Engine displacement:
the swept volume of all cylinders

What displacement measures

When a piston travels from the top to the bottom of its cylinder it sweeps out a cylinder-shaped volume. Displacement is that volume, added up for every cylinder. It says how much air and fuel mixture the engine can draw in over one cycle, which is why it is the headline figure for engine size.

Engine capacity is quoted in cubic centimetres (cc) or in litres. One litre equals 1,000 cc, so an engine of 1,809.56 cm³ is about 1.8 litres. Motorcycles and scooters are usually described in cc, while cars are commonly described in litres.

The formula, step by step

1. 1Square the bore: 8² = 64.
2. 2Multiply by π ÷ 4 (about 0.7854): 64 × 0.7854 = 50.265 cm², the area of the piston.
3. 3Multiply by the stroke: 50.265 × 9 = 452.39 cm³ per cylinder.
4. 4Multiply by the number of cylinders: 452.39 × 4 = 1,809.56 cm³.

Unit traps

Specifications often list bore and stroke in millimetres, such as 80.0 × 90.0 mm. Squaring a millimetre figure gives mm², and the final answer is in mm³, which is a million times larger than a litre-sized number would suggest.

The simplest method is to convert mm to cm first, dividing by 10, so 80 mm becomes 8 cm and 90 mm becomes 9 cm. Then the result lands in cc, and your sense of scale stays intact.

Short stroke, long stroke and square engines

The ratio of bore to stroke tells you how the engine is shaped. Here it is 8 ÷ 9 = 0.89, which is slightly undersquare: the stroke is longer than the bore. Undersquare engines tend to make torque at lower speeds. Oversquare engines have a bore larger than the stroke and tend to rev more freely.

Two engines can share the same displacement with different shapes. A 2-litre engine could be 4 cylinders of 500 cm³ each, or 6 cylinders of about 333 cm³ each. Displacement alone does not say how much power an engine makes; that also depends on breathing, fuel, turbocharging and tuning.

Using the cylinder volume on its own

Sometimes you only need a single cylinder, for example when comparing a single-cylinder motorcycle with one cylinder of a multi-cylinder engine. The per-cylinder figure for the example is 452.39 cm³. A cylinder-volume tool computes π × r² × h, so enter a radius of half the bore, 4 cm, and the stroke of 9 cm as the height.

Finding the bore or stroke you need

The formula can be rearranged when you know the target capacity and one dimension. To find the stroke for a 1,809.56 cm³, 4-cylinder engine with an 8 cm bore, divide the capacity by the cylinders and by the piston area: 1809.56 ÷ 4 = 452.39 cm³; piston area 50.265 cm²; stroke = 452.39 ÷ 50.265 = 9.0 cm.

Likewise, if you know displacement and cylinder count, you get the cylinder volume. A 1,000 cc three-cylinder engine has 333.3 cm³ per cylinder. With a square design where bore equals stroke, the cube of the bore is 333.3 × 4 ÷ π = 424.4, so the bore is about 7.5 cm. This kind of back-calculation is useful when comparing designs or checking a claimed capacity.

Displacement is not compression ratio

Displacement and compression ratio are often mixed up. Displacement is the swept volume, a measure of size. Compression ratio compares the total cylinder volume at the bottom of the stroke with the small clearance volume left at the top. A compression ratio of 10:1 means the mixture is squeezed into one-tenth of its original volume.

With a swept volume of 452.39 cm³ per cylinder, a 10:1 ratio implies a clearance volume of 452.39 ÷ (10 − 1) = 50.27 cm³ above the piston at the top. Higher displacement lets an engine move more air, while compression ratio affects how efficiently the burn converts fuel into work. Both appear on spec sheets, but they answer different questions.

Capacity also interacts with how the engine is used. A larger engine at low load can be less efficient than a smaller one working harder, which is one reason turbocharged small-capacity engines have become common. The swept-volume figure remains the starting point for any such comparison.

Why the quoted figure is rounded

Manufacturers publish rounded capacity, such as 1,798 cc or '1.8 L', and the official figure is often calculated from bore and stroke measured to a tenth of a millimetre. A tiny change in the bore, such as 0.1 mm after a rebore, changes displacement by a fraction of a per cent.

• Tax, insurance and licensing classes in many places are based on displacement, so the exact value can matter.
• Competition classes set strict limits, which is why overbore and stroker kits are regulated.
• Fuel consumption tends to rise with displacement, but turbocharged small engines can blur that rule.
• Two-stroke and four-stroke engines of the same cc make power differently.