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mmol/l to mg/dl and back again...Why's it 18 times?

I posted this around 10 years ago, but now I have a whole new set of followers, thought I'd post it again!

Americans use mg/dl as the unit for measuring glucose levels. Most other countries use mmol/l. The relationship between the two is that 1mmol/l = 18mg/dl. I was interested to understand this relationship (as a former chemist) and also find out what it meant in practical terms. It is a bit sad, but here is my calculation:

The unit mmol/l stands for milli-moles per litre. (or liter in the US). milli means a thousandth, so what is a mole (other than a small rodent-like animal)? A mole is that quantity of a substance whose mass in grams is the same as its formula weight (atomic weight). Each molecule of glucose has 6 Carbon atoms, 12 Hydrogen atoms and 6 Oxygen atoms. A carbon atom weighs 12 units, a hydrogen atom weighs 1 unit and an oxygen atom weighs 16 units. These units are called relative atomic mass units (don't need to go into why). So the atomic weight of glucose is (6x12) + (12x1) + (6x16) = 180. Therefore one mole of glucose weighs 180g. So now we are in a position to look at mmol/l. 1 mmol of glucose is 0.18g. So 1 mmol/l is 0.18g in 1 litre of water.So now you can see the relationship to mg/dl. A decilitre is a tenth of a litre or 100ml. A miligram is a 1000th of a gram. Therefore 0.18g is the same as 180mg. We are only dealing with a 10th of the amount of water (100ml or 1dl) so therefore can divide this number by 10 giving 18mg/dl. Thus 1 mol/l = 18 mg/dl.

Finally, for those who are interested in how sensitive our glucose meters are, think about this. Mine does graduations in 0.1 mmol/l increments. As shown about 0.1mmol is 0.018g. I think it is remarkable that I have a handheld, portable device that can tell me differences of 0.018g of a substance in a litre of liquid! Probably bored you silly, but I didn't know why this relationship existed until I sat down and calculated it, so at least I have learnt something!

One more thing has struck me. How many grains of sugar is 0.018g? After some research, I think I may have found the answer. According to a site I have found, the density of granulated sugar is 849kg/meter cubed. Another site says that granulated sugar granules are cubes of side 0.5mm. Knowing the density and the volume of them you can work out the mass. Mass = Volume x Density. Not to bore you with the maths...1 grain of sugar weighs 0.106mg (as long as I have got my conversions right). Therefore 0.018g of sugar equates to about 170 grains.


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