I've seen this A/R ratio for turbine (or compressor) housings described as the
unitless ratio between the inlet (or outlet) area, and the radius.

But the ratio between an area and a distance will have units of length.
So that ratio isn't unitless. It depends on which unit you choose.
Now, I think a 0.62 metric turbine housing is the same as an american
0.62 turbine housing, so it probably really is a unitless number.

Is it A / R^2 ?
Or the radius to the centroid of the inlet area divided by the scroll housing radius?
Or what? I think it might be the latter based on the appearance of typical housings.

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