Engine Displacement Formula and Worked Example

Engine displacement is the total volume swept by all the pistons as they move from top dead center to bottom dead center. Use the formula V = (π/4) × bore² × stroke × number of cylinders; enter bore, stroke, and cylinder count to calculate the engine’s swept volume in cubic centimetres, litres, or cubic inches.

Formula

For a cylindrical cylinder, swept volume is its circular cross-sectional area multiplied by the piston’s travel. Multiply that volume by the number of cylinders:

V = (π/4) × B² × S × N

• V is total engine displacement.
• B is cylinder bore, the cylinder’s internal diameter.
• S is stroke, the distance the piston travels between its upper and lower limits.
• N is the number of cylinders.
• π is approximately 3.14159.

The calculator takes bore and stroke in millimetres. The formula first gives cubic millimetres; dividing by 1,000 converts that result to cubic centimetres (cc). Divide cc by 1,000 for litres, or by 16.387064 for cubic inches. The first result is rounded to the nearest whole cc; the litre result to two decimal places and the cubic-inch result to one decimal place.

Worked Example

Using the calculator’s defaults—an 86 mm bore, an 86 mm stroke, and four cylinders:

1. Area of one cylinder’s circular cross-section: (π/4) × 86² = about 5,808.8 mm².
2. Volume swept by one piston: 5,808.8 × 86 = about 499,557 mm³.
3. For four cylinders: 499,557 × 4 = about 1,998,228 mm³.
4. Convert to cc: 1,998,228 ÷ 1,000 = 1,998.228 cc, or 1,998 cc rounded to a whole cc.

The same result is about 2.00 L and 121.9 in³. The conversions use the unrounded displacement, which avoids adding rounding error along the way.

What Engine Displacement Means

Each piston sweeps a fixed volume as it travels through its cylinder. Adding the swept volumes of all cylinders gives the engine’s displacement. A four-cylinder engine with a 500 cc swept volume per cylinder, for example, has a total displacement of 2,000 cc, or 2.0 L.

Displacement is not the same as the engine’s total internal volume. The formula excludes the space left above each piston at top dead center, called the combustion chamber or clearance volume. That space matters when calculating compression ratio, but it is not part of swept displacement.

Displacement is also not a direct measurement of power. It is one factor in an engine’s potential airflow and output; design, tuning, operating speed, fuel, and forced induction can all affect power. Two engines with the same displacement can perform quite differently.

How to Find Bore and Stroke

Engine specifications commonly list bore and stroke, often in millimetres or inches. Check the technical specification for the exact engine variant: engines sold under the same model name may have different dimensions. If specifications are unavailable, accurate measurement requires access to the cylinders and suitable measuring tools. Bore is measured across the cylinder’s inside diameter; stroke is the piston’s full travel, not the connecting rod’s length.

For a simple geometric calculation, bore and stroke must use the same unit. If both are in millimetres, the formula produces mm³ before conversion. If both are in inches, it produces in³ directly. Do not combine a bore in millimetres with a stroke in inches without converting one first.

Units, Rounding, and Common Mistakes

Engine displacement is commonly reported in cc, litres, or cubic inches. One litre equals 1,000 cc, and one cubic inch equals exactly 16.387064 cubic centimetres. Specifications may round a nominal displacement for convenient naming, so a stated 2.0 L engine need not calculate to precisely 2,000 cc.

• Use bore as a diameter: The formula uses bore² as part of the circle-area calculation. Do not halve the bore first; the π/4 factor already accounts for radius.
• Use the full stroke: Stroke is the total distance from one piston limit to the other, not half that distance.
• Count every cylinder: Calculate one cylinder’s swept volume, then multiply by the actual cylinder count.
• Keep units consistent: Convert dimensions before calculating if they are expressed in different units.
• Round at the end: Intermediate rounding can cause small differences, especially when converting between cc, litres, and cubic inches.

Where the Formula Applies—and Its Limits

The standard formula assumes each cylinder has a circular bore and that the piston’s swept distance is the same for every cylinder. It applies to common reciprocating piston engines, including inline, V-shaped, and horizontally opposed layouts; cylinder arrangement does not change the arithmetic. Multiply the volume of one cylinder by the total number of cylinders.

Rotary engines do not have conventional cylinder bores and piston strokes, so this piston-engine formula does not directly describe their displacement. Their displacement specifications use conventions that can differ by context. Likewise, the calculation gives geometric swept volume, not actual air intake, fuel consumed, or power output.

Frequently Asked Questions

How do you calculate engine displacement in litres?
Calculate (π/4) × bore² × stroke × cylinder count using consistent units. If dimensions are in millimetres, divide the result in mm³ by 1,000,000 to get litres.

Is engine displacement the same as engine size?
In ordinary engine specifications, “engine size” often refers to displacement. It is the combined swept volume of the cylinders, not the engine’s external dimensions or total internal volume.

Does a larger displacement always mean more power?
No. A larger displacement can allow more air and fuel to be processed, but power also depends on factors such as engine design, operating speed, and tuning. Displacement alone cannot establish an engine’s output.

What is the difference between cc and cubic inches?
They are volume units: 1,000 cc equals one litre, and 1 in³ equals 16.387064 cc. The same engine has the same displacement regardless of which unit is used.

Does displacement include the combustion chamber?
No. Displacement measures only the volume swept by the pistons. Clearance volume above the piston at top dead center is included in calculations such as compression ratio, not swept displacement.

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in b | Bore | mm | 86 | 0
in s | Stroke | mm | 86 | 0
in c | Number of cylinders | - | 4 | 1
out cc | Engine displacement | cc | (pi / 4) * b ^ 2 * s * c / 1000 | 0
out l | Engine displacement | L | cc / 1000 | 2
out ci | Engine displacement | in³ | cc / 16.387064 | 1