Cross sectional area can't be measured directly we need to use some maths but it will result in:-
2.5mm² = 1.784124116mm diameter
4mm² = 2.256758334mm diameter
6mm² = 2.763953196mm diameter
10mm² = 3.568248232mm diameter
16mm² = 4.513516668mm diameter
Using =2 * POWER(A1/PI(),0.5) in excel. Or =PI()*POWER(B1/2,2) to convert other way around.
However in the main we are looking at insulation as well using data given on manufacturers web sites like
this one with Batt Cables we see the outer dimensions. But it will vary between manufacturers and cable types.
I would normally try to fit Red, Blue, Yellow or other marked terminals or butt connectors Red = approx 1.5mm², Blue = approx 2.5mm², Yellow slack = 4mm² tight = 6mm² then on marked on bare connectors.
I think to try using a vernier to measure between 2.26 and 2.76 is a little too hit and miss. Also to work out if PVC or LSZH is hard unless written on the cable and 4mm² LSZH will carry near the same current as 6mm² PVC. Unless found on cable I would assume PVC.
Modified for Taylortwocities although I think to not auto read the ² one has to be a bit thick. I have no ² key so have to write in Word and transfer I suppose next I'll be picked up on not leaving a space between number and mm?