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In the UK, the size increment is supposedly a 'barleycorn' (= 1/3") but it is the last rather than the shoe that is designated, with men's and women's sizes being theoretically the same. The last is intended to be longer than the foot by 'around' 1/2", but there is no clear agreement as to foot length; a UK11 shoe being variously said to fit a foot almost anywhere between 11" and 12" long! It is my understanding that US sizes also have 'barleycorn' increments; the sizing formula being quoted thus: 'Today in America, the sizing generally adheres relatively closely to a formula of 3 times the length of the foot in inches (the barleycorn length), less a constant (22 for men and 21 for women)'. So, a foot measuring 11" would equate to a size of USM11 or USW12, which I find odd as perceived wisdom suggests that a number difference of two (not one) between male and female sizes is generally the case. Or is that 'plus one' a purely theoretical difference, as in most cases the shape and fit of the female shoe requires 'plus two' in sizing? (I know that my feet - equivalent to USM12 or 12.5 - require a full USW14 if to fit properly. You quote USW9 as being 9 7/8" (although 1/3" increments would suggest 9 2/3" or 10"). And the 'formula' would suggest USW9 = 10". I'm sure that neither of us would quibble over these tiny theoretical differences, but taking actual measurements in millimetres to identify sizes (as the Eu system does) is less controversial. That is how I got the Eu38:40 ratio of 95%. I may have misunderstood your application of the percentage, in that I was suggesting that the steepness of an Eu38 4" heel is the same as that of an Eu40 4.25", obtained by dividing 4 by 0.94. But we are both agreed that (obviously) the apparent steepness of a given heel height decreases with increasing foot length and in the same proportions.