Displacement is the volume the pistons sweep through in one full cycle — the area of one cylinder times the stroke, times the number of cylinders. It is the single number most used to describe an engine and it leaves out almost everything that matters.
The formula
One cylinder's swept volume is pi over four times the bore squared, times the stroke. With both in millimetres that gives cubic millimetres, so divide by a thousand for cubic centimetres.
An 86 by 86 mm four cylinder works out to 499.6 cc per cylinder, or 1,998 cc — which gets badged as a 2.0 litre. Almost every advertised displacement is rounded like this.
Cubic centimetres divide by 16.387 to give cubic inches. A 350 Chevrolet measures 349.8 cubic inches, which is 5,733 cc — badged 5.7 litres, and never exactly 350.
Bore counts twice, stroke once
Because the bore appears squared in the formula, a small increase in bore gains more volume than the same increase in stroke.
This is why overboring is the cheap way to add displacement during a rebuild. A 0.5 mm overbore on an 86 mm bore adds about 1.2 percent — modest, but it comes free with the machining the engine needed anyway.
Stroking an engine is the bigger lever but it requires a different crankshaft and usually different rods, which is a far more involved build.
Bore to stroke ratio tells you the character
An oversquare engine — bore wider than stroke — has lower piston speed at a given rpm and more room in the head for valves. Those two things together are why oversquare engines rev and breathe well.
An undersquare or long-stroke engine has more leverage on the crank, so it makes torque lower down, and its piston speed climbs faster so it runs out of revs sooner.
Neither is better. A motorcycle engine is strongly oversquare because it lives at high rpm; a tractor diesel is strongly undersquare because it lives at 1,800.
What displacement does not tell you
It does not include the combustion chamber volume, which sits above the piston at top dead centre and is not swept. That is why compression ratio needs the chamber, the gasket, the piston dish and the deck clearance as separate numbers.
It says nothing about how much air the engine actually breathes, which is what makes power. Forced induction changes that completely — a 2.0 litre turbo can move more air than a 3.5 litre naturally aspirated engine.
And it says nothing about the rev range, which is the other half of the power equation. Power is torque times rpm, so two engines of the same displacement can differ by a factor of three in output.
Why badges do not match
Manufacturers round displacement to the nearest tenth of a litre for badging, and sometimes round generously. A 1,998 cc engine becomes a 2.0; a 2,967 cc becomes a 3.0.
Tax and racing classes are the other reason. Where a class boundary sits at exactly 2,000 cc, engines get designed to come in a few cc under it, and 1,998 cc is a suspiciously common figure.
So a badge is a marketing round number. Bore and stroke are the actual specification, and they are what this calculator works from.