what is the compression ratio for a r56 s

 

10.5:1

More interesting information here.

 

For the 'S' model, the cylinder charge has already been compressed by the Turbo-Charger making the total compression much greater than a Normaly Asperated engine @ 10.5.

 

I think the compression ratio is 11.0:1 for the naturally-aspirated Cooper. And the JCW cars have a lower 10.0:1 ratio because of the higher boost from the turbo.

In short, for the R55/56/57,

Cooper - 11:1
'S' - 10.5:1
JCW - 10:1