Right then. You got your engine apart and it's an old heap... You got all the parts and are putting in together, but you need to write down the actual measurements in order to figure out your new or revised compression ration. In this example, we are installing deeper dish pistons in order to try and achieve the 8.5 CR the guys stated up on ebay. Being a turbocharged engine, we aim to lower compression to allow more boost, to achieve more power safely. So you ask google for a compression ratio formula, and the answer is very simple - total volume at BDC divided by the compressed volume at TDC. Pretty simple right? Wrong. You need to have all the needed measurements and then plug them into the more detailed formula... [cylinder volume aka displacement + deck clearance volume + piston volume dish-positive/dome-negative + gasket volume + chamber volume] divided by/ [deck clearance volume + piston volume dish/dome + gasket volume + chamber volume]. Right then. Get your caliper out.
For the simplicity of this exercise we are ignoring ring depth since if you're usually messing about with metal parts and installing oversize pistons, you'll end up honing & boring your block, and usually the fight will be snug to say the least, since the new bore is tailored to fit your new (usually forged) pistons set. So the volume that can fit in between the block walls and pistons, coming down to the depth of the first compression piston ring, is negligible to say the least.
So, the above example... stock bore*stroke was 86x86mm. The volume formula is bore*bore*0.7854*stroke/depth/height. To make it simple, we deduct the total displacement to be 86*86*0.7854*86 mm3 / 1000 to get to ccs = 499.55cc*4 = 1998.23cc total engine. Yes, it'a a two liter. Or it was... now we have 87mm forged pistons, i.e. 87*87*0.7854*86/1000=511.24cc*4=2044.97cc. It's a bit more than a 2 liter now. But, coming back to compression. Stock specs showed us an 8.8 CR from the factory. Now we have the poor man's handy tip! Easy way to calculate your piston dish volume and combustion chamber volume. If you have dome pistons (N/A usually with high compression ratios), you could make a fast clay mold of your piston's head.
Right then. The poor man's top tip. With your head fully assembled, take your handy syringe and fresh clean oil and start sucking oil into it, and pouring it into your horizontally laid cylinder head with valves in place. Of course your valve seating must be perfect for this to work... So you need to fill it with oil until it's filled to the brim and all flat horizontal. In our case, 46ml which you guessed it equals 46cc. Liquid volume is handy here, 1ml=1cc. For our fresh dished pistons we moved it a tad below TDC and measured it while in the block, it was roughly 12ml/cc. That's it then. We had all the measurements we needed. BDC volume is displacement + all other volume numbers that fit above the piston head (and in it). So... 511.24cc plus 12cc in dish, plus 46cc in the cylinder head. We also need the head gasket volume and deck clearance.
Go back to the first picture. Does it look ok to you? If you have a keen eye, you will notice we cursed and ranted for a whole day at the previous owner and the other "motorsport" garage that did some work to it... We weren't sure how much our guys shaved when leveling the block and head for our rebuild, but we figured out it could never be close to 1 WHOLE mm. Yes, that is a piston head having -0.5mm deck clearance at TDC if you can believe it. Right then... -2.97cc from this surprise. Head gasket had to be changed at this point, going for a custom 1.7mm (approx) multi layer gasket, new fresh gasket guides were put in place also, just in case. Volume for the gasket is... 88mm bore, 1.7mm thickness, about... 10,34cc.
You can use this handy excel we put here... It's an actual replica of an online CR calculator (like this one - www.csgnetwork.com/compcalc.html) Feel free, the excel is handy and useful ;-) docs.google.com/spreadsheets/d/1H3W82ayxGY47QtBXZwoCyYMUjmRYicOL3Q2U0sni51A/edit?usp=sharing
Back to CR. Volume at TBC is 511.24 +16(dish) -2.97(deck) +10.34(gasket) +46(chamber) = 576.61cc / 65.37cc = 8.821 CR. Success... we managed with 8.5 decompression forged pistons and the 1.7mm gasket, to reach the actual stock CR of 8.8. Bollocks... At least the build was ok and the car runs great. Happy boosting!