Body Weight-Height Ratios
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.
Reciprocal Ponderal Index is another calculation based only on weight and height. High RPI values represent slenderness whereas high BMI value represent a heavier build. RPI's are little 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 adjustment is sometimes made to make the index more fairly comparable over a wide range of subject heights.
Some studies (e.g. Kouri, et al) have 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 by this means, the studies suggest the average FFMI for a male non-steroid user is around 19 and that an adult male will rarely have an FFMI above about 25 without assistance from steroids.