Engine Displacement Calculator

displacement = π/4 × bore² × stroke × cylinders

bore

Cylinder bore (diameter), in mm

stroke

Piston stroke, in mm

cylinders

Number of cylinders

Use it when you have a bore and a stroke from a workshop manual or a parts listing and want the engine size in the units your market uses, or when you are comparing two engines that are quoted in different ones. It is also the quick way to check a claim: a 2.0 litre four-cylinder with an 86 mm bore needs a stroke of about 86 mm, so a figure implying 75 mm or 100 mm is worth a second look.

1. A 2.0 litre four-cylinder: 86 mm × 86 mm

   1. Bore and stroke are both 86 mm, so the engine is square — a bore-to-stroke ratio of exactly 1.000
   2. One cylinder: π/4 × 86 × 86 × 86 = 499,557 mm³
   3. Four cylinders: 499,557 × 4 = 1,998,229 mm³
   4. Cubic centimeters: 1,998,229 ÷ 1,000 = 1,998 cc
   5. Liters: 1,998 ÷ 1,000 = 2.00 L, which is the 2.0 on the badge
   6. Cubic inches: 1,998 ÷ 16.387064 = 121.9 in³

   The badge says 2.0 and the geometry says 1,998 cc. Every round displacement on a car is a rounded one, and this is the case where the difference is worth knowing: the tax bracket, the insurance group and the parts listing all key off the same 1,998.

2. A 350 cubic inch V8: 4.00 in × 3.48 in

   1. 4.00 in is 101.6 mm and 3.48 in is 88.392 mm, so the bore and stroke go in as millimeters
   2. Bore-to-stroke: 101.6 ÷ 88.392 = 1.149 — oversquare, a wide bore and a short stroke
   3. One cylinder: π/4 × 101.6 × 101.6 × 88.392 = 716,622 mm³
   4. Eight cylinders: 716,622 × 8 = 5,732,978 mm³
   5. Cubic centimeters and liters: 5,732,978 ÷ 1,000 = 5,733 cc = 5.73 L
   6. Cubic inches: 5,733 ÷ 16.387064 = 349.8 in³, the 350 the engine is named after

   The name says 350 and the geometry says 349.8. American engines are named by rounding to the nearest familiar figure, which is why the same machine is a 350 in one catalogue and a 5.7 in another — and why neither number is wrong.

Only the swept volume is calculated. The combustion chamber, the piston crown, the head gasket and the deck clearance are all outside it, which is why the compression ratio is a number you measure rather than one you derive from these three inputs. The bore and stroke have to be the true ones: an engine bored 0.030 in over is no longer the size on its data plate, and a stroker crank moves it further still. The range stops at 16 cylinders, which is the W16; anything larger is an aero or marine engine and not what this page is for. A rotary is out of scope altogether — a Wankel's nominal displacement is a different definition and does not follow this formula. No rounding is applied between steps, so a displacement landing within a cubic centimetre of a round figure is a coincidence rather than a guarantee.

How do you work out engine displacement?

Multiply the area of one cylinder by the stroke to get that cylinder's swept volume, then multiply by the number of cylinders. In one line: π/4 × bore² × stroke × cylinders. An 86 mm bore and an 86 mm stroke across four cylinders comes to 1,998 cc, which is the 2.0 litre on the badge. The bore is a diameter, so the π/4 belongs there — using plain π gives a figure 27% too large.

What is the difference between cc and liters?

A factor of 1,000. 1,998 cc is 1.998 litres, which every brochure rounds to 2.0. Cubic centimetres are what the specification sheet and the registration document use; litres are what the model name uses. The two never disagree by more than that rounding, so there is no conversion to get wrong — only a decimal point to move.

Why is the same engine also quoted in cubic inches?

Because the United States sizes engines by cubic inch while most of the rest of the world uses the litre. One cubic inch is exactly 16.387064 cm³, so a 5,733 cc engine is 349.8 in³ and gets called a 350. There is no second formula — it is the same swept volume divided by a different constant, which is why a 5.7 and a 350 are one engine.

Does the number of cylinders change anything but the total?

Not the displacement — it is the swept volume of one cylinder multiplied by the count, so four cylinders of 499.6 cc and a single cylinder of 1,998 cc are the same displacement and entirely different engines. What separates them is the bore to stroke ratio and the cylinder count together: more, smaller cylinders can rev higher, fewer and larger ones deliver their torque lower down.

What does the bore to stroke ratio tell me?

Whether the engine is oversquare, meaning a ratio above 1 with a wide bore and a short stroke, or undersquare, meaning below 1 with a narrow bore and a long stroke. Oversquare engines rev freely and make their power high in the range; undersquare ones make torque low down and run out of breath early. Two engines can share a displacement and have opposite characters: 86 × 86 is square at 1.000, while 101.6 × 88.392 is oversquare at 1.149.

• NIST Guide to the SI, Special Publication 811 — US National Institute of Standards and Technology
• The International System of Units (SI Brochure) — Bureau International des Poids et Mesures