863-71. - Haycock G.B., Schwartz G.J.,Wisotsky D.H. Geometric method for measuring body surface area: A height weight formula validated in infants, children and adults.
*The Journal of Pediatrics*1978 93:1:62-66 - Gehan EA, George SL, Estimation of human body surface area from height and weight.
*Cancer Chemother Rep*1970 54:225-35. - Boyd E, The growth of the surface area of the human body. Minneapolis: university of Minnesota Press, 1935. (I never found the original source. Instead, I copied the formula from: http://www.ispub.com/journals/IJA/Vol2N2/bsa.htm )
- Lam TK, Leung DT: More on simplified calculation of body-surface area.
*N Engl J Med*1988 Apr 28;318(17):1130, (letter) - Clinical Guidelines on the Identification, Evaluation, and Treatment of Overweight and Obesity in Adults. National Heart, Lung and Blood Institute. June 17, 1998
*Understanding Nutrition*, by Whitney and Rolfes.- Halls SB. Weight distribution of 3992 adult cancer patients referred for CT scans. May 1999. Edmonton, Alberta, Canada.
- Halls SB. Heights & Weights of 600 adult cancer patients. May 1999. Edmonton, Alberta, Canada.
- National Population Health Survey 1996/1997. (Canadian data n=77,403 age & sex stratified.)
- Nutrition Canada, Anthropometry Report 1980 of data from Nutrition-Canada Survey 1971. (n=13,691)
- Pediatric growth charts, from Ross Laboratories. Adapted from Hamill PVV, Drizd TA TA, Johnson CL, Reed RB, Roche AF, Moore WM. Physical growth: National Center for Health statistics percentiles. Am J Clin Nutr 32: 607-629, 1979.
- NHANES III. 1988-1994 data from USA.
- Wang Y, Moss J, Thisted R. Predictors of body surface area. J Clin Anesth. 1992; 4(1):4-10.

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