# References and formulas used by the Body Surface Area Calculator.

## Formulas for Body Surface Area.

The Mostellerą formula

BSA (m˛) = ( [Height(cm) x Weight(kg) ]/ 3600 )˝        e.g. BSA = SQRT( (cm*kg)/3600 )

or in inches and pounds:     BSA (m˛) = ( [Height(in) x Weight(lbs) ]/ 3131 )˝

The DuBois and DuBois˛ formula
BSA (m˛) = 0.20247 x Height(m)0.725 x Weight(kg)0.425

A variation of DuBois and DuBois15 thats gives virtually identical results is:

BSA (m˛) = 0.007184 x Height(cm)0.725 x Weight(kg)0.425

The Haycockł formula
BSA (m˛) = 0.024265 x Height(cm)0.3964 x Weight(kg)0.5378

The Gehan and George4 formula

BSA (m˛) = 0.0235 x Height(cm)0.42246 x Weight(kg)0.51456

The Boyd formula5
BSA (m2) = 0.0003207 x Height(cm)0.3 x Weight(grams)(0.7285 - ( 0.0188 x LOG(grams) )

The Mosteller formula is recommended6.  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.

### Formulas for Lean Body Weight & Ideal Body Weight

Lean Body Weight (men) = (1.10 x Weight(kg)) - 128 ( Weight2/(100 x Height(m))2)
Lean Body Weight (women) = (1.07 x Weight(kg)) - 148 ( Weight2/(100 x Height(m))2)

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)

### 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 classification8 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 50th percentile, is at the average weight of the population.  An adult at the 90th percentile is quite heavy.

The oldest version of the calculator used weight data from a study9 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 study10 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 data13. Adult data for median height and weight came from Canadian 1997 data11. The variances for height and weight and the weight for height data comes from Canadian 1971 data12.  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 survey14 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

1. Mosteller RD: Simplified Calculation of Body Surface Area. N Engl J Med 1987 Oct 22;317(17):1098 (letter)
2. 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.
3. 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
4. Gehan EA, George SL, Estimation of human body surface area from height and weight.   Cancer Chemother Rep 1970 54:225-35.
5. 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 )
6. Lam TK, Leung DT: More on simplified calculation of body-surface area. N Engl J Med 1988 Apr 28;318(17):1130, (letter)
7. Clinical Guidelines on the Identification, Evaluation, and Treatment of Overweight and Obesity in Adults.  National Heart, Lung and Blood Institute. June 17, 1998
8. Understanding Nutrition,  by Whitney and Rolfes.
9. Halls SB.  Weight distribution of 3992 adult cancer patients referred for CT scans. May 1999. Edmonton, Alberta, Canada.
10. Halls SB.  Heights & Weights of 600 adult cancer patients. May 1999. Edmonton, Alberta, Canada.
11. National Population Health Survey 1996/1997.  (Canadian data n=77,403  age & sex stratified.)
12. Nutrition Canada, Anthropometry Report 1980 of data from Nutrition-Canada Survey 1971.  (n=13,691)
13. 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.
14. NHANES III.  1988-1994 data from USA.
15. Wang Y, Moss J, Thisted R. Predictors of body surface area. J Clin Anesth. 1992; 4(1):4-10.