Engine Displacement Formula in Inches (CID)

This calculator works out an engine’s displacement in cubic inches (CID) from its bore, stroke, and number of cylinders. You enter the bore (cylinder diameter) and stroke (piston travel distance) in inches, plus the cylinder count, and you get the total swept volume in cubic inches (and liters). The formula is: displacement = (π/4) × bore² × stroke × number of cylinders.

Formula

In words: displacement = (π ÷ 4) × bore² × stroke × number of cylinders.

Symbols: D = (π/4) × B² × S × N

• D – displacement, in cubic inches (in³)
• B – bore (cylinder diameter), in inches (in)
• S – stroke (piston travel from bottom to top), in inches (in)
• N – number of cylinders (unitless)
• π – approximately 3.14159

To convert to liters, multiply the cubic inch result by 0.0163871 (since 1 L = 61.0237 in³).

Worked Example

Using the default values: bore = 4.0 in, stroke = 3.5 in, cylinders = 8.

1. Square the bore: 4.0² = 16.0 in²
2. Multiply by π/4: 16.0 × 0.785398 = 12.5664 in² (this is the piston area)
3. Multiply by stroke: 12.5664 × 3.5 = 43.9824 in³ (one cylinder volume)
4. Multiply by 8 cylinders: 43.9824 × 8 = 351.86 in³
5. Convert to liters: 351.86 × 0.0163871 = 5.77 L

The calculator shows 351.86 in³ and 5.77 L, matching this classic small-block V8 size.

Why Engine Displacement Matters

Displacement is the total volume swept by all pistons in one full engine cycle. It is a fundamental spec that indicates engine size and is used for:

• Comparing engines – a 5.0 L V8 vs. a 2.0 L four-cylinder tells you the larger one can ingest more air/fuel per revolution, typically producing more torque.
• Vehicle classification – many jurisdictions use displacement for taxes, insurance, or license classes (e.g., motorcycles under 125 cc).
• Estimating power potential – all else equal, more displacement means more air and fuel burned, so more power. But design factors (compression, valve timing, forced induction) heavily affect the actual output.
• Fuel economy expectations – larger displacement engines usually consume more fuel, though modern small-displacement turbo engines can match older larger engines in power with better efficiency.

How to Measure Bore and Stroke

Bore is the diameter of the cylinder, measured with an inside micrometer or bore gauge across the cylinder walls at the top (where wear is minimal). Stroke is the distance the piston travels between top dead center (TDC) and bottom dead center (BDC), which equals the crankshaft throw times two. Manufacturers publish these specs; you can also find them in service manuals or online databases.

If you have a stroker or overbore kit, use the actual machined measurements, not the stock values. For example, a 0.030-inch overbore on a 4.00-inch bore makes it 4.030 inches.

Common Mistakes and Misconceptions

• Mixing units – if bore is in millimeters and stroke in inches, the result is nonsense. Convert everything to inches first (1 mm = 0.03937 in).
• Forgetting the π/4 factor – some use the shortcut bore² × stroke × 0.7854 × cylinders. That 0.7854 is exactly π/4. Don’t double it.
• Using radius instead of diameter – the formula uses bore (diameter). If you mistakenly use the radius, you’ll get a quarter of the correct volume.
• Confusing displacement with total engine volume – displacement excludes combustion chamber volume (the space above the piston at TDC). Compression ratio accounts for that.
• Assuming displacement directly equals power – a high-revving small engine can make more power than a lazy big one. Displacement is only one factor.

Limits of the Displacement Formula

The formula gives the geometric swept volume, assuming a perfectly cylindrical bore and a flat piston top. Real engines have slight variations due to:

• Piston dome or dish volume (affects compression, not displacement)
• Cylinder wear or taper
• Connecting rod length and crank throw (stroke is fixed by crank)

For practical purposes, the formula is accurate to within a fraction of a percent. It does not account for volumetric efficiency (how well the engine actually fills the cylinders with air), which is why a 350 in³ engine might produce anywhere from 150 to 600+ horsepower depending on tuning.

Displacement in Other Units

While this calculator works in inches, you’ll often see displacement in:

• Cubic centimeters (cc) – common for motorcycles and small engines. 1 in³ = 16.3871 cc.
• Liters (L) – used for car engines. 1 L = 1000 cc = 61.0237 in³.

To convert from cubic inches to cc, multiply by 16.3871. To get liters, divide cc by 1000 or multiply cubic inches by 0.0163871. For example, a 350 in³ engine is 5,735 cc or 5.7 L.

Frequently Asked Questions

What is the formula for engine displacement in cubic inches?

The formula is: (π/4) × bore² × stroke × number of cylinders. Bore and stroke must be in inches. For a V8 with a 4-inch bore and 3.5-inch stroke, it’s 0.7854 × 16 × 3.5 × 8 = 351.86 in³.

How do I convert cubic inches to liters?

Multiply the cubic inch value by 0.0163871. For example, 350 in³ × 0.0163871 = 5.735 L. Conversely, multiply liters by 61.0237 to get cubic inches.

Does the formula work for any engine type (V8, inline-4, rotary)?

It works for any reciprocating piston engine (V, inline, flat, etc.) because you just multiply one cylinder’s volume by the total number of cylinders. It does not apply to Wankel rotary engines, which have a different displacement definition.

What is the difference between displacement and compression ratio?

Displacement is the volume swept by the piston, while compression ratio is the ratio of the total cylinder volume (swept + combustion chamber) at BDC to the combustion chamber volume at TDC. A high compression ratio can increase efficiency and power, but it’s independent of displacement.

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

Power depends on airflow, fuel delivery, ignition timing, valve timing, compression ratio, and engine speed. Two 2.0 L engines can differ by 100 horsepower if one is turbocharged and the other naturally aspirated, or if one revs to 7,000 rpm and the other to 5,000 rpm.

Is a bigger displacement always better?

Not necessarily. Bigger displacement usually means more torque and power potential, but it also means more internal friction, weight, and fuel consumption. Smaller turbocharged engines can offer similar power with better fuel economy, though they may have different driving characteristics.

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in bore | Bore (diameter) | in | 4.0 | 0
in stroke | Stroke | in | 3.5 | 0
in cyl | Number of cylinders | - | 8 | 1
out cid | Displacement | in³ | (pi/4) * bore^2 * stroke * cyl | 2
out liters | Displacement | L | cid * 0.0163871 | 2