Three calculators for the cylinder arithmetic behind engine rebuilds, head and block machining and the engine repair test. The first takes bore, stroke and cylinder count and gives the swept volume per cylinder and the total displacement in cc, liters and cubic inches, with the bore-to-stroke ratio. The second builds the clearance volume from the chamber in the head, the gasket bore, the deck clearance and the piston dish or dome, and gives the static compression ratio; a quick mode takes swept and clearance volumes straight from a question. The third shows what milling the head or changing the gasket does to the ratio, and works backwards from a target ratio to the clearance volume it needs. One toggle sets millimeters or inches for every length on the page; volumes stay in cc with cubic inches alongside. Defaults are loaded (a 96 × 92 mm four-cylinder gives 2,663.7 cc, 2.66 L or 162.5 in³; the same cylinder with a 52 cc chamber, a 97 × 1.0 mm gasket, 0.5 mm deck clearance and a 3 cc dish is 11.09:1; milling 0.5 mm takes it to 11.67:1), and the working is printed under each result in the form a test answer takes.
One unit setting for the whole page. Bore, stroke, gasket and deck dimensions are in mm; volumes are always in cc (1 cc = 1 mL), with cubic inches shown alongside.
Engine displacement
Compression ratio
Change of compression ratio
01Engine displacement: the formula and a worked example in both unit systems
Displacement is the volume the pistons sweep in one full cycle: the volume of one cylinder between top dead center and bottom dead center, multiplied by the number of cylinders. Each cylinder is a circle of the bore diameter extruded along the stroke, so the swept volume is the area of the bore times the stroke. In symbols,
V = π/4 × bore² × stroke × cylinders
π/4 is 0.7854. The same thing written with the radius is π × r² × stroke, and the two are identical because r = bore/2 and (bore/2)² = bore²/4. Use whichever the formula sheet gives, but do not mix them: putting the bore where the radius belongs multiplies the answer by four.
In millimeters. A 96 mm bore and a 92 mm stroke: 0.7854 × 96² × 92 = 0.7854 × 9,216 × 92 = 665,917 mm³. There are 1,000 mm³ in a cubic centimeter, so that is 665.92 cc per cylinder. Four cylinders: 665.92 × 4 = 2,663.7 cc, which is 2.664 L. Divide by 16.387 for cubic inches: 162.5 in³.
In inches. The same engine is 3.7795 in bore and 3.6220 in stroke (divide millimeters by 25.4). 0.7854 × 3.7795² × 3.6220 = 40.637 in³ per cylinder; times four is 162.5 in³. Multiply by 16.387 to get back to cc: 2,663.7 cc. The two routes agree to within rounding, which is the check to run when a question gives one unit and the options are in the other.
The calculator also prints the bore-to-stroke ratio. Bore larger than stroke (96 / 92 = 1.043 here) is oversquare; stroke longer than bore is undersquare; equal is square. The ratio changes nothing in the displacement arithmetic, but the terms turn up in engine descriptions and in questions about engine design, and the calculator names the case so you can check your own reading of it.
02Why displacement is quoted in liters, and how the figure is rounded
A cubic centimeter and a milliliter are the same volume, and 1,000 of either make a liter, so 2,663.7 cc is 2.6637 L. Engines are sold by the liter because the number is short. The exact displacement lives in the service information; the badge, the model name and most parts catalogs use a rounded figure, normally to the nearest tenth of a liter. 2,663.7 cc rounds to 2.7 L, even though it is closer to 2.66 than to 2.70. That is why the liter figure cannot be run backwards through the displacement formula: 2.7 L could be anything from 2,650 to 2,749 cc, and two engines with different bores and strokes can carry the same badge.
The rounding is not always to the nearest tenth. A manufacturer may choose the figure that fits a model naming scheme or a tax class, so an engine can be marketed at a figure a tenth away from where arithmetic would put it. Treat the badge as a name, not a measurement, and identify an engine by its engine code or VIN when you are ordering parts or looking up specifications.
North American engines were quoted in cubic inches for decades, and older service literature still is. The conversion is 1 in³ = 16.387 cc, so 1 L = 61.02 in³. An engine of 350 in³ is 350 × 16.387 = 5,735 cc, which is sold as 5.7 L. The calculator prints all three units so you can match whichever one a question or a manual uses.
03Compression ratio: what the clearance volume is made of, with a full worked example
Compression ratio compares the volume above the piston at bottom dead center with the volume above it at top dead center. The volume at BDC is the swept volume plus the clearance volume; the volume at TDC is the clearance volume alone. So
CR = (swept volume + clearance volume) / clearance volume
for one cylinder. Swept volume is the single-cylinder figure from the displacement formula, not the whole engine. Clearance volume is everything that is still open above the piston crown when the piston is at TDC, and on a real engine it has four parts:
- The combustion chamber in the head, measured with a burette and a plate, or taken from service information or the head manufacturer.
- The head gasket bore: a cylinder the diameter of the gasket opening and the height of the compressed gasket thickness. The gasket bore is normally a little larger than the cylinder bore.
- The deck clearance: the space between the piston crown and the block deck at TDC, a cylinder the diameter of the bore and the height of that gap. If the piston sits below the deck the volume is added; if the crown protrudes above the deck it is subtracted, and the calculator takes a negative deck figure for that.
- The piston crown: a dish or valve reliefs add volume, a dome takes it away. Piston manufacturers quote this as a cc figure, positive for a dish and negative for a dome, and the calculator uses the same sign convention.
Worked example (the calculator's defaults). Bore 96 mm, stroke 92 mm, chamber 52 cc, gasket bore 97 mm at 1.0 mm compressed, piston 0.5 mm below the deck, 3 cc dish.
Swept volume = 0.7854 × 96² × 92 / 1,000 = 665.92 cc.
Gasket volume = 0.7854 × 97² × 1.0 / 1,000 = 7.39 cc.
Deck volume = 0.7854 × 96² × 0.5 / 1,000 = 3.62 cc.
Clearance volume = 52 + 7.39 + 3.62 + 3 = 66.01 cc.
CR = (665.92 + 66.01) / 66.01 = 731.93 / 66.01 = 11.09:1.
The gasket and deck together are 11.0 cc, about a sixth of the clearance volume. Leave them out and the ratio comes out at 12.36:1 instead of 11.09:1, which is the kind of gap a set of multiple-choice options is built around. A question that gives only a chamber volume and calls it the clearance volume is telling you to use the quick mode; a question that lists gasket and deck figures expects you to add them.
04Static versus dynamic (effective) compression, and why cam timing changes it
Everything above is the static or geometric ratio, fixed by the metal. The dynamic or effective ratio is what the charge actually sees, and it is lower, because the intake valve does not close at bottom dead center. It closes some way into the compression stroke, and until it does the cylinder is still open to the intake port, so the piston is not compressing anything. Only the part of the stroke after intake valve closing counts. A camshaft with a later intake closing point, which is what longer duration means, lowers the effective ratio, and it lowers it most at low engine speed, where there is no intake ram effect to keep filling the cylinder against the rising piston. That is why an engine built for a long-duration cam is usually given a higher static ratio to compensate, and why a mild cam in a high-compression engine can bring on detonation at low speed. Boost from a turbocharger or supercharger works the other way: it raises the pressure in the cylinder at valve closing without changing either ratio, which is why boosted engines are built with lower static ratios. When a question says compression ratio without qualification it means the static ratio, and the calculators on this page compute the static ratio only.
05Diesel engines: why the ratio is higher
A diesel has no spark plug. It compresses air alone until the air is hot enough to ignite the fuel that is injected into it near the top of the stroke. That is the whole reason its compression ratio is much higher than a gasoline engine's: the ratio has to deliver ignition temperature by compression alone, every stroke, including a cold start. A gasoline engine compresses a mixture of fuel and air, and its ratio is limited in the other direction, because too much compression makes the mixture ignite on its own before the spark, which is detonation. Each fuel is matched to a compression ratio the engine designer chose for that fuel's ignition behavior. The specific ratio for a given engine is in its service information; it is not something to guess at from the fuel type.
The geometry of the clearance volume is different too. A direct-injection diesel usually has a nearly flat head face and puts most of the chamber in a bowl in the piston crown, so the piston dish figure is large and the head chamber figure is small, and the deck clearance (or piston protrusion above the deck) is a tightly controlled dimension.An indirect-injection diesel adds a prechamber in the head, which is part of the clearance volume as well. The compression ratio calculator handles all of these: enter the bowl as a positive dish, the flat head's small chamber volume, and a negative deck figure for protrusion.
For a test question, the arithmetic is the same as for any engine. What changes is the diagnostic reasoning around it: low compression in a diesel shows up as hard starting and white smoke before it shows up as lost power, because the air is not reaching ignition temperature, and a compression test on a diesel is read against the manufacturer's figure and the spread between cylinders rather than a general rule of thumb.
06Milling the head or changing the gasket, and the reverse example
The compression ratio changes whenever the clearance volume changes, and the swept volume stays as it is. Two of the common ways the clearance volume moves in a rebuild are the head face and the gasket.
Milling the head face to true it up removes metal from the chamber side, so the chamber gets shallower and the ratio goes up. The simplest estimate treats the metal removed as a disc the diameter of the bore and the thickness of the cut: ΔV ≈ π/4 × bore² × cut. With the example engine, a 0.5 mm cut removes about 0.7854 × 96² × 0.5 / 1,000 = 3.62 cc. Clearance volume falls from 66.01 to 62.39 cc, and CR = (665.92 + 62.39) / 62.39 = 11.67:1, up from 11.09:1.
This is an approximation, and it errs on the high side. The chamber outline at the head face is usually smaller than the bore, with the quench or squish area of the head filling the rest, so the volume actually taken off the chamber is less than a full bore-diameter disc. Head manufacturers sometimes publish cc per millimeter or per thousandth of an inch for a given casting; if you have that figure, use it. Otherwise measure the chamber with a burette after machining. Milling also has side effects that are not about ratio: on an overhead-cam engine it shortens the distance between the crank and the cam, which retards the valve timing unless the chain or belt tension and the cam sprocket allow for it, it reduces valve-to-piston clearance, and on a V engine it moves the head faces inward so the intake manifold may need to be machined to match.
A thicker gasket does the opposite. Going from a 1.0 mm to a 1.5 mm compressed thickness with the same 97 mm bore adds 0.7854 × 97² × 0.5 / 1,000 = 3.69 cc. Clearance volume rises to 69.70 cc and CR = (665.92 + 69.70) / 69.70 = 10.55:1. This is one of the ways a shop restores the ratio after a head has been milled, and the reason gasket thickness is a specification rather than a convenience.
The reverse question: what clearance volume gives a chosen ratio? Rearrange CR = (S + C) / C to C = S / (CR − 1). For 12:1 with the example cylinder, C = 665.92 / 11 = 60.54 cc. The present clearance is 66.01 cc, so 5.47 cc has to go. Spread over the bore area that is 5.47 / (0.7854 × 96² / 1,000) = about 0.76 mm off the head face, or the same volume taken out with a thinner gasket, a piston with a smaller dish, or a combination. The third calculator prints this working for any target ratio.
07Common mistakes
- Radius where the bore belongs. The formula is π/4 × bore² or π × radius², and the two agree. Putting the bore into the radius version gives four times the true volume. If a displacement comes out at over 10 L for a four-cylinder car engine, this is why.
- Forgetting the gasket and deck volumes. They are small next to the chamber but they are not nothing. In the worked example they are 11.0 cc together, and leaving them out moves the ratio from 11.09:1 to 12.36:1.
- Mixing millimeters and inches. Bore in inches and stroke in millimeters, or a bore of 3.78 typed into a page set to millimeters, gives nonsense that can still look like a plausible number. Convert everything to one system before you start (25.4 mm to the inch), and set the toggle on this page before you type. Volumes are the one thing that do not change with the toggle: a 52 cc chamber is 52 cc either way.
- Worrying about cc versus mL. This one is not a mistake. A cubic centimeter and a milliliter are the same volume by definition, so a 52 mL chamber and a 52 cc chamber are the same thing. Burettes read in mL; specifications say cc. Use them interchangeably.
- Getting the dome sign backwards. A dish or valve relief adds to the clearance volume and lowers the ratio; a dome fills part of the chamber and raises it. Piston catalogs follow that sign (dish positive, dome negative), and so does the calculator. Entering a 3 cc dome as +3 instead of −3 in the example moves the ratio to 11.09:1 instead of 12.10:1.
- Dividing swept by clearance. The ratio is (swept + clearance) / clearance, not swept / clearance. The second gives exactly one less: 10.09 instead of 11.09 in the example, and question writers know it.
- Using the whole engine's displacement in the ratio. Compression ratio is per cylinder. Total displacement over one clearance volume gives a ratio four, six or eight times too large.
- Treating the milling estimate as exact. The bore-area estimate overstates the volume removed when the chamber outline is smaller than the bore. Measure after machining.
08Where this shows up on ASE tests
On the ASE A1 Engine Repair test, the cylinder head and the block are their own content areas: cylinder head and valve train diagnosis and repair is 6 questions and engine block diagnosis and repair is 4, of the 45 scored. Their task lists cover checking the head and block deck for warpage, measuring the cylinder bore, and installing the gasket and head, which is where milling, gasket thickness and deck clearance questions come from.
General engine diagnosis, area A, is the largest part of the A1 test at 18 questions, and it includes cranking, running and relative compression tests and leak-down tests. You will not be asked to compute a compression ratio from a compression gauge reading (they are different things), but you will be asked to read a set of compression results, and knowing what clearance volume does to cylinder pressure helps.
Learn the two formulas: displacement = 0.7854 × bore² × stroke × cylinders, and CR = (swept + clearance) / clearance. Then practice building the clearance volume from all four parts, because leaving out the gasket or the deck volume is the wrong answer a question writer will offer.
The free A1 questions include engine items in the same four-option format as the test.
09Sources
- ASE (National Institute for Automotive Service Excellence): certification tests and study guides the test specifications (content areas and question counts) and task lists for the Automobile tests, which the ASE sections on this page paraphrase.
- Compression ratio (reference article) the static compression ratio definition (swept plus clearance volume over clearance volume) and the static versus dynamic distinction used on this page.
10Questions people ask
- How do you calculate engine displacement?
- Multiply pi/4 (0.7854) by the bore squared, by the stroke and by the number of cylinders. In millimeters the answer is in cubic millimeters; divide by 1,000 for cc and by another 1,000 for liters. A 96 mm bore and 92 mm stroke four-cylinder is 0.7854 x 96^2 x 92 x 4 / 1,000 = 2,663.7 cc, or 2.66 L. In inches the same formula gives cubic inches; multiply by 16.387 for cc.
- How do you calculate compression ratio?
- Add the swept volume of one cylinder to the clearance volume and divide by the clearance volume: CR = (swept + clearance) / clearance. The clearance volume is the combustion chamber in the head plus the head gasket bore volume plus the deck clearance volume plus any piston dish (a dome subtracts). For a 665.9 cc cylinder with a 66.0 cc clearance volume, CR = (665.9 + 66.0) / 66.0 = 11.09:1.
- What happens to compression ratio if you mill the head?
- It goes up, because the chamber gets shallower and the clearance volume falls while the swept volume stays the same. The volume removed is roughly pi/4 x bore^2 x the depth of the cut; on a 96 mm bore a 0.5 mm cut removes about 3.6 cc, which takes the example engine from 11.09:1 to 11.67:1. That estimate overstates the change slightly when the chamber is smaller than the bore, so measure the chamber after machining. A thicker head gasket brings the ratio back down.
- Is a cc the same as a mL?
- Yes. A cubic centimeter and a milliliter are the same volume by definition, and 1,000 of either make one liter. Combustion chambers are measured with a burette in milliliters and specified in cc, and the two figures are interchangeable. A cubic inch is 16.387 cc.
- What is the difference between static and dynamic compression ratio?
- The static ratio is the geometric one, fixed by bore, stroke and clearance volume, and it is what a specification or test question means by compression ratio. The dynamic or effective ratio is lower, because the intake valve closes after bottom dead center and compression only begins from that point. A camshaft with later intake valve closing lowers the effective ratio, most of all at low engine speed, which is why engines built for long-duration cams are given higher static ratios.
11Practice for the test
Displacement, compression and machining questions sit in the cylinder head, block and diagnosis areas of the A1 test. ToolboxPrep practice tests follow each ASE test specification area by area, and every answer is explained, including why each wrong option is wrong. You can try free sample questions with no account.
Ten free questions per test, no account: free practice questions. How our questions are written and checked: how our questions are made.
Related guides
ToolboxPrep is an independent study site. It is not affiliated with or endorsed by ASE (the National Institute for Automotive Service Excellence). Our questions are original practice questions written to the published ASE test specifications; they are not actual test questions.