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@gbj_tester
Depends on:
rim profile, particularly the inside width and height above the bead, but other factors influence the final size too;
true casing width of the tyre, as 23c can be anything from 20 to 25mm wide when mounted on the rim;
tread thickness, which ranges from approx. bugger all on a Veloflex Record to nearly 5mm on a touring tyre.
Typically, if you measure the true width of the mounted and inflated tyre and add twice that and twice the tread thickness to 626mm you won't be far out.