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When beginning a build and determining the compression ratio wanted for this application, how do you know what piston, connecting rod length, and head gasket thickness to use to accomplish this.
Sorry for the late reply.
Piston selection is usually limited* and there should be information on the manufacturer's site on the nominal bump or recess volume. The other factor with pistons is deck height, how far below, or above, the deck the piston is, and some will machine the block deck to decrease the unswept volume. * You can have custom pistons made, but that's for experienced builders.
Connecting rod length is normally fixed for the engine, again, custom parts can be made but...
You do generally have some variation in gasket thicknesses, and they can be useful for fine tuning the CR, especially when the block has been decked too far..
Do you have a specific engine/application in mind?