How is an engine's displacement calculated?

Sometimes, we assume that certain basic terms we use when talking about engines are familiar to everyone. For that reason, we’re launching a new section on our website where we’ll answer many questions like these, so that everyone can understand how internal combustion engines work.

We’re always talking about 2-liter engines, 1.5-liter turbocharged engines… and we assume that everyone understands what that means. If you’re not quite sure, don’t worry—this article will clear things up for you.

What is an engine’s displacement?

An engine’s displacement is defined as the volume occupied by all of the engine’s cylinders. In other words, it’s the sum of the volume of each of the engine’s cylinders. For example, if an engine has 4 cylinders, each with a volume of 500 cubic centimeters, its total displacement will be 4 × 500 = 2,000 cubic centimeters, or 2 liters.

Why is it important to know an engine’s displacement?

Knowing an engine’s displacement is important. Not just to boast that your car’s engine is bigger, but because it has a number of technical and legal implications:

• It allows you to estimate the power and torque the engine can generate. Generally speaking, the larger the displacement, the greater the power. Obviously, there are exceptions.
• It helps categorize vehicles into different segments and compare models. For example, small compact cars typically have engines ranging from 1,200 to 1,500 cc. A midsize vehicle usually has an engine of around 2 liters, while larger vehicles typically feature engines like the V6, which generally range from 3 liters and up.
• It’s useful for calculating a vehicle’s taxes and insurance costs, which are usually based on engine displacement. Although it may sound ridiculous, in many countries—such as Spain—engine displacement is the figure used to determine the “fiscal horsepower.”
• It helps mechanics identify the correct parts to repair or maintain a specific engine.

Therefore, this technical specification provides valuable information about an engine’s performance and characteristics for various purposes. Now that we know this, let’s explain how to calculate it.

Formula for Calculating an Engine’s Displacement

An engine’s displacement is calculated using a simple mathematical formula that takes three main factors into account:

• The cylinder area: determined by the cylinder’s internal diameter.
• The stroke: the vertical distance the piston travels inside the cylinder.
• The number of cylinders in the engine.

The complete formula is as follows:

Displacement (cc) = Cylinder area (cm²) * Stroke (cm) * Number of cylinders

Let’s take a closer look at each of these components:

Cylinder Diameter

This refers to the internal diameter of each cylinder, which is usually constant in an engine. It is measured in centimeters and determined using precision instruments when the engine is disassembled. In small engines, it is about 5 cm, while in large engines it exceeds 15 cm.

Piston stroke

This is the vertical distance traveled by each piston from top dead center (the highest position) to bottom dead center (the lowest position) inside the cylinder. The longer the stroke—for a given diameter—the greater the displacement. The typical stroke ranges from 8 to 12 cm in most car engines.

Number of Cylinders

The total number of cylinders, together with the previous variables, defines the total displacement. Engines generally have 3, 4, 5, 6, or 8 cylinders, arranged in a straight line (longitudinally) or in a V-shape (transversely). Today, inline 3- and 4-cylinder engines are most common in small and midsize cars.

Calculation Example

Let’s imagine a 6-cylinder engine, with an internal diameter of 10 cm for each cylinder and a stroke of 9 cm. First, we find the area of each cylinder using the formula for the area of a circle:

Area of each cylinder = π * radius² = 3.1416 * (10 cm / 2)² = 3.1416 * 5 cm * 5 cm = 78.5 cm²

Then we apply the main formula:

Total displacement = 78.5 cm² × 9 cm (stroke) × 6 cylinders = 4.167 cc = 4.2 liters

Units of Measurement for Displacement

It is standard practice to use units from the International System of Units (SI). However, there are several ways to express the same value in the automotive industry. The most commonly used units for measuring an engine’s displacement are as follows:

• Cubic centimeters (cc or cm³): This is the unit of the metric system. It directly expresses volume in centimeters.
• Liters (L): Equivalent to 1,000 cc, making it very useful for expressing the displacement of large engines more simply.
• Cubic inches (in³): used primarily in North America and the United Kingdom. One cubic inch is approximately equal to 16.39 cc.

The conversions between these units are easy to calculate; you just need to remember how many cc are in a liter or a cubic inch. There are also calculators and conversion tables available online.

Factors That Influence Displacement

When designing an engine, engineers must carefully choose the displacement based on several factors, which we’ll discuss below:

• Engine size: Displacement is directly related to physical dimensions. A larger, heavier engine can accommodate pistons with greater diameter and stroke.
• Performance and power: With a larger displacement, greater power and torque can be achieved by optimizing variables such as the compression ratio, turbocharger, etc. This affects the vehicle’s performance.
• Fuel consumption: Engines with high displacement require more fuel to operate. This results in higher operating costs for the user. There is a trade-off between power and efficiency.

In conclusion, there is no universal ideal displacement, as this will depend on the type of vehicle, intended use, emissions regulations, and other factors. Manufacturers seek the best balance in each case. In addition, many European manufacturers have chosen to downsize their engines—that is, make them smaller but boost their power with turbochargers—in order to comply with the emissions regulations that have been implemented in the EU.

How to Find an Engine’s Displacement

It’s interesting to know how displacement is measured. However, you certainly don’t want to take your engine apart to do the calculations. There are several ways to find out the displacement of an engine already installed in a vehicle. The main ones are:

In the vehicle’s documentation

The most straightforward way is to look for this technical data in the vehicle’s original documentation:

• Owner’s Manual: All owner’s or user’s manuals detail the main technical specifications, including the engine’s displacement or capacity. It is usually expressed in cubic centimeters or liters.
• Technical specifications: This is a formal document containing the vehicle’s complete technical characteristics. Among them is the engine displacement. When you bought your car—whether new or used—you were given a set of technical specifications. You can also access this document online. For example, in Spain, you can do so through the DGT’s Digital Portal.

Both the manual and the technical specifications sheet provide the manufacturer’s displacement figure, which is very useful as a reference. The drawback may be not having these documents on hand, although in countries like Spain, this document is required to complete the sale.

Using the License Plate

Another option is to use the vehicle identification number (VIN) or license plate number to look up the vehicle’s specifications in specialized databases:

• Identification codes: VINs contain codes that allow you to identify the engine displacement. The first digits represent the manufacturer and model, while the tenth digit indicates the engine size. This information can be found in detailed tables for each make and model.
• License plate: by paying for a report on specialized websites such as CARFAX.