How to calculate compression ratio

The compression ratio is the volume above a piston at bottom dead centre (BDC) divided by the volume of the combustion chamber – the space above the piston at top dead centre (TDC). Because of the complex shapes of the combustion chamber, normally you calculate its volume by manually measuring the volume of liquid it can hold, which means removing the cylinder head to then get to the combustion chamber, although most standard engines should have this figure already calculated.

The equation for compression ratio of an engines cylinder is as follows:

(Stroke * (Bore/2)2 * π + Vc) / Vc

You can also write it as:

(Stroke * bore2 * (π/4) + Vc ) /Vc

Where:

Stroke is the distance of the piston travels from BDC to TDC measured in centimetres (cm) Bore is the diameter of the cylinder, divided by 2 to get the radius measured in centimetres (cm) π is Pi, the mathematical ratio between a circles circumference and its diameter, typically 3.14 to 2 decimal places Vc is the volume of the combustion chamber – or commonly known as the clearance volume which is the space above the piston at TDC measured in cubic centimetres (cc)

The below diagram shows what the 2 volumes graphically:

Compression Ratio

So, given that the cylinders combustion chamber holds 18cc of liquid, the stroke is 7cm and the bore is 6cm the compression ration would be 12 : 1 based upon the equation:

(7cm * (6cm/2)2 * 3.14 + 18cc) / 18cc = (7cm * 9 * 3.14) + 18cc) / 18cc = (197.82cc + 18cc) / 18cc = 215.82cc / 18cc = 11.99 = 12 (rounded up)

Remember if you measure bore and stroke in millimetres to convert either these figures to centimeters or convert Vc to cubic millilitres.

The higher the compression ratio the more mechanical force is generated and a stronger spark is needed to ignite the mixture. This also means that knocking/ pre-ignition can occur due to the high compression which is why higher compression ratios use higher octane rated fuels – octane being the measure of a unit of fuels ability to burn while resisting pre-ignition.

Typical values for compression ratios on the average petrol engine are usually not much higher than 10 : 1. The above calculation does not take into account loss of compression via the inlet valve which remains open just after BDC and occurs more commonly at low speeds, this calculation is known as dynamic compression ratio. Dynamic compression ratio is always lower than the static model calculated above and takes into account cam timing, heat expansion and piston velocity but generally you only need to start calculating this for high performance race engines.

You can increase the compression ratio slightly by using thinner cylinder body gaskets and by machining the base of the cylinder to reduce it’s height thus increasing the compression ratio minimally. Also valve timing and overlap will have an effect on compression – race bikes with high valve overlap will typically idle very poorly due to low compression but at high engine speeds will have better compression where as road bikes with smaller overlaps work in the opposite way.

Engines need high compression to create the pressure neccessary to create enough force to rotate the crankshaft, if the piston seals, valves or gaskets are damaged then the engine will not be able to produce the required pressure – typically manifesting itself in very poor idle, difficulty in starting and running very lumpy. You can check that your engine has good compression by doing a compression test.

Compression Ratio Calculator

Stroke (cm)
Bore (cm)
Combustion Chamber Volume (Vc) (cc)
Compression Ratio to 1

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