BMI is calculated using standard metric and imperial unit conversions, as well as the modern Oxford University modification designed to account for non-linear allometric scaling in very tall and very short individuals:
1. Standard Metric Formula (WHO Standard)
$$\text{BMI} = \frac{\text{Weight (kg)}}{[\text{Height (m)}]^2}$$
Step-by-step Example: For an individual weighing $72\text{ kg}$ with a height of $178\text{ cm}$ ($1.78\text{ m}$):
$1.78 \times 1.78 = 3.1684\text{ m}^2$
$72 \div 3.1684 = \mathbf{22.72\text{ kg/m}^2}$ (Normal Weight)
2. Standard Imperial Formula
$$\text{BMI} = \frac{\text{Weight (lbs)} \times 703}{[\text{Height (inches)}]^2}$$
Step-by-step Example: For an individual weighing $165\text{ lbs}$ standing $5\text{ ft } 10\text{ in}$ ($70\text{ inches}$):
$70 \times 70 = 4,900\text{ in}^2$
$(165 \times 703) \div 4,900 = 115,995 \div 4,900 = \mathbf{23.67}$ (Normal Weight)
3. Modern Oxford University "New BMI" (Trefethen Formula)
$$\text{BMI}_{\text{new}} = 1.3 \times \frac{\text{Weight (kg)}}{\text{Height (m)}^{2.5}} = 5734 \times \frac{\text{Weight (lbs)}}{\text{Height (inches)}^{2.5}}$$
Developed by Professor Nick Trefethen of Oxford University, this formula corrects the traditional square exponent bias ($h^2$) that disproportionately categorizes short people as artificially "too thin" and tall people as artificially "overweight."
