Body Weight-Height Indexes
The Body Mass Index (BMI) formula is well over 100 years old. Since 1972 it's been used extensively as an aid in assessing 'healthy' body weights. Clearly taking only weight and height into account only gives a crude indication of what is a healthy weight. Apart from neglecting body shape and composition, BMI stays the same if weight increases in proportion to the square of height. In fact people don't 'scale' this way, so taller people's BMI's are unfairly too high and shorter people's too low.
Trefethen, a numerical analysis professor at Oxford, has suggested a way to better allow for the latter effect by comparing weight against height raised to the power of 2.5 rather than height squared - as used for BMI. For a height of 169cm Trefethen's adjusted value corresponds with the regular value.
Without implying a causal relationship, studies comparing BMI values with longevity seem to suggest that, on average, longevity peaks for BMI values of about 23 ... often considered to be mildly 'overweight'.
Reciprocal Ponderal Index is another calculation based only on weight and height. High RPI values represent slenderness whereas high BMI values represent a heavier build. RPI's are not so commonly known, but have apparently found some use with assessing the potential of track athletes.
BMI values average mid 20s (and are increasing) for developed world populations while RPI values are around 40.
A shortcoming of these indexes is that they take no account of body composition. In particular they can't differentiate between the proportions of fat and muscle contributing to body weight. Thus the BMI of a lean but strongly muscled person may lie in the range sometimes regarded as unhealthily high.
To more accurately correlate 'lean' or fat-free mass (FFM) to height, a Fat-free Mass Index (FFMI) may be used. FFMI is calculated in a similar way to BMI except that fat-free weight is used rather than total body weight. Calculating the index therefore requires the subject's body fat to be known. A further study by Kouri, et al suggested an adjustment to this formula which they considered to more fairly comparable values over a wide range of subject heights.
The same researchers also attempted to establish FFMI norms among anabolic androgenic steroid (AAS) users and non-users. Although it's never possible to determine with certainty whether or not someone is an AAS user based on one such simple formula, their studies suggested the average FFMI for a male non-steroid user may be around 19 and that few adult males will have an FFMI above about 25 without assistance from steroids. This study is now almost 30 years old, and more recent 'experts' have suggested that non-AAS users with FFMIs of between 25 to 30 may be more common that the original research study concluded.
Finally, the biggest source of error in any calculations involving FFMI is demonstrably the lack of a reliable means of estimating total body fat. The advent of cheap and readily available BIA scales for home use has certainly not helped!