I know 1 way of doing so is to measure the difference between the piston at TDC and BDC, but is there a way check it after all the parts are installed?

 

The only real way to do it is to cc the combustion chamber for each bore while the piston is at TDC. Once you know that, figuring out the C/R is simple math.

 

Its really a trick of discovering the difference in volume of the cylinder at TDC and when the piston is all the way down. Since piston rings leak air, using pressure can be tricky...you could do it with a SEALED cylinder. Since pistons and cylinder heads are not simple shapes, you can't just get out a ruler. You really have to take someone's word for it Also, if the pistons and/or head is a different shape than stock this below method will not work...you can still get an estimate however.

One way is to compare a difference from stock. You would essentialy compute the distance from the block ridge to the piston and compare it to stock. Using Algebra and the CR and displacement of a stock car, you have the info you NEED to compute the CR because the stroke is still the same length.

An example...and this is ONLY an example. Assume that stroke and bore are identical in both as is piston and head shape.

The stock car has a 10:1 CR and each cylinder has a displacement of 500cc. The height from the ridge to the piston is 10 cm, the 10:1 CR says stroke is 9mm. That leaves 1mm...10/1=10 which is the CR. Since the cylinder has a displacement of 500cc and a 10:1 CR, the volume of the cylinder at TDC is 50cc.

The modded car has a ridge to piston height of 9.5 cm. Since the stroke is 9mm, that leaves .5cm. 9.5/.5=19...19:1 compression ratio.

This is actually oversimplified...compound curves in the head and funny shaped pistons make an exact measurement difficult to obtain...you generally take the manufacturer's word.