Displacement Calculation Formula & How to Use It

This calculator works out the displacement of an engine from its bore, stroke, and number of cylinders. Enter those three values and you get the total swept volume in cubic centimeters (cc) or cubic inches (ci), plus the displacement per cylinder. The formula multiplies the area of one cylinder by the stroke length, then by the number of cylinders.

Formula

The standard engine displacement formula is:

Displacement = (π/4) × bore² × stroke × number of cylinders

Where:

• Bore = diameter of one cylinder (mm or in)
• Stroke = distance the piston travels from top dead center to bottom dead center (mm or in)
• Number of cylinders = how many cylinders the engine has (4, 6, 8, etc.)
• π/4 = constant that converts bore diameter to the circular area of the cylinder (π × r² = π × (bore/2)² = π/4 × bore²)

If you use millimeters, the result is in cubic millimeters; divide by 1,000 to get cubic centimeters (cc). If you use inches, the result is in cubic inches (ci). To convert cc to ci, divide by 16.3871.

Worked Example

Using the default values: bore = 86 mm, stroke = 86 mm, cylinders = 4.

1. Area of one cylinder = π/4 × (86)² = 0.7854 × 7,396 = 5,809.9 mm²
2. Volume of one cylinder = 5,809.9 × 86 = 499,651 mm³ = 499.65 cc
3. Total displacement = 499.65 × 4 = 1,998.6 cc
4. In cubic inches: 1,998.6 / 16.3871 = 121.96 ci

The calculator shows 1,998.6 cc and 122.0 ci, matching the steps above.

Why Displacement Matters

Displacement is the total volume swept by all pistons in one complete cycle. It is a rough indicator of an engine’s power potential: larger displacement can burn more fuel and air per revolution, so it typically produces more torque and power at lower RPM. However, modern turbocharging and variable valve timing mean a small-displacement engine can outperform a larger naturally aspirated one. Displacement is also used for vehicle taxation in many countries, insurance classes, and racing class regulations.

How to Measure Bore and Stroke

Bore is measured with a caliper or bore gauge across the cylinder’s inner diameter, usually at the top of the cylinder where wear is minimal. Stroke is measured by rotating the crankshaft and measuring the piston travel from TDC to BDC, or by reading the crankshaft spec. For an engine that has been bored or stroked (modified), you must use the actual measured values, not the factory specs. If you only know the engine code, look up the original bore and stroke, but be aware that overbore kits can increase bore by 0.5–1 mm.

Common Mistakes and Misconceptions

• Mixing units: If you mix inches and millimeters, the result is off by a factor of 25.4³ (about 16,387). Always use consistent units.
• Forgetting the π/4: Some people use π × r² but forget that bore is a diameter, not a radius. Using bore² without π/4 gives a result 27% too large.
• Using the wrong stroke: Stroke is the piston travel, not the connecting rod length. Many beginners mistakenly use rod length.
• Rounding too early: Rounding bore or stroke to the nearest millimeter can change displacement by several cc. Use precise measurements (e.g., 86.5 mm) for accuracy.

Limits of the Formula

The formula gives the swept volume of the cylinders. It does not account for the combustion chamber volume, piston dome or dish, head gasket thickness, or deck clearance. Those affect the compression ratio, not displacement. The formula also assumes a perfectly cylindrical bore; in reality, cylinders taper slightly with wear. For a rebuilt engine, the bore is usually oversize (e.g., +0.5 mm), so the displacement increases slightly. For a stock engine, the factory bore and stroke are exact enough for most purposes.

Frequently Asked Questions

What is the difference between displacement and engine size?

They are the same thing. Engine size, engine capacity, and displacement all refer to the total swept volume of all cylinders. In cars, it is usually expressed in liters (e.g., 2.0 L = 2,000 cc) or cubic inches (e.g., 350 ci). Motorcycles and small engines are often in cc.

Does a bigger displacement always mean more power?

Not necessarily. Displacement is one factor; compression ratio, valve timing, fuel delivery, turbocharging, and RPM range all affect power. A turbocharged 1.5 L engine can produce more power than a naturally aspirated 2.5 L engine. However, for similar technology, larger displacement generally produces more torque and power.

How do I convert cc to cubic inches?

Divide the cc value by 16.3871. For example, 2,000 cc ÷ 16.3871 = 122.05 ci. Conversely, multiply cubic inches by 16.3871 to get cc.

What does “bored over” mean?

It means the cylinder bore has been enlarged by machining, usually to remove wear or to increase displacement. A typical overbore is 0.5 mm or 1 mm. For example, a 350 ci engine bored 0.030 inches (0.76 mm) over becomes about 355 ci.

Does displacement include the combustion chamber?

No. Displacement is only the volume swept by the piston between TDC and BDC. The combustion chamber volume (above the piston at TDC) is separate and is used to calculate compression ratio. The total cylinder volume is displacement plus combustion chamber volume.

Why do some engines have the same displacement but different power?

Because power depends on more than displacement. Two 2.0 L engines can differ by 50 hp due to compression ratio, camshaft profiles, intake/exhaust flow, fuel injection tuning, and forced induction. Displacement is just the physical volume; efficiency and RPM determine how much power is extracted from that volume.

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in bore | Cylinder bore | mm | 86 | 0
in stroke | Piston stroke | mm | 86 | 0
in cyl | Number of cylinders | - | 4 | 1
out disp_cc | Displacement (cc) | cc | pi/4 * bore^2 * stroke * cyl / 1000 | 1
out disp_ci | Displacement (cu in) | cu in | pi/4 * bore^2 * stroke * cyl / 1000 / 16.3871 | 2
out per_cyl | Per cylinder (cc) | cc | pi/4 * bore^2 * stroke / 1000 | 1