Engine Displacement Calculator

How engine displacement is calculated

Displacement is the volume the pistons sweep in one stroke, added up over all the cylinders. Each piston travels the length of the stroke inside a bore of known diameter, so every cylinder sweeps a short column with the area of the bore as its base: π/4 × bore² × stroke. Multiply by the number of cylinders and you have the engine’s displacement, the figure that usually ends up as its name.

Displacement does not include the combustion chamber or anything else above the piston at top dead center. That volume matters for the compression ratio calculator, not for engine size. It has nothing to do with rpm either: it is fixed by bore, stroke and cylinder count, which is why it is the standard way to compare engines of different eras and layouts.

US builders talk in cubic inches, most of the world in liters or cc. The calculator gives all three at once with the exact factor of 16.387064 cc per cubic inch, so you never chain rounded conversions. Used as an engine displacement calculator in cc, it also gives the swept volume of each cylinder, and you can type the bore and stroke in millimeters by switching to metric.

What to enter and where to find it

• Cylinder bore. The finished diameter of the cylinder, from the machine shop’s work order or the block’s specification. A rebuilt engine has often been bored oversize, so the original figure may no longer apply. Don’t use the piston diameter: pistons are made slightly smaller than the bore to leave running clearance.
• Stroke. Twice the crank throw, from the crankshaft’s specification; a stroker crank is sold by its stroke. On an assembled engine it is the distance the piston travels from top dead center to bottom dead center.
• Cylinders. Every cylinder counts the same, whatever the layout: inline, V or flat.
• New bore and stroke (Stroker tab) and target displacement (third tab). The combination you are considering, or the size you want to reach. In metric units the target is typed in liters.

Cylinder bore and stroke: square, oversquare and undersquare

The bore/stroke ratio describes the shape of the cylinder, not its size. Above 1 an engine is oversquare, with a bore larger than its stroke; at 1 it is square; below 1 it is undersquare, or long-stroke. Heywood’s Internal Combustion Engine Fundamentals gives 0.8 to 1.2 as the usual range for small and medium-size engines.

A big bore leaves room for larger valves and keeps the piston moving more slowly at a given rpm, which suits an engine built to rev; the piston speed calculator shows that side of it. A long stroke reaches the same displacement with a smaller bore and a more compact combustion chamber. Neither is better on its own: it depends on what the engine is built to do.

Used as a bore stroke calculator, the third tab answers the reverse question: what bore a target size needs with the stroke you have, and what stroke it needs with the bore you have.

Stroker calculator: what a new crank or an overbore adds

Displacement grows with the square of the bore but only in direct proportion to the stroke. That makes the bore look like the better lever, but in practice a block can only be bored a few hundredths of an inch before its cylinder walls get too thin, while a stroker crank can add a quarter of an inch or more of stroke.

The Stroker tab compares the engine as it is with the new combination and gives the change in cubic inches and in percent; the drawing overlays the two cylinders to scale. The table under the first tab’s result does the same for the common overbore sizes. A longer stroke also lifts the piston higher at top dead center, so it usually needs a shorter rod or a piston with a shorter compression height; check the new deck clearance with the deck height tab of the compression ratio calculator.

The engine displacement formula

Every result comes from the volume of a cylinder. Nothing here is an estimate: the only uncertainty is in the bore and stroke you enter.

1. Displacement (ci) = π/4 × bore (in)² × stroke (in) × cylinders
2. Liters = cubic inches × 0.016387064
3. cc = cubic inches × 16.387064
4. Bore = √(4 × displacement ÷ (π × stroke × cylinders))
5. Stroke = 4 × displacement ÷ (π × bore² × cylinders)
6. Bore/stroke ratio = bore ÷ stroke

The π/4 × bore² part is the area of the bore, a circle; times the stroke it becomes the volume of one cylinder. The two conversion factors are exact by definition: an inch is exactly 25.4 mm, so a cubic inch is exactly 16.387064 cc, and a liter holds 61.0237 cubic inches. With a bore and stroke in millimeters the formula gives cubic millimeters, and a million of those make a liter; switching the calculator to metric does that conversion for you.

Because the bore is squared, it moves the displacement twice as much as the stroke does, percent for percent; that is also why solving the formula for the bore, in the fourth line, takes a square root.

Worked example

Three questions engine builders ask, worked out with the same functions that run the calculator.

Typical bore and stroke combinations

The table works out a range of bore and stroke combinations found in four-, six- and eight-cylinder engines, using the same formula as the calculator. Most car engines have a bore/stroke ratio between 0.8 and 1.2; short-stroke V8s built to rev go past it on the oversquare side.

The first two rows show how little displacement says about the engine: a square four-cylinder and an undersquare one with almost the same size. Further down, the V8 rows show the usual stroker steps, where a longer crank does most of the work.

Common mistakes

• Using the piston diameter as the bore. Pistons are made smaller than the bore to leave running clearance. The difference is small, but it is a measurement of the wrong part.
• Entering the crank throw as the stroke. The throw, the offset of the crankpin from the crank’s center, is half the stroke. Entering it as the stroke halves the displacement.
• Rounding too early. Converting a metric bore to inches and rounding it to two decimals before squaring can move a V8’s result by close to a cubic inch. Let the calculator take the millimeters directly.
• Expecting the badge to match. Engines are named with rounded figures, so the calculated displacement rarely matches the name exactly; the cubic inches to liters page explains the rounding.
• Forgetting the overbore after a rebuild. A block bored oversize displaces more than it did from the factory. The table under the result shows how much each common overbore adds.