What is the engine displacement formula?

Displacement V = (π/4) × bore² × stroke × cylinders. Bore and stroke must be in the same unit; converting mm to cm first gives the result directly in cc (cm³). To get litres divide by 1,000; to get cubic inches divide by 16.387.

What is a square, over-square, or under-square engine?

When bore equals stroke the engine is square. A bore larger than the stroke (bore:stroke ratio above 1) is over-square — typically high-revving and found in sports cars and motorcycles. A bore smaller than the stroke (ratio below 1) is under-square or long-stroke — producing more torque at lower RPM and common in diesel and truck engines.

How is compression ratio calculated?

Compression ratio CR = (swept volume + clearance volume) / clearance volume, where swept volume is displacement divided by the number of cylinders. For example a 500 cc per-cylinder engine with a 50 cc clearance chamber gives CR = (500 + 50) / 50 = 11:1. Higher CR generally means more efficiency and power but requires higher-octane fuel.

How do I convert engine displacement from cc to litres?

Divide by 1,000. A 1,998 cc engine is a 2.0 litre engine. Manufacturers often round to one decimal place — a "2.0L" engine may actually be 1,984 cc or 1,998 cc depending on the bore/stroke combination chosen.

How do I convert cc to cubic inches?

Divide by 16.387064. A 5,700 cc (5.7L) engine is approximately 347.8 cubic inches, often marketed as a "350" in American muscle-car tradition (slightly rounded).

Why does engine displacement affect power?

Larger displacement means more air and fuel can be burned per cycle, producing more torque and — when multiplied by RPM — more power. However, how that displacement is achieved matters: an over-square engine with a short stroke can rev higher and gain power at the top end, while an under-square long-stroke engine delivers peak torque lower in the rev range.

Engine Displacement Calculator

The engine displacement calculator applies the exact engineering formula used by manufacturers and tuners worldwide. Enter any three of bore, stroke, cylinders, and total displacement and the tool instantly solves for the fourth — no pencil or conversion tables needed.

How it works

Every piston engine’s swept volume is a straightforward geometry problem. Each cylinder is a tube, and the piston sweeps through a cylindrical volume on every stroke. The formula is:

V = (π / 4) × bore² × stroke × cylinders

Bore and stroke are typically given in millimetres on modern spec sheets. Converting millimetres to centimetres (divide by 10) gives the volume directly in cubic centimetres (cc). To get litres, divide by 1,000. To get cubic inches (common in the United States) divide by 16.387064.

The calculator can also flip the formula around. If you know the target displacement, the number of cylinders and the stroke, it solves for the bore using:

bore = sqrt(4 × V / (π × stroke × cylinders))

Similarly it will derive a missing stroke or — useful for competition-class research — tell you how many cylinders a certain bore-and-stroke combination implies for a given displacement target.

Bore:stroke ratio

Once both bore and stroke are known the tool reports the bore:stroke ratio:

Over-square (ratio above 1): bore is larger than stroke. These engines rev freely and suit sport and racing applications.
Square (ratio near 1): balanced design, common in general-purpose petrol engines.
Under-square (ratio below 1): stroke exceeds bore. Long-stroke engines generate substantial low-speed torque, common in diesel and commercial-vehicle engines.

Compression ratio

If you supply the clearance volume (combustion chamber volume at top-dead-centre, in cc per cylinder), the calculator also reports the static compression ratio:

CR = (swept volume per cylinder + clearance volume) / clearance volume

A higher CR extracts more energy per cycle, which is why performance engines run 11:1 or higher — provided the fuel octane and combustion-chamber geometry can withstand the increased pressure without knock.

Worked example — Toyota 2AZ-FE 2.4 L four-cylinder

The 2AZ-FE has a bore of 88.5 mm and a stroke of 96.0 mm with 4 cylinders:

Per-cylinder swept volume = (π/4) × 8.85² × 9.6 = 591.0 cc
Total displacement = 591.0 × 4 = 2,363 cc ≈ 2.4 L
Bore:stroke ratio = 88.5 / 96.0 = 0.922 → under-square (torque-oriented)

Clearance volume is approximately 57 cc per cylinder, giving:

CR = (591.0 + 57) / 57 = 11.37:1

Plug those numbers into the calculator and you will see exactly the same results. To cross-check in cubic inches: 2,363 / 16.387 = 144.2 cu in, often cited as “2.4 litres” in North American marketing.

Reference displacement table

Engine	Bore (mm)	Stroke (mm)	Cyl	Displacement
Honda B16A	81	77.4	4	1,595 cc
Toyota 2JZ-GE	86	86	6	2,997 cc
Ford 5.0 Coyote	92.2	92.7	8	4,951 cc
BMW S65 V8	92	75.2	8	3,999 cc
Cummins ISX 15	137	169	6	14,956 cc (15 L)

All figures computed with the same formula above — try them in the calculator to verify.

Every calculation runs entirely in your browser. Nothing is uploaded or stored.