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It's not that hard to work out if you can measure the volume of the combustion chamber.
The chamber is divided into 3 sections:
Piston dish, including the volume from the piston to the block deck. (It can also be -ve, if the piston sits above the block deck).
Gasket volume,
Cylinder head volume.
If you know the bore and stroke you know the swept volume.
So if you cc the head, and cc the piston dish, measure the crushed height of the gasket and its bore, you can add them all up and divide the swept volume by that total chamber volume.
There is a useful discussion on CR measuring here.
If you know the current CR and want to calculate the new CR with increased gasket thickness, just add the difference in volume it would displace to the total chamber volume.
With an 81.0 mm bore and 86.4 mm stroke, I make the cc/cylinder volume 445.219 cc.
With a CR of 9:1 I make the total combustion chamber volume 49.47 cc.
With a stock 82 x 1.5 mm head gasket the gasket volume would be 7.92 cc.
By adding another head gasket 2nd layer (1mm) to get a 2.5 mm thick head gasket, I make the gasket volume now 13.2 cc, making the new CR 8.13 cc.
I would show my workings, but they are a right mess.
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