What is the formula for engine displacement?

Displacement is pi times the bore squared, times the stroke, times the number of cylinders, all divided by four. The bore squared and the pi over four are the area of the circle the piston sweeps; the stroke turns that area into a volume, and the cylinder count multiplies it. A square engine with an 86 mm bore and an 86 mm stroke over four cylinders comes to 1,998.23 cc, which is 1.998 litres and 121.94 cu in. The page prints that line with your own numbers in it.

Why is a 2.0 litre engine only 1,998 cc?

Because the badge is rounded and the geometry is not. The 86 mm bore and 86 mm stroke above sweep 1,998.23 cc, and rounded to the tenth of a litre an engine is badged with, that is a 2.0 L. Almost every badge works this way, so a figure that lands a few cc under or over a round number is the normal case rather than a sign that something was typed wrong.

How do I convert cc to cubic inches?

Divide by 16.387064. The inch is defined as exactly 25.4 mm, so a cubic inch is exactly 25.4 cubed cubic millimetres, or 16.387064 cc, and the conversion is a definition rather than a measurement. 1,998.23 cc is 121.94 cu in. Going the other way, a 4.00 in bore and 3.48 in stroke over eight cylinders is 349.85 cu in, which is 5,732.98 cc or 5.733 litres.

How do I work out the displacement of one cylinder?

Set the cylinder count to 1. The same 86 mm bore and stroke give 499.56 cc for a single cylinder, and the page also prints the per-cylinder figure beside the total whatever the count is, so a four cylinder engine shows 1,998.23 cc and 499.56 cc each in the same view.

Can it work out compression ratio or horsepower?

No, and that is deliberate. Displacement is swept volume: the space the piston passes through. Compression ratio needs the clearance volume left above the piston at the top of its travel, which depends on the combustion chamber, the head gasket, the piston crown and the deck height, none of which is bore or stroke. Power depends on far more than either. This page stays with the geometry and says so.

What do square, oversquare and undersquare mean?

They describe bore against stroke and nothing more. Bore equal to stroke is square, a bore wider than the stroke is oversquare, and a stroke longer than the bore is undersquare. The page names which one your figures are and prints the ratio. It draws no conclusion from it: two engines of the same displacement can be built either way.

Engine Displacement Calculator

Displacement is one piece of geometry: a cylinder is a circle of the bore's diameter swept through the stroke, and an engine has several of them. This page does that arithmetic and shows it. Type the bore, the stroke and the cylinder count in millimetres, centimetres or inches, and the swept volume comes back in cc, litres and cubic inches together, with the formula written out with your numbers in it and the volume of one cylinder beside the total. It refuses rather than guesses: a bore of zero, half a cylinder or a measurement longer than the field accepts gets a message naming the field, not a rounded answer.

Bore 86 mmStroke 86 mm4 cylinders

bore      86 mm
stroke    86 mm
cylinders 4

(pi / 4) x (86 mm)² x 86 mm x 4 = 1,998,228.86 mm³ = 1,998.23 cc

1,998.23 cc   1.998 L   121.94 cu in
499.56 cc per cylinder

Displacement: 1,998.23 cc
Litres: 1.998
Cubic in: 121.94
Cylinders: 4
Per cylinder: 499.56 cc

Bore 86 mm and stroke 86 mm, both read in millimetres, across 4 cylinders.
Bore to stroke is 1: they are equal, which is what a square engine means.
The inch is exactly 25.4 mm, so a cubic inch is exactly 16.387064 cc and a litre is exactly 1,000 cc.
Rounded the way an engine is badged, this one is a 2.0 L.

The engine

Bore is the width across one cylinder, stroke is how far the piston travels, and both are read in the unit you pick. A workshop manual quotes them in millimetres; an American engine is usually quoted in inches.

BoreStrokeMeasured in

Cylinders

Fields take up to 24 characters and refuse anything longer rather than quietly shortening it. A count has to be a whole number, and a bore or stroke of zero is refused rather than answered with zero.

Swept volume only: the clearance volume left above the piston is not part of it, so no compression ratio is worked out here.
Geometry only: nothing here estimates power or torque, and nothing here says what a change of bore or stroke would do to an engine.

Worked examples

Each one runs through the same function as your own numbers. Load one to see it in the fields.

86 x 86, 4 cyla square engine: bore equal to stroke
1,998.23 cc (1.998 L, 121.94 cu in)
Single cylinderthe same 86 x 86 bore and stroke, once
499.56 cc (0.5 L, 30.48 cu in)
Inches in4.00 x 3.48 in across 8 cylinders
349.85 cu in (5,732.98 cc, 5.733 L)

Swept volume, and only that. Exact geometry: pi times bore squared times stroke times the cylinder count, divided by four. It is the swept volume only, so it says nothing about compression, output or what any change would do to an engine.

Common questions

What is the formula for engine displacement?: Displacement is pi times the bore squared, times the stroke, times the number of cylinders, all divided by four. The bore squared and the pi over four are the area of the circle the piston sweeps; the stroke turns that area into a volume, and the cylinder count multiplies it. A square engine with an 86 mm bore and an 86 mm stroke over four cylinders comes to 1,998.23 cc, which is 1.998 litres and 121.94 cu in. The page prints that line with your own numbers in it.
Why is a 2.0 litre engine only 1,998 cc?: Because the badge is rounded and the geometry is not. The 86 mm bore and 86 mm stroke above sweep 1,998.23 cc, and rounded to the tenth of a litre an engine is badged with, that is a 2.0 L. Almost every badge works this way, so a figure that lands a few cc under or over a round number is the normal case rather than a sign that something was typed wrong.
How do I convert cc to cubic inches?: Divide by 16.387064. The inch is defined as exactly 25.4 mm, so a cubic inch is exactly 25.4 cubed cubic millimetres, or 16.387064 cc, and the conversion is a definition rather than a measurement. 1,998.23 cc is 121.94 cu in. Going the other way, a 4.00 in bore and 3.48 in stroke over eight cylinders is 349.85 cu in, which is 5,732.98 cc or 5.733 litres.
How do I work out the displacement of one cylinder?: Set the cylinder count to 1. The same 86 mm bore and stroke give 499.56 cc for a single cylinder, and the page also prints the per-cylinder figure beside the total whatever the count is, so a four cylinder engine shows 1,998.23 cc and 499.56 cc each in the same view.
Can it work out compression ratio or horsepower?: No, and that is deliberate. Displacement is swept volume: the space the piston passes through. Compression ratio needs the clearance volume left above the piston at the top of its travel, which depends on the combustion chamber, the head gasket, the piston crown and the deck height, none of which is bore or stroke. Power depends on far more than either. This page stays with the geometry and says so.
What do square, oversquare and undersquare mean?: They describe bore against stroke and nothing more. Bore equal to stroke is square, a bore wider than the stroke is oversquare, and a stroke longer than the bore is undersquare. The page names which one your figures are and prints the ratio. It draws no conclusion from it: two engines of the same displacement can be built either way.
What units and limits does it take?: Bore and stroke in millimetres, centimetres or inches, with one unit for both, and a whole number of cylinders from 1 to 128. Fields take up to 24 characters and refuse anything longer rather than quietly shortening it, a bore or stroke over 10,000 mm is refused with the ceiling named, and every refusal says which field to fix. Nothing you type leaves the browser.

Exact geometry: pi times bore squared times stroke times the cylinder count, divided by four. It is the swept volume only, so it says nothing about compression, output or what any change would do to an engine.