Blood glucose and HbA1c relationship ?

This chart show the relationship between HbA1C and blood glucose ...

Hi and welcome!

The hba1c is, as you said, a kind of rough average over 2-3 months.

The fasting blood glucose test is a snapshot of your blood glucose on the morning of the test, before you ate anything.

Blood glucose rises and falls throughout the day, due to carb intake, stress, exercise and a few other things.

Both tests can be used to indicate diabetes, and many docs will request both tests, (and maybe a glucose tolerance test as well, to confirm the diagnosis.)

The chart @Art Of Flowers posted shows the way they compare.

Hope that helps.

Bear in mind that the relationship is only approximate, since they are measuring different things. (Sorry if that's obvious)
e.g. I believe the numbers at the low end can change differently if you switch to a low carb diet, generally the hba1c goes down, but some people find the low carb diet raises their fasting bg. Also as Brunneria said, fasting glucose levels can vary for lots of reasons. This guy said his fasting glucose went down a few days after he stopped eating breakfast, but I've seen other people say the opposite.

I used to just assume that hba1c was by far the superior measure, but more recently I've read that it can vary with some blood parameters* so some people consistently have higher/lower hba1c than an "ideal" test. Maybe they'll produce an adjusted version of the number one day.

Lower is better, for all the tests, but how low is required for best or reasonable health is uncertain.

* Sorry, I don't remember what parameters, iron levels or red blood count or cell size or something ...

This is my personal take on it.
As said above it is an approximation to the truth. Hba1c measures the amount our blood cells are 'permanently' affected by blood glucose over the time until our blood cells are renewed. An average for replacement of all of them is c.12 weeks, but some of us hang on to them longer (hence their hba1c is higher than it should be) whereas others change them all earlier, hence their hba1c is lower than the reference levels.
Some also believe the time spent with high blood glucose causes more haemoglobin to register change (in relative terms) than similar changes at a lower level in blood glucose.

In maths parlance, Hba1c should be the area under graph of instantaneous changing blood glucose with time.
regards
D.