Piston Displacement Calculator

Every time a piston goes down inside of a cylinder it displaces some volume of gas. The sum of the volumes displaced by each cylinder is the displacement volume of an engine. This single value determines the power output of an engine and the pumping capacity of a compressor. This tool calculates the displacement volume from bore diameter, stroke length and number of cylinders and can also be used in reverse. If any one field is left blank then that value will be calculated.

What is piston displacement?

The displacement of a piston is the volume that it displaces. Calculated per revolution this gives the engine displacement as quoted in technical data sheets, such as for a 2.0 litre car engine or a motorcycle with a 1000cc engine. Calculated per unit time this gives the volumetric flow rate which is used by manufacturers of compressors and vacuum pumps as a basis for specifying equipment performance.

This is based on the geometric concept of cylinder volume. The bore diameter is the inner diameter of the cylinder, while the stroke length is the distance traveled by the piston between top dead center (TDC) and bottom dead center (BDC). Multiplying the circular area of the piston face by the stroke length gives the volume displaced by a single cylinder. Further multiplying this by the number of cylinders yields the total displacement volume of the engine.

The formula for calculating the cylinder swept volume is:

For the displacement volume per revolution, the total displacement is the product of the piston surface area, stroke length and number of cylinders.

D is the bore diameter, L is the stroke and n is the number of cylinders. The first value is the area of the circular cross section of the bore. Multiplying this area by the stroke and the number of cylinders gives the total intake gas volume. To express the volume in a flow rate, it is multiplied by the rotational speed N, which is the number of revolutions per unit time.

Both volumes are based on the same geometric relationship. When expressed as a flow rate, only the rotational speed of the machine is taken into account in addition. Therefore larger engines or engines with higher rotational speeds can pump more air.

Calculation example:

Let's consider a four-cylinder compressor with a bore diameter of 80 mm, a stroke of 60 mm and a speed of 1450 rpm. The area of one cylinder is:

If a single cylinder covers this area over a distance of 60 mm, the volume is approximately 0.000302 cubic meters. Therefore, the volume per revolution of the four cylinders is about 1.21 liters, or 1206 cm³. At a speed of 1450 rpm, this results in:

The capacity of this machine is therefore 1.2 litres. At a speed of 1,450 rpm the theoretical flow rate is about 105 cubic metres per hour.

Instructions for using this calculator:

Enter the bore diameter, stroke and number of cylinders to instantly display engine displacement. The unit is either cubic centimeters or liters. If you also enter the rpm, then you can calculate volumetric air flow. Airflow units can be selected between cubic meters per hour, liters per minute, CFM (cubic feet per minute) and gallons per minute so that you can use the unit which is common in your field of study.

It can also be used in reverse. If you leave the speed blank and enter the desired volumetric air flow, the tool will calculate the required speed to achieve that airflow. You can also leave the bore diameter blank to determine suitable cylinder dimensions for given operating conditions. Regardless of which individual field you leave blank, the calculation tool will prompt you for a value in this field. No mode selection is needed.

Engine displacement and specifications in cubic centimeters:

The number next to the word "cc", such as "1998 cc" or "2.0 liters", indicates the volume of air that can be moved in cubic centimeters per revolution. This is essentially a measure of how much air an engine can inhale, and thus has a direct relationship with the power output of the motor. Therefore it's a common shorthand for indicating the size of an engine. A "100 cc" scooter and a "6.2 liter" V8 are at opposite ends of the same scale.

This tool displays this value as the main engine displacement volume, in addition to the volumetric swept volume of a single cylinder and the bore/stroke ratio. These two values are indicators that are often used by engine manufacturers.

Ratio of bore to stroke

The ratio of bore to stroke gives an indication of the characteristics of an engine. If the bore is larger than the stroke it is referred to as an "over-square" or "short-stroke" engine. This design is typical for sports gasoline engines, since it allows a high revving rate and power output at higher revs. If the stroke is longer than the bore, then it is an "under-square" or "long-stroke" engine. These engines produce more torque at lower revs, have a moderate increase in revs, and are often used in diesel engines or engines where durability is important.

The average piston speed is the product of stroke length and revolutions per second and is used as an indicator to limit the safe operating speed of an engine. In production engines, the average piston speed is generally kept below about 25 meters per second. Only race engines exceed this figure, and only with special components. Since the average piston speed depends on the stroke, long-stroke engines will reach the limit at lower revs than short-stroke engines. This is one of the reasons why long-stroke engines have a lower maximum rev count.

compression ratio

Once the cylinder's swept volume is known, the compression ratio can be calculated. The compression ratio is the ratio of the total volume of the cylinder (sum of the swept and clearance volumes) to the clearance volume at top dead center.

By opening the "Compression Ratio" tab and entering the clearance volume of a single cylinder, the calculator will provide you with the geometric compression ratio. Gasoline engines generally operate at a compression ratio from about 8 to 1 up to 12 to 1 while diesel engines have higher compression ratios, typically from about 14 to 1 up to 22 to 1.

Selection of a compressor (efficiency, mass flow rate, cooling)

The displacement volume is a theoretical maximum. A real piston compressor will not achieve this value. The gas remaining in the clearance space, the time required to open and close the valves, as well as leakages at the piston rings all reduce the flow rate. The proportion of actual flowing gas is called volumetric efficiency and for properly built machines it usually lies between about 75 percent and 90 percent. If you open the "Volumetric Efficiency" layer, you can reduce the theoretical value according to the percentage in order to obtain the actual flow that the machine delivers.

In refrigeration and air-conditioning systems two other values can be derived from the volume delivered. If you multiply the actual volume delivered by the density of the vapour at the compressor inlet, then you get the mass flow rate of the refrigerant. If you then multiply this mass flow rate by the cooling effect, i.e. the amount of heat absorbed per kilogram of refrigerant in the evaporator, then you get the cooling capacity. This is usually quoted in kilowatts or tons of refrigeration. In the "Cooling Capacity" tab these two values are calculated simultaneously.

Applications of the displacement volume

The same formula can be used for many applications. It can determine the specifications of engines for cars and motorcycles, air compressors to supply workshops with compressed air, vacuum pumps for industrial pipelines, and reciprocating compressors that are the heart of refrigeration systems. With slight modifications it can also represent double-acting compressors (where both ends of the piston work) and four-stroke engines. A four-stroke engine does not suck in a new air-fuel mixture on every turn, but only every two turns.