Inverting BMI: weight = BMI × height(m)²
BMI is normally calculated as weight ÷ height². Rearranging that formula to solve for weight instead gives weight = BMI × height² — so plugging in the WHO's normal-range cutoffs (18.5 and 25) at a given height produces a low and high weight boundary.
A worked example: 170cm
At 170cm (1.70m), height squared is 2.89 m². The low end: 18.5 × 2.89 ≈ 53.5kg. The high end: 25 × 2.89 ≈ 72.3kg. So the healthy weight range for 170cm is roughly 53.5kg to 72.3kg.
A shorter height, a narrower absolute range
At 160cm (1.60m), height squared is 2.56 m². The same two cutoffs give a range of 47.4kg to 64.0kg — a range of 16.6kg, versus 18.8kg at 170cm. Because both boundaries scale with the square of height, a shorter height produces a proportionally similar but numerically smaller range.
Why the range is deliberately wide
The WHO's normal BMI band spans a full 6.5 points (18.5 to 25) specifically because BMI alone doesn't capture body composition — muscle mass, frame size, and other factors mean a single "ideal" number would be misleading. The range approach acknowledges that many different weights can be equally healthy for the same height.