For example, if I have a text file thats 1000K, then run bzip2 on it (probably the best widely available text compressor), it's 200K, then the compression ratio is 5:1.

Some compression algorithms are lossy, typically multimedia ones, e.g. JPEG and MPEG. This means that when things are decompressed, they are not exactly the same as when they were compressed. This usually allows a higher compression ratio. Some algorithms allow quality settings to trade off quality against compression ratio.

In general, the compression ratio depends to some extent on the input. Some things, such as, say a very repetitive text document, will compress very well; while others, say a phonebook, which doesn't have that much repetition will not compress so well. So, for example, bzip2's typical compression ratio is anywhere from 2:1 to 5:1, depending on what you try to compress.

However, a recent trend for some applications is fixed compression ratios; automatically fixing the compression ratio, then trading off quality as necessary. For example, MP3 (more accurately: MPEG-1 Audio Layer III) audio encoders usually have a fixed compression ratio. If you compress a stereo 16-bit 44.1KHz (i.e. CD-quality) recording to 128kbps MP3, it will be an 11:1 compression ratio. MP3 does have support for variable bit-rate technology (i.e. for bits that need lots of aural detail, you bump up the bitrate ... i.e reduce the compression ratio), but nobody seems to use it.

Typical compression ratios for gasoline engines are in the neighborhood of about 9:1. A higher compression ratio gives more power out of an engine, but requires the use of a fuel with a higher octane rating. This increase in power (both horsepower and torque) causes engine components to wear more quickly and the engine must be kept in better operating condition.

Diesel engines have much higher compression ratios than gasoline engines, usually like 18:1 (sometimes as high as 24:1). The fuel/air mix must be compressed much more tightly in a diesel engine so it will combust on it's own. Diesel engines don't have spark plugs, making for a much simpler engine (They do have glow plugs which are used to preheat the cylinders to make starting easier in cold weather.) Because of this higher compression ratio, diesel engines are much more stout - their cylinder walls and piston heads are thicker and heavier than those in a gasoline engine.

The thermal efficiency of an internal combustion engine is related to the compression ratio by the following equation:

Efficiency = 1-(1/compression ratio)^(1-gamma)

Gamma is the ratio of specific heats of the working fluid involved. For pure air it would be 1.4. However, this involves a lot of simplification, and I have found that setting gamma to 1.175 gives an accurate, real-world efficiency result for gasoline engines.

From this equation, it is obvious that raising the compression ratio of an engine will increase thermal efficiency, and power. However, this effect only takes place at compression ratios up to 17:1. Above 17:1, the efficiency and power actually drop (this is not represented in the formula).

Also, increasing the compression ratio requires an increase in fuel octane. The grades of fuel and their corresponding maximum compression ratios are shown below (This is only a rough guide. The actual octane requirement depends on a myriad of factors)

Regular (87 AKI): 8:1

Mid-Grade (89 AKI): 9:1

Premium (93 AKI): 10:1

Regardless, knowing how to calculate your engine's C/R is especially important when you're seeking to improve performance.

There are dozens of simple formulas out there, but they are often a good percentage off from the actual C/R. And being slightly off in your calculation could mean the difference between an engine that purrs like a kitten and an engine that detonates and sends a piston through your crankshaft.

Point being, you don't fuck around with compression ratios. You must precisely measure each of the specifications, then perform the correct calculation. Here's what you'll need to know.

Measurements

• Cylinder Bore
  This is the diameter of the cylinders of your engine block. Since you'll most likely have a machine shop bore or hone your cylinders, it is best that you have then perform this measurement down to the thousandth of an inch (or, to a hundredth of a millimeter) and give you that number.
• Crackshaft Stroke
  This is the distance the piston travels from the top to the bottom of the cylinder. You measure this from the centerline of the crankshaft to the centerline of one of its arms. Then double it. Or, you could have the machine shop measure this for you as well.
• Combustion Chamber Volume
  Combustion chamber, in this instance, refers to the bottomside of the head, where the valves are sitting. One can measure this with some Play-Do, but that's not extremely accurate. You want extremely accurate. Have the shop measure this. And while they're doing that, why not have them do a port and polish and 5-angle valve job?
• Crown (-) or Dish (+) Volume
  Some pistons are not flat-topped. They may have extrusions, known as crowns, or indentations, known as dishes. While the shop guys are calculating the volume of your combustion chambers, have them figure out how much volume is reduced by the piston crown, or increased by the piston dish.
• Head Gasket Thickness
  When you buy a head gasket, it will typically state how thick it is. Just look on the box. If you're still not sure, use a micrometer to gauge thickness.
• Head Gasket Bore
  This is the diameter of the cylinder holes in the head gasket. Typically, they are NOT exactly the same size as your cylinder bore - So measure them.
• Deck Height
  This is the distance between the crankshaft centerline (when mounted in the engine block) and the deck. The deck is the flat surface which the cylinders are embedded in.
• Compression Height
  The compression height is the distince between the centerline of the piston wrist pin and the top of the piston. If the piston has a crown or dish, you do not count it - You only count the major flat portion of the piston.
• Connecting Rod Length
  This is the distince between the centerline of the piston wrist pin and the centerline of the crankshaft.

Math

1. Determine Cylinder Volume
   The formula for calculating the volume of a cylinder is:
   ( π * ( r ² ) * h )
   Radius is one-half of the cylinder bore. Height is equal to the crankshaft stroke. Work this formula out and you now have the displacement of an individual cylinder.
2. Determine Combustion Chamber Volume
   This combustion chamber volume is very different from that listed above. It takes into account the size of the head combustion chambers, the volume contained in the head gasket, the volume between the top of the deck and the top of the piston, and the volume subtracted/added by the piston crown/dish. Therefore, determining this has several steps of its own.
   1. Determine Head Gasket Volume
      You use the same formula for head gasket volume as you did for cylinder volume, since they're both cylindrical in nature.
   2. Determine Volume Between Deck and Piston
      This one's trickier, but not much. You know the diameter of the cylinder already, so you can easily find the radius. We know deck height. But how far from the deck is the piston? Simply add the Compression Height to the Connecting Rod Length. Then subtract that number from the Deck Height. You've now got the height portion of this equation. Use the cylinder formula and you'll have this measurement.
   
   Now, you have Head Chamber Volume, Gasket Volume, Deck to Piston Volume, and Crown Volume. Add them up! This gives you the volume of gasses after the piston has reached top dead center of its stroke.
3. Determine Compression Ratio
   You're almost home. Now, compression ratio, as stated in the previous wus, is the ratio of the volume of the air present in the cylinder at bottom dead center compared to the amount at top dead center. At BDC, the volume is the total between Cylinder Volume and Combustion Chamber Volume. At TDC, it's just the Combustion Chamber Volume. That leaves us with this formula:
   

   ( (Cylinder Volume) + (Combustion Chamber Volume) ) / (Combustion Chamber Volume)

   Do the math and voila! You've got your compression ratio!

This concludes the lesson on how to calculate compression ratios. Go forth and hot rod.