Editing Compression ratio (section)

==Mathematical formula==
In a [[reciprocating engine]], the static compression ratio (<math>\mathrm{CR}</math>) is the ratio between the volume of the [[cylinder (engine)|cylinder]] and combustion chamber when the piston is at the [[bottom dead center|bottom of its stroke]], and the volume of the combustion chamber when the piston is at the [[top dead center|top of its stroke]].<ref>{{citation
|last=Encyclopædia Britannica
|title=Compression ratio
|url=https://www.britannica.com/technology/compression-ratio
|access-date=2009-07-21}}
</ref> It is therefore calculated by the formula<ref>{{cite web |title=Calculated Compression Ratios |website=SQ Engineering |url=https://www.sq-engineering.com/tech-articles/calculating-compression-ratios/ |url-status=live |archive-url=https://web.archive.org/web/20090907212047/http://s-86.com/s-cr.html |archive-date=7 September 2009}}</ref>
<math display="block">\mathrm{CR} = \frac { V_d + V_c} {V_c}</math>

where
*<math>V_d</math> is the displacement volume. This is the volume inside the cylinder displaced by the piston from the beginning of the compression stroke to the end of the stroke.
*<math>V_c</math> is the clearance volume. This is the volume of the space in the cylinder left at the end of the compression stroke.

<math>V_d</math> can be estimated by the [[cylinder#Volume|cylinder volume]] formula:
<math display="block">V_d = \tfrac{\pi} {4} b^2 s</math>

where
*<math>b</math> is the [[cylinder (engine)|cylinder]] [[Bore (engine)|bore]] (diameter)
*<math>s</math> is the [[piston]] [[stroke (engine)|stroke]] length

Because of the complex shape of <math>V_c</math> it is usually measured directly. This is often done by filling the cylinder with liquid and then measuring the volume of the used liquid.