Analytical science: Secrets of the Mary Rose
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# 4.2 Determining height and weight

Determining the height and weight of an individual requires access to the skeleton or skeletal fragments. Although bones can easily be measured, it is important to remember that bodies shrink slightly after death, so the original height of a living individual will be slightly greater than that measured directly from a corpse.

An accurate method of determining the height is to measure the length of specific long bones (i.e. the three long leg bones - femur, tibia and fibula - and the three long arm bones - humerus, radius and ulna; see Figure 6 in Section 4.1). This method assumes that different parts of the adult body are in proportion with each other, and that the relative proportions between height and leg or arm length vary according to the gender and the ethnicity of the individual. By averaging measurements from many individuals in a specific ethnic group (and separating them into male and female), the average relationship between height and limb length can be established. This is then used to calculate the full body height of any other individual from that group, by applying a method called regression analysis.

Regression analysis involves measuring changes in one item (called a variable) to predict how a related variable will change. For example, changes in the length of a long bone can be used to determine an individual's full height. The relationship between long bones and full height is determined by taking measurements of different long bones in modern adult corpses and comparing them directly with the individual's measured height. A mathematical equation can then be applied to link the changes in bone length to overall height. The multiplying factors used in the equation differ according to:

- the type of long bone used
- the broad ethnic origin
- the gender of the individual being investigated (Table 1).

When the ethnicity or gender of an individual is unknown, an equation can be used to allow an approximate height to be calculated.

## Table 1 Equations for calculating full adult height in cm for males and females from different ethnic groups, using long bone measurements.

Bone type | Ethnicity | Male equation | Female equation
--- | --- | --- | ---
femur | Caucasian | (length × 2.32) cm + 65.53 cm | (length × 2.47) cm + 54.13 cm
| African | (length × 2.10) cm + 72.22 cm | (length × 2.28) cm + 59.76 cm
| Asian | (length × 2.15) cm + 72.57 cm | not available
tibia | Caucasian | (length × 2.42) cm + 81.93 cm | (length × 2.90) cm + 61.53 cm
| African | (length × 2.19) cm + 85.36 cm | (length × 2.45) cm + 72.56 cm
| Asian | (length × 2.35) cm + 81.45 cm | not available
fibula | Caucasian | (length × 2.60) cm + 75.50 cm | (length × 2.93) cm + 59.61 cm
| African | (length × 2.34) cm + 80.07 cm | (length × 2.49) cm + 70.90 cm
| Asian | (length × 2.40) cm + 80.56 cm | not available

(Source: Rice University.)

Calculate the true height (to the nearest cm) of a Caucasian male whose tibia measures 39.0 cm.

## Answer

The true height is 176 cm:

(39.0 × 2.42) cm + 81.93 cm = 176.31 cm = 176 cm (to the nearest cm).
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