How Engine Displacement Is Calculated

For a piston engine, displacement is the total swept volume of all cylinders. Bore determines cylinder area, stroke determines how far the piston travels, and cylinder count determines how many individual cylinder volumes contribute to the engine's total displacement.

Basic relationship

Total displacement is cylinder area multiplied by stroke and the number of cylinders:

Total Displacement = Cylinder Area × Stroke × Number of Cylinders

Because a cylinder's bore is its diameter, its cross-sectional area is:

Cylinder Area = π ÷ 4 × Bore²

Combining the two relationships gives the standard displacement formula:

Displacement = (π ÷ 4) × Bore² × Stroke × Number of Cylinders

Worked example

Inputs

Bore: 4.000 inches
Stroke: 3.480 inches
Number of cylinders: 8

Displacement of one cylinder

(π ÷ 4) × 4.000² × 3.480 ≈ 43.73 cubic inches

Total engine displacement

43.73 × 8 ≈ 349.8 cubic inches

Using the unrounded calculation, this is approximately 5733 cc, or 5.73 liters.

Why bore is squared

Bore determines the circular cross-sectional area of the cylinder. Because circle area depends on the square of the diameter, even a relatively small change in bore can noticeably change displacement.

Stroke affects displacement directly: if bore and cylinder count remain unchanged, increasing stroke increases swept volume in direct proportion to the stroke change.

Unit conversions

When bore and stroke are entered in inches, the formula produces cubic inches. When they are entered in millimeters, the result is cubic millimeters and must be converted to a more convenient unit.

1 cubic inch = 16.387064 cubic centimeters
1 liter = 1000 cubic centimeters
1 cubic centimeter = 1000 cubic millimeters

Bore, stroke and engine geometry

Two engines can have similar total displacement while using different bore and stroke combinations. Increasing bore increases cylinder area, while increasing stroke increases the distance swept by the piston. Displacement alone therefore does not describe the complete geometry or operating characteristics of an engine.

Important assumptions

Bore and stroke measurements use the same length unit before calculating volume.
All cylinders are assumed to have the same bore and stroke.
The calculation represents geometric swept volume between top dead center and bottom dead center.
Combustion-chamber, gasket, piston-dish or dome, and deck-clearance volumes are not part of engine displacement.

Common mistakes

Forgetting to square the bore: cylinder area depends on bore squared.
Using radius in a diameter-based formula: the formula above expects bore diameter.
Mixing inches and millimeters: use consistent units before calculating volume.
Forgetting cylinder count: the single-cylinder swept volume must be multiplied by the number of cylinders.
Confusing displacement with combustion-chamber volume: displacement is swept volume, not total cylinder volume at bottom dead center.

When to use this calculation

Engine displacement calculations are useful when comparing bore-and-stroke combinations, checking the effect of an overbore or stroke change, documenting an engine build, and supplying displacement for other airflow or performance calculations.

Limitations

This calculation determines geometric engine displacement from bore, stroke and cylinder count. It does not by itself predict horsepower, torque, airflow, compression ratio or engine efficiency. Those depend on additional engine dimensions and operating conditions.

Try it

Open the Engine Displacement Calculator →

Learn how compression ratio is calculated →