# Engine displacement

Engine displacement is the swept volume of all the pistons inside the cylinders of a piston engine. The engine displacement does not include the volume of the combustion chambers.

The displacement is often used to represent the size of the engine, therefore it is sometimes referred to in the model name of a vehicle or to determine the road tax for the vehicle. The common metric units for displacement are cubic centimetres (cc or cm3) and litres (L), while the common imperial unit is cubic inches (CID or cu in).

## Definition

Engine displacement for a typical reciprocating piston engine is a volume calculated by multiplying together three values, the distance travelled by the piston (i.e. the stroke length) multiplied by the circular area determined by a cylinder's bore, multiplied by the number of cylinders. If the bore and stroke are in inches, the displacement will be given in cubic inches, and if in millimetres or centimetres, it will be in cubic centimetres or litres. Occasionally, vehicle manufacturers will publicize an engine's bore and stroke in inches but switch to metric cc or L for displacement.

The formula is:

${\displaystyle {\text{Displacement}}={\text{stroke length}}\times {\pi }\times ({\tfrac {1}{2}}\times {\text{bore}})^{2}\times {\text{number of cylinders}}}$

Variant types of internal combustion engines, like the Wankel engine or the oval-piston Honda NR motorcycle, use unique formulas for their nominal displacement, and sometimes scaling factors motorsport rules or displacement-based taxation systems.

## Governmental regulations

In several countries, the vehicle road taxes are proportional to the engine displacement. In countries where this is practiced, vehicle manufacturers often seek to increase power output through higher-revving engines or turbocharging, instead of increasing the displacement.

Examples of countries where the road taxes are based upon engine displacement:

• In some European countries, and which predates the EU, there is one charge for engines over 1.0 litre, and another at the level of about 1.6 litres.
• In the United Kingdom, cars registered after 1 March 2001 are taxed based on the exhaust emissions. However, cars registered before this date are taxed based on engine displacement. Cars under 1549 cm3 qualify for a lower tax rate.[1]
• In Japan, the engine displacement is one of the factors (along with overall vehicle size and power output) used to determine the vehicle size class and therefore the cost of road tax for the vehicle
• In France and some other EU countries, mopeds with a displacement of less than 50 cc (3.1 cu in) can be driven with minimum qualifications. This led to all light motorbikes having a displacement of about 49.9 cm3.
• In many areas of the United States, Canada (except Quebec[2]), Australia and New Zealand, the road taxes are not based on engine displacement. However, the engine displacement is often used in low-powered scooters or mopeds to determine whether a licence is required to operate the vehicle. A common threshold is 50 cc (3.1 cu in).

Wankel engines are able to produce higher power levels for a given displacement. Therefore, they are generally taxed as 1.5 times their stated physical displacement (1.3 litres becomes effectively 2.0, 2.0 becomes effectively 3.0), although actual power outputs can be higher than suggested by this conversion factor.

## Automotive model names

Historically, many car model names have included the engine displacement. Examples include the 1923–1930 Cadillac Series 353 (powered by a 353-cubic-inch engine), the 1963–1968 BMW 1800 (a 1.8-litre engine) and the 2000–2006 Lexus LS430 (a 4.3-litre engine).

However, trends towards turbocharging and hybrid/electric drivetrains since 2010 have resulted in far fewer model names being based on the engine displacement.