# Formula for BMI has an ‘ill-founded definition’

Have you ever calculated your BMI and been given a reading of ‘overweight’, when you clearly aren’t? Or maybe you’ve been training hard in the gym but your BMI has increased?

Many of us, including GPs and fitness instructors, use BMI as an indicator of whether we are ‘fit and healthy’ and reliably use it to adjust our lifestyle. However, mathematician Nick Trefethen, Professor of Numerical Analysis at Oxford University, has proposed that the formula is poorly defined and has proposed an alternative.

He claims that the BMI formula, which is calculated as weight in kilograms divided by the square of the height in meters, is an ill-founded definition of body size, and isn’t a useful measure.

He sent a letter to the Economist newspaper explaining his thoughts on why the current formula is wrong:

SIR – The body-mass index that you (and the National Health Service) count on to assess obesity is a bizarre measure. We live in a three-dimensional world, yet the BMI is defined as weight divided by height squared. It was invented in the 1840s, before calculators, when a formula had to be very simple to be usable. As a consequence of this ill-founded definition, millions of short people think they are thinner than they are, and millions of tall people think they are fatter.

Nick Trefethen
Professor of numerical analysis
University of Oxford

Nick Trefethen says that the BMI formula is more of an approximation to compare the weights of groups of people of different heights and has proposed a new formula:

$\text{BMI} = \frac{1.3 \times \text{weight}}{ (\text{height})^{2.5}}$

This is designed to take into consideration factors that the old BMI does not. Human beings are three-dimensional, but cubing the height would be too much, since humans don’t grow evenly in all directions. The choice of $2.5$ as a figure for this is supported by evidence from a reader that the original inventor of BMI intended $(\text{height})^{2.5}$ for adults. The factor of $1.3$ scales it so that the new BMI matches the old BMI for an average human.

Trefethen has however also stated that there may not in fact be an optimum BMI formula that is suitable for all, saying “human beings are complicated, and any BMI formula will deliver just one number. No single number can be right.” He also adds that he is not a biologist.

This article on the BBC News website points out that there have been other attempts to change BMI before, and it is unlikely this will actually catch on.

New BMI on Nick Trefethen’s website.

BMI: Does the Body Mass Index need fixing? at the BBC News website

• #### Harsimrat Kaur

Third year Mathematics Student at University of Reading. Has a keen interested in learning new mathematical ideas, politics, mainly in how one can make a difference, and empowering women via a group called Kaurs Corner.