Engine Displacement Formula & How to Calculate It

This calculator works out an engine’s displacement — the total volume swept by all its pistons — from the bore (cylinder diameter), stroke (piston travel distance), and number of cylinders. Enter those three values in either metric or imperial units, and you get the displacement in cubic centimeters (cc), liters, and cubic inches. The formula is: displacement = (π/4) × bore² × stroke × number of cylinders.

Formula

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

Where:

• Bore is the diameter of each cylinder (in mm, cm, or inches).
• Stroke is the distance the piston travels from top dead center (TDC) to bottom dead center (BDC) (in the same unit as bore).
• Number of cylinders is the count of cylinders in the engine (e.g., 4, 6, 8).
• π/4 is a constant that converts the bore diameter into the circular area of the cylinder face (since area = π × (bore/2)²).

The result is the total swept volume — the volume the pistons displace as they move. It does not include the combustion chamber volume (the space above the piston at TDC), which is part of the compression ratio calculation.

Worked Example

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

1. Convert bore to cm: 86 mm = 8.6 cm (we’ll work in cm to get cc directly).
2. Calculate the area of one cylinder: π × (8.6/2)² = 3.14159 × 4.3² = 3.14159 × 18.49 = 58.088 cm².
3. Multiply by stroke: 58.088 × 8.6 = 499.56 cm³ (cc) per cylinder.
4. Multiply by number of cylinders: 499.56 × 4 = 1998.2 cc.
5. Convert to liters: 1998.2 cc ÷ 1000 = 1.998 L (rounds to 2.0 L).
6. Convert to cubic inches: 1998.2 cc ÷ 16.387 = 121.9 cu in.

So a 4-cylinder engine with 86 mm bore and 86 mm stroke has a displacement of about 1998 cc, or 2.0 liters — a common engine size.

Why Displacement Matters

Displacement is a fundamental engine specification because it directly relates to how much air and fuel the engine can draw in per revolution. In general, a larger displacement means a larger potential power output (all else being equal), because more air-fuel mixture can be burned per cycle. This is why car models often use displacement in their names (e.g., “2.0L” or “5.0L V8”).

However, displacement alone does not determine power. Modern turbocharged engines with small displacement can produce more power than larger naturally aspirated engines because forced induction packs more air into the same volume. Efficiency, fuel consumption, and torque characteristics also depend on valve timing, compression ratio, fuel type, and tuning.

How to Measure Bore and Stroke

You typically don’t need to disassemble an engine to find bore and stroke — they are published in the vehicle’s service manual or online specifications. But if you’re building an engine or verifying specs, here’s how they’re measured:

• Bore: Measured across the cylinder’s inner diameter using a bore gauge or caliper. It’s the widest point of the cylinder wall.
• Stroke: Measured as the distance the piston travels from TDC to BDC. This is determined by the crankshaft’s throw (the offset of the rod journal from the main journal) — stroke = 2 × crank throw.

If you only know the crank throw, multiply it by 2 to get stroke. For example, a crank with a 43 mm throw gives an 86 mm stroke.

Common Mistakes and Unit Mix-ups

The most frequent error is mixing units. If you measure bore in inches but stroke in millimeters, the result will be wildly wrong. Always convert everything to the same unit before calculating. Here are other pitfalls:

• Forgetting the π/4 factor: Some people mistakenly use bore (not bore²) or skip the π/4, giving an area that’s too small.
• Using diameter instead of radius: The formula uses bore (diameter) with π/4; if you use radius, you must use π × r² instead. Both work, but mixing them gives wrong results.
• Including the combustion chamber volume: Displacement is only the swept volume. The chamber volume is added separately for compression ratio calculations.
• Rounding too early: Rounding bore or stroke to fewer decimals can shift the result by a few cc, which matters for racing classes or tax brackets.

Limits of the Formula

The formula assumes perfectly cylindrical cylinders and a flat piston top. In reality, pistons have domes or dishes, and cylinders may be slightly tapered after wear, but for standard calculations these differences are negligible. The formula gives the nominal displacement, which is what manufacturers list. Actual displacement can vary slightly due to manufacturing tolerances and wear.

Also, the formula does not account for the volume of the head gasket, the piston-to-wall clearance, or the combustion chamber — those are part of the compression ratio, not displacement. If you need the exact swept volume for a high-performance build, measure components individually and use the same formula with precise values.

Frequently Asked Questions

What does “cc” stand for?

cc stands for cubic centimeters, a metric unit of volume. 1 cc = 1 milliliter. Engine displacement is often quoted in cc (e.g., 1998 cc) or liters (1.998 L).

How do I convert cc to cubic inches?

1 cubic inch = 16.387 cc. So divide cc by 16.387 to get cubic inches. For example, 1998 cc ÷ 16.387 ≈ 121.9 cu in.

Does displacement affect fuel economy?

Generally, larger displacement engines consume more fuel because they pump more air and fuel per revolution. However, a small-displacement engine working hard may use more fuel than a larger engine cruising easily. Real-world economy depends on vehicle weight, gearing, driving style, and engine load.

Can I increase displacement?

Yes, by overboring (increasing the cylinder bore) or using a crankshaft with a longer stroke (stroker kit). This is a common engine modification, but it requires machining and may affect reliability and emissions compliance. Always consult a professional before modifying.

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

Because displacement is only one factor. Compression ratio, valve timing, camshaft profile, intake/exhaust flow, fuel delivery, and forced induction all affect power. Two 2.0L engines can differ by 50% or more in output.

Is displacement the same as engine size?

Yes, “engine size” in everyday language usually refers to displacement (e.g., a 2.0L engine). It is the total swept volume of all cylinders, not the physical dimensions of the engine block.

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in bore | Bore diameter | mm | 86 | 0
in stroke | Stroke length | mm | 86 | 0
in cyl | Number of cylinders | - | 4 | 1
out disp_cc | Displacement | cc | (pi/4) * bore^2 * stroke * cyl / 1000 | 1
out disp_l | Displacement | L | (pi/4) * bore^2 * stroke * cyl / 1000000 | 2
out disp_cu | Displacement | cu in | (pi/4) * bore^2 * stroke * cyl / 16387.064 | 1