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Engine Displacement Calculator

CID equals N times pi over 4 times bore squared times stroke

Solution

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How It Works

Engine displacement is the total swept volume of every cylinder in one full cycle: CID = N × (π/4) × B² × S, where N is the number of cylinders, B is the bore diameter (cylinder ID), and S is the stroke (the distance the piston travels from bottom dead center to top dead center). The result is in cubic inches (CID); divide by 61.024 for liters or multiply by 16.387 for cubic centimeters. It is a purely geometric quantity — it does not depend on RPM, compression ratio, or volumetric efficiency.

Example Problem

A V8 engine has a 4.00-inch bore and a 3.48-inch stroke. Calculate total engine displacement in cubic inches and liters.

  1. Identify inputs: N = 8 cylinders, B = 4.00 in, S = 3.48 in.
  2. Compute bore area: (π/4) × B² = 0.7854 × 16.00 = 12.566 in².
  3. Multiply by stroke: 12.566 × 3.48 = 43.731 in³ per cylinder.
  4. Multiply by cylinder count: 43.731 × 8 = 349.85 in³.
  5. Convert to liters: 349.85 / 61.024 ≈ 5.73 L — a classic small-block 350.

Key Concepts

Displacement is the headline spec for combustion engines because it sets the upper bound on how much air the engine can ingest per cycle. A 5.0 L V8 sweeps 5 liters every two crankshaft revolutions (one complete four-stroke cycle), so at 6000 RPM it sweeps 15,000 L/min = 530 CFM if volumetric efficiency were 100%. Real engines fall short of that target — typical naturally aspirated street engines hit 80-90% VE. Bore-to-stroke ratio also affects character: over-square (bore > stroke) engines favor high-RPM horsepower; under-square engines favor low-end torque.

Applications

  • Engine building and rebuilding — verifying that bore-and-stroke choices hit the target displacement
  • Performance tuning — computing displacement before sizing an intake manifold, carburetor, or throttle body
  • Regulatory compliance — checking that an engine falls within a displacement-based class (e.g., racing class limits, tax tier in some countries)
  • Engine swap planning — comparing the displacement of a donor engine to the original
  • Educational and study reference for automotive technology students

Common Mistakes

  • Using bore radius instead of bore diameter — the formula uses B² where B is the full diameter, so squaring the radius gives ¼ of the right answer
  • Mixing units — entering bore in millimeters but stroke in inches without converting, or expecting an answer in liters when the formula returns cubic inches
  • Forgetting to multiply by cylinder count — single-cylinder displacement is per-cylinder, not total
  • Confusing displacement with effective displacement — turbo or supercharged engines effectively move more air than their geometric displacement implies
  • Using nominal sizes — a 350 ci engine is approximately 350; the actual bore/stroke of a Chevy 350 is 4.00 × 3.48 = 349.85 in³

Frequently Asked Questions

How do you calculate engine displacement?

Use CID = N × (π/4) × B² × S where N is the number of cylinders, B is the bore diameter in inches, and S is the stroke in inches. Multiply bore² by 0.7854 (which is π/4) to get bore area, then multiply by stroke and cylinder count.

What is the formula for engine displacement?

CID = N × (π/4) × B² × S, equivalent to CID = 0.7854 × N × B² × S. With B and S in inches the result is in cubic inches; divide by 61.024 for liters.

How do I convert cubic inches to liters?

Divide cubic inches by 61.024. For example: 350 in³ / 61.024 ≈ 5.74 L; 454 in³ / 61.024 ≈ 7.44 L; 302 in³ / 61.024 ≈ 4.95 L (often rounded to 5.0 L).

What is the difference between bore and stroke?

Bore is the inner diameter of the cylinder — how wide it is. Stroke is the distance the piston travels from bottom dead center to top dead center. Bore-to-stroke ratio influences whether an engine favors high-RPM horsepower (over-square) or low-end torque (under-square).

Does displacement include the combustion chamber?

No. Displacement is the swept volume only — the volume the piston actually moves through. The volume above top dead center (the combustion chamber, head gasket, and piston deck) is the clearance volume and is used to compute compression ratio, not displacement.

Why is a 5.0 L V8 sometimes called a 302?

Ford's 5.0 L V8 displaces 302 in³ (302 / 61.024 ≈ 4.95 L, rounded up to 5.0). Marketing uses metric, engineers use SAE. Chevy's 350 ci is 5.7 L, and the Hemi 426 is 7.0 L.

Reference: Heywood, John B. 1988. Internal Combustion Engine Fundamentals. McGraw-Hill.

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