Engine Displacement Calculator

The displacement formula, in plain English

Displacement is the volume that all the pistons sweep as they travel from the bottom of the bore to the top. You do not need a dyno or a spec sheet to get it. You need three numbers: the bore, which is the width of one cylinder, the stroke, which is how far the piston travels, and the number of cylinders.

The math is the volume of a cylinder multiplied by the cylinder count. The area of the bore is 0.7854 times the bore squared, because 0.7854 is pi divided by four. Multiply that area by the stroke and you have the swept volume of one cylinder. Multiply by the cylinder count and you have the whole engine.

So the formula reads: displacement = 0.7854 × bore² × stroke × cylinders. With a 4.000 in bore, a 3.480 in stroke and eight cylinders, that is 0.7854 × 16 × 3.48 × 8, which comes to 349.85 cubic inches. Multiply by 0.016387 to convert cubic inches to liters and you get 5.73 L.

One detail matters more than people expect: displacement counts swept volume only. The space left above the piston at top dead center, where the fuel burns, is not part of it. That space is the clearance volume, and it is the reason two engines with identical displacement can run wildly different compression ratios.

Worked example: a 350 cubic inch small block

Take the engine that has been rebuilt in more garages than any other, the 350 Chevy. Bore is 4.000 in, stroke is 3.480 in, and there are eight cylinders.

• Bore area: 0.7854 × 4.000 × 4.000 = 12.566 square inches
• One cylinder: 12.566 × 3.480 = 43.73 cubic inches
• Eight cylinders: 43.73 × 8 = 349.85 cubic inches
• In metric: 349.85 × 16.387 = 5,733 cc, or 5.73 L

Run the same steps on a modern four cylinder with an 86 mm bore and an 86 mm stroke. Convert 86 mm to 3.3858 in each way, and you get 0.7854 × 11.4638 × 3.3858 × 4 = 121.94 cu in, which is 1,998 cc. That is the engine sold as a 2.0 L.

A 5.7 L Hemi shows how the numbers drift. Its bore is 3.917 in and its stroke is 3.578 in, so the math gives 344.93 cu in, or 5.65 L. Chrysler badges it 5.7 L and the aftermarket calls it a 345. Both are rounding the same measured figure in different directions.

This is why a rebuild sheet and a sales brochure rarely agree. The measured number is what you use when you order pistons, rings or a head gasket. The badge is a marketing label that rounds to the nearest size shoppers recognize.

Cubic inches to liters, without a conversion site

One liter is 61.02 cubic inches, and one cubic inch is 16.387 cc. Those two numbers cover almost every conversion you will need. To go from cubic inches to liters, divide by 61.02. To go from liters to cubic inches, multiply by 61.02.

The old muscle car sizes land where you would expect. A 350 is 5.73 L, a 400 is 6.55 L, a 454 is 7.44 L and a 502 is 8.23 L. In the other direction, a 2.0 L four is 122 cu in, a 3.5 L V6 is 214 cu in, and a 6.2 L V8 is 376 cu in.

Keep the two conversions apart in your head. Cubic inches to liters is a division by 61.02. Cubic inches to cc is a multiplication by 16.387, which is the same as dividing by 0.061024. Mixing the two up gives answers that are off by a factor of a thousand, which is the most common error on a build sheet.

Compression ratio is not displacement

These two numbers get used as if they were the same thing, and they are not. Displacement is how much the pistons sweep. Compression ratio is how tightly the mixture is squeezed into the space that is left.

The formula for compression ratio is the swept volume of one cylinder plus the clearance volume, divided by the clearance volume. Clearance volume is everything above the piston at top dead center: the combustion chamber in the head, the head gasket thickness, any deck clearance, and the volume of a dished or domed piston.

Put numbers on it. A 350 has 43.73 cu in per cylinder, which is 716.6 cc. Add a 76 cc chamber, a 9 cc gasket, 5 cc of deck clearance and a 12 cc dish, and the clearance volume is 102 cc. The ratio is (716.6 + 102) / 102 = 8.03 to 1. Swap to a 64 cc chamber with a flat top piston and the clearance volume drops to 84 cc, so the ratio becomes 9.53 to 1. The displacement never moved. It is still 349.85 cu in.

What changes displacement is a different crank, different rods or a bigger bore. What changes compression ratio is the chamber, the gasket, the piston and how far the piston sits below the deck. A stroker kit raises both, which is why builders check piston to valve clearance after a stroke change.

Measured displacement against the badge

Every manufacturer rounds. The table below shows the measured figure next to the name the engine is sold under, using the same formula the calculator runs.

Notice how often the badge rounds up. The 4.94 L V8 became 5.0, the 5.65 L became 5.7, and the 6.16 L became 6.2. None of those labels is wrong, but none of them is the measured figure either. The EPA fuel economy guide lists displacement as the manufacturer reports it, which is why the same engine can appear as 5.7 L in one place and 345 cu in in another.

Rules that cap displacement by class, such as some racing classes and a few state fee schedules, use the measured number. If you are building to a limit, run the calculator and use its output, not the badge.

What an overbore does to displacement

When a block is worn or scored, a machinist bores the cylinders oversize and fits larger pistons. The common steps are 0.030 in and 0.060 in. Each one adds displacement, but less than people hope.

Five cubic inches on a 350 is not a power upgrade. It is a repair. The gain in airflow is small, and the thin cylinder walls of a heavily bored block can cost more in ring seal than the extra volume returns. The reason to bore is a straight, round cylinder, and the extra displacement is a side effect.

A stroker crank is the other route, and it moves the number much further. Going from a 3.480 in stroke to a 3.750 in stroke on the same 4.000 in bore gives 0.7854 × 16 × 3.75 × 8 = 376.99 cu in, a gain of 27 cu in, or 7.7%. That is where the 383 and 377 stroker kits come from.

Bore, stroke and how the shape changes the engine

Two engines can share a displacement and behave nothing alike. The ratio of bore to stroke tells you which way the designer leaned.

An oversquare engine has a bore larger than its stroke. The 4.000 × 3.480 small block is 1.15 to 1. Short stroke means lower piston speed at a given rpm, so the engine can rev higher before parts are stressed. A square engine, with bore equal to stroke, sits near 1.0, like the 86 mm × 86 mm four.

An undersquare engine has a longer stroke than bore. The 6.7 L Cummins at 4.21 × 4.88 is 0.86 to 1. Long stroke means higher piston speed and a torque peak low in the rev range, which suits a truck that pulls a trailer. It also means the engine runs out of breath sooner.

Displacement is one input to power, not the answer. A 5.7 L V8 and a 6.7 L diesel six are close in size, yet one is built for horsepower and the other for torque. Forced induction bends the rule further: a 2.0 L four at 20 psi of boost moves roughly 2.4 times the air of the same engine at atmospheric pressure, close to what a 4.7 L engine breathes. The EPA emissions testing program and the NHTSA fuel economy rules both treat displacement as a fixed attribute of the engine, which is exactly what it is: a measurement of geometry, not a promise about output.