Engine Displacement Calculator

Background.

The figure on an engine's badge — 1.6, 2.0, 5.7 — is a rounded name for one geometric quantity: the volume every piston sweeps as it travels from the top of its cylinder to the bottom, added up across all the cylinders. Three measurements fix it completely. The bore is the cylinder's inside diameter, the stroke is how far the piston travels, and the cylinder count multiplies the result. The FAA's Aviation Maintenance Technician Handbook writes it as π × (bore ÷ 2)² × stroke × number of cylinders, and the same geometry holds for a car, a motorcycle, an outboard or a generator.

The rounding on the badge can be generous. Ford's famous 5.0 has a 4.00 in bore and a 3.00 in stroke, which works out to 301.6 cubic inches, or about 4.94 litres. Chevrolet's 350, with a 4.00 in bore and a 3.48 in stroke, is 349.85 cubic inches — the 5.7 L it was sold as. Working from the dimensions shows you what the engine actually is rather than what it is called.

That matters most when the dimensions change. Rebuilders bore worn cylinders oversize, and because the bore is squared, a 1% wider cylinder adds just over 2% to displacement while a 1% longer stroke adds only 1%. A different crankshaft can change the stroke outright. Either way the new figure can move an engine across a racing class, a licence category or a tax band drawn at a set number of cubic centimetres.

The bore-to-stroke ratio comes out alongside the volume. Square engines have bore equal to stroke; oversquare engines have a wider bore than stroke; undersquare engines have a longer stroke than bore. The label describes shape, which influences how fast the piston travels and how much room there is for valves, but by itself it does not set an engine's power or character.

What is engine displacement calculator?

Displacement, also called swept volume or piston displacement, is the volume a piston passes through between top dead centre and bottom dead centre, multiplied by the number of cylinders. Each cylinder's share is a plain geometric cylinder whose base is the circle of the bore and whose height is the stroke. It is quoted in cubic centimetres (cc), litres (1 L = 1,000 cc) or, for older American engines, cubic inches (1 cu in = 16.387064 cc exactly). It does not include the clearance volume left above the piston at top dead centre — the combustion chamber, head-gasket thickness and any space between the piston crown and the deck — so it is a measure of engine size, not of the total gas volume in the cylinder. Nor is it the amount of air an engine actually draws in, which depends on speed, valve timing and whether a turbocharger or supercharger is pressing more air in.

How to use this calculator.

1. 01Find the bore and stroke. A workshop manual or the manufacturer's specification table lists both; for a rebuilt engine use the finished bore measured after machining and the stroke of the crankshaft actually fitted.
2. 02Choose millimetres or inches. Both dimensions must be in the same unit, so convert one first if your sources disagree — 1 in is exactly 25.4 mm.
3. 03Enter the number of cylinders as a whole number. Every cylinder is assumed to share the same bore and stroke.
4. 04Read the total in cc, litres and cubic inches, and the volume of a single cylinder — useful for motorcycles and for comparing engines with different cylinder counts.
5. 05Check the bore-to-stroke ratio and its label to see whether the engine is square, oversquare or undersquare.

The formula.

For one cylinder the swept volume is the area of the bore circle times the stroke: V₁ = π × (B ÷ 2)² × S. Total displacement is V = V₁ × N, where N is the cylinder count. Inch dimensions are first converted with the exact definition 1 in = 25.4 mm, so the arithmetic runs in cubic millimetres. Dividing by 1,000 gives cubic centimetres, dividing again by 1,000 gives litres, and dividing cubic centimetres by 25.4³ ÷ 1,000 = 16.387064 gives cubic inches, an exact factor rather than a rounded one. The bore-to-stroke ratio is B ÷ S in the same unit, so it carries no unit. It is labelled square only when bore and stroke are exactly equal; any ratio above 1, however slight, is oversquare and any ratio below 1 undersquare. The sensitivity of the result follows from the exponents. Bore enters squared, so a small change in diameter is magnified: making the bore 1% larger raises displacement by 2.01%, while the same percentage change in stroke raises it by exactly 1%. Cylinder count enters linearly, which is why engine families built on a common bore and stroke come in neat steps — two, four or six of the same cylinder. The model is an ideal cylinder of constant diameter with every cylinder identical. It does not apply to rotary (Wankel) engines, whose chambers are not cylinders, or to opposed-piston designs where two pistons share one bore, and it ignores piston crown shape, which changes the clearance volume but not the swept volume.

A worked example.

Frequently asked questions.

References& sources.

1. [1]FAA. Aviation Maintenance Technician Handbook — General, cylinder displacement section and formula pi x (bore/2)^2 x stroke x number of cylinders.
2. [2]FAA. Aviation Maintenance Technician Handbook — Powerplant, Chapter 1; defines piston displacement and derives it from circular area, stroke, and cylinder count.
3. [3]U.S. Department of Energy. Internal Combustion Engine Basics; explains the fixed cylinder, moving piston, crankshaft, and four-stroke cycle context.
4. [4]MIT OpenCourseWare. Internal Combustion Engines measurement record; treats bore, stroke, and displacement as distinct measured engine quantities.
5. [5]NIST. SI Units — Length; official exact inch-to-millimeter relationship used for unit conversion.