Engine Displacement Calculator
Enter the bore, the stroke and how many cylinders. This gives the capacity in cc, litres and cubic inches, and says what the bore-to-stroke ratio implies.
Displacement
2litres
- Total displacement
- 1,998 cc
- In litres
- 2 L
- In cubic inches
- 121.9 cu in
- Per cylinder
- 499.6 cc
- Bore to stroke
- 1 : 1
- Square — bore and stroke are within a few per cent of each other, which is the compromise most ordinary engines are built to.
- Displacement is the volume the pistons sweep, and nothing more. It says little about power on its own: compression, breathing, valve timing and forced induction all matter more, which is why a 2.0 turbo can out-power a 3.0 without one.
- The advertised size is rounded. An engine sold as a 2.0 is rarely exactly 2,000cc — 1,998 and 2,035 are both "2.0".
About engine displacement
Displacement is the total volume the pistons sweep in one full cycle. Each cylinder sweeps a circle the width of the bore through the length of the stroke, and the engine's capacity is that volume multiplied by the number of cylinders.
It is the number engines are named after and it says less than people assume. Compression ratio, valve timing, how well the engine breathes and whether it is turbocharged all matter more to power output. A 2.0 litre turbo comfortably out-powers a 3.0 without one, which is why displacement-based tax bands have been quietly abandoned in most places.
What displacement does describe well is the engine's character, and the bore-to-stroke ratio describes it better still. An over-square engine — bore wider than stroke — has room for larger valves and less piston speed at high revs, so it likes to rev and makes its power at the top. An under-square engine has a longer stroke, which gives more leverage on the crank, so it makes torque low down and runs out of appetite earlier.
The advertised size is always rounded. An engine sold as a 2.0 is rarely exactly 2,000cc — 1,998 is a very common answer, and so is 2,035.
What it works out
- Displacement in cc, litres and cubic inches
- Volume per cylinder
- The bore-to-stroke ratio and what it implies
- Any cylinder count
The formula
Displacement = π × (Bore ÷ 2)² × Stroke × Cylinders
One cylinder sweeps the area of a circle through the length of the stroke. The area is π times the radius squared, and the radius is half the bore.
With an 86mm bore the radius is 43mm, so the area is 5,809 square millimetres. Multiplied by an 86mm stroke that is 499,557 cubic millimetres — 499.6cc per cylinder, since a cubic centimetre is a thousand cubic millimetres.
Four of those gives 1,998cc, which is 2.00 litres or 121.9 cubic inches. This is exactly why so many engines are advertised as 2.0 litre and measure 1,998.
Bore and stroke here are both 86mm, giving a ratio of 1.000 — a square engine, which is the compromise most ordinary engines are built to. Push the bore wider than the stroke and it becomes over-square and revs more willingly; lengthen the stroke past the bore and it becomes under-square and makes its torque lower down.
- Bore
- The cylinder diameter in millimetres. Halved to get the radius for the area.
- Stroke
- How far the piston travels between top and bottom, in millimetres.
- Cylinders
- How many cylinders the engine has. Layout — inline, V or flat — makes no difference to capacity.
A worked example
A four cylinder engine with an 86mm bore and an 86mm stroke.
That works out to 2 litres.
- Total displacement
- 1,998 cc
- In litres
- 2 L
- In cubic inches
- 121.9 cu in
- Per cylinder
- 499.6 cc
- Bore to stroke
- 1 : 1
Questions
How do I calculate engine displacement?
Take π times the square of half the bore, multiply by the stroke, then by the number of cylinders. An 86 x 86mm four cylinder works out at 1,998cc, or 2.0 litres.
What is bore and stroke?
The bore is the diameter of the cylinder and the stroke is how far the piston travels within it. Together with the cylinder count they define the capacity completely.
What does over-square mean?
That the bore is wider than the stroke. It allows larger valves and lower piston speed at high revs, so an over-square engine tends to rev freely and make its power high up. Under-square is the reverse: more torque low down, less appetite for revs.
Why is a 2.0 litre engine actually 1,998cc?
Because the advertised figure is rounded to a convenient number. Bore and stroke are chosen for engineering reasons, and 1,998 or 1,984 or 2,035 are what those choices produce. All are sold as 2.0.
Does more displacement mean more power?
Not reliably. Compression, breathing, valve timing and forced induction all matter more. A 2.0 litre turbocharged engine routinely produces more power than a naturally aspirated 3.0.
How do I convert cc to cubic inches?
Divide by 16.387. A 1,998cc engine is 121.9 cubic inches, and a 5.0 litre V8 is about 305.
Does the engine layout change the displacement?
No. Inline, V and flat engines with the same bore, stroke and cylinder count all have identical capacity. Layout affects balance, packaging and sound rather than volume.
What about rotary engines?
They do not work this way at all. A Wankel has no bore or stroke, and its chamber volume is measured differently — which is why rotary capacity has always been contentious for tax and racing classes.