Motor Displacement Calculator: Formula and Examples

A motor displacement calculator estimates the volume swept by a piston as it moves through one cylinder’s full stroke, then multiplies that volume by the engine’s cylinder count. Enter the cylinder bore, stroke, and number of cylinders to get displacement in cubic centimeters, liters, and cubic inches.

Formula

The calculator treats each cylinder as a circular bore and calculates the cylinder volume swept by the piston. Total engine displacement is that volume multiplied by the number of cylinders:

Displacement = (π ÷ 4) × bore² × stroke × cylinder count

In this calculator, bore and stroke are entered in millimeters. The result in cubic millimeters is divided by 1,000 to get cubic centimeters (cc). Divide cubic centimeters by 1,000 for liters, or by 16.387064 for cubic inches.

• Bore: the cylinder’s internal diameter, in millimeters.
• Stroke: the distance the piston travels from top dead center to bottom dead center, in millimeters.
• Cylinder count: the number of cylinders whose swept volumes are included.
• π: pi, approximately 3.14159.

The formula gives swept volume, not the total space inside a cylinder. It does not include the combustion chamber volume above the piston at top dead center.

Worked Example

Using the calculator’s default values—an 86 mm bore, an 86 mm stroke, and four cylinders—calculate the swept volume of one cylinder first:

π ÷ 4 × 86² × 86 = approximately 499,557.7 cubic millimeters.

Multiply by four cylinders and convert cubic millimeters to cubic centimeters:

499,557.7 × 4 ÷ 1,000 = 1,998.2 cc. Rounded to the calculator’s zero decimal places, the headline result is 1,998 cc.

Convert that same result to liters: 1,998.2 ÷ 1,000 = 1.9982 L, which displays as 2.00 L. In cubic inches, 1,998.2 ÷ 16.387064 = approximately 121.9 cu in, displayed as 121.9 cu in.

What Engine Displacement Means

Engine displacement is the combined volume swept by all pistons during one complete stroke from bottom dead center to top dead center. It describes a geometric property of an engine. A larger displacement generally means the cylinders draw in a greater volume of air-fuel mixture in a naturally aspirated four-stroke engine, but displacement alone does not determine power, fuel consumption, or performance.

Displacement is commonly reported in liters or cubic centimeters for many metric-market vehicles, and in cubic inches in some contexts. The terms “cc,” “cm³,” and “cubic centimeters” refer to the same volume unit. For scale, 1 liter equals 1,000 cc, while 1 cubic inch equals exactly 16.387064 cubic centimeters.

When to Use the Calculator

Use the calculation when you know an engine’s bore, stroke, and cylinder count and want to verify its geometric displacement, compare engine configurations, or understand a specification. It also helps show why cylinder count matters: two engines with the same bore and stroke but different numbers of cylinders have different total displacement.

• Use the manufacturer’s or engine-builder’s stated bore and stroke where available.
• Enter both dimensions in millimeters. If your measurements are in inches, convert them first: 1 inch = 25.4 mm.
• Enter the total number of cylinders, not the number of pistons per bank or the number of strokes in a cycle.
• Compare results in the same unit and at the same rounding precision.

For example, a 3.50-inch bore is 88.9 mm, and a 3.25-inch stroke is 82.55 mm. Do not enter those inch figures into fields labeled millimeters: because bore is squared in the formula, using the wrong unit can produce a particularly large error.

Measurements, Rounding, and Limits

Use bore diameter rather than radius. The formula contains bore², so entering a radius instead of a diameter makes the result one quarter of the correct value for each cylinder. Measure or source the actual cylinder bore if precision matters: a nominal engine size or rounded specification may not match the exact dimensions.

The calculator rounds the headline cc value to a whole cubic centimeter, liters to two decimal places, and cubic inches to one decimal place. Those display choices do not mean the underlying measurements are exact to that precision. Manufacturing tolerances, wear, machining, and the precision of the supplied measurements affect the result. The unrounded figure is useful for checking conversions; the rounded figure is usually easier to compare with published engine descriptions.

This is a geometric calculation for conventional piston-cylinder engines. It does not estimate compression ratio, which also requires the clearance volume at top dead center, nor does it determine horsepower or torque. For a rotary engine or a different engine design, the meaning and reporting convention for “displacement” may differ, so a piston-engine bore-and-stroke formula may not be appropriate.

Frequently Asked Questions

How do you calculate engine displacement?
Multiply π ÷ 4 by bore squared, stroke, and cylinder count. Keep bore and stroke in matching units, then convert the resulting volume to cc, liters, or cubic inches as needed.

How many cc are in one liter?
One liter is 1,000 cubic centimeters. To convert cc to liters, divide by 1,000; to convert liters to cc, multiply by 1,000.

How do I convert cubic inches to cc?
Multiply cubic inches by 16.387064. For example, 100 cu in is about 1,638.7 cc, or 1.64 L.

Does displacement mean the volume of the combustion chamber?
No. Displacement is the volume swept by the piston during its stroke. Combustion-chamber clearance volume is the remaining space when the piston is at top dead center and is a separate measurement.

Can displacement tell me how much power an engine makes?
No. Displacement is one factor among many. Engine design, air supply, operating speed, tuning, and other characteristics also affect power, so this formula does not calculate horsepower or torque.

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in bore | Cylinder bore | mm | 86 | 0
in stroke | Piston stroke | mm | 86 | 0
in cylinders | Number of cylinders | - | 4 | 0
out cc | Engine displacement | cc | pi / 4 * bore ^ 2 * stroke * cylinders / 1000 | 0
out liters | Engine displacement | L | cc / 1000 | 2
out cubic_inches | Engine displacement | cu in | cc / 16.387064 | 1