How to Calculate Engine Displacement
One formula, three units, and one detail that surprises most people: bore counts twice as much as stroke.
Last updated · 6 min read
Engine displacement is simply the total volume the pistons sweep in one full cycle. It is the sum of a cylinder volume repeated for however many cylinders the engine has — and the whole thing reduces to the formula for the volume of a cylinder.
Why the Formula Looks Like That
The volume of a cylinder is π × radius² × height. In engine terms the height is the stroke, and the radius is half the bore. Since squaring the radius means dividing the bore by two and then squaring, the ÷4 appears naturally:
- π × (bore ÷ 2)² × stroke
- = π × bore² ÷ 4 × stroke
- = (π ÷ 4) × bore² × stroke
Multiply by the cylinder count and you have total displacement. That is the entire calculation — there is no correction factor, no allowance for combustion chamber volume, and no difference between engine layouts. A V8, a flat-eight and a straight-eight with identical bore and stroke all displace exactly the same.
Worked Example in Cubic Inches
Take a classic small-block V8 with a 4.000" bore and 3.480" stroke:
- Bore squared: 4.000 × 4.000 = 16.000
- Times π ÷ 4 (0.7854): 16.000 × 0.7854 = 12.566
- Times stroke: 12.566 × 3.480 = 43.731
- Times 8 cylinders: 43.731 × 8 = 349.8 cubic inches
Which is the engine everyone calls a 350. Manufacturers round to a marketable number, so a "350" is really 349.8 ci and a "5.7 litre" is really 5,735 cc.
The Metric Version
Identical formula, millimetres instead of inches. A 2.0 litre four-cylinder with an 86 mm bore and 86 mm stroke:
- 86 × 86 × 0.7854 = 5,808.8 mm²
- × 86 mm stroke = 499,557 mm³ per cylinder
- × 4 cylinders = 1,998,229 mm³
- ÷ 1,000 = 1,998 cc, sold as a 2.0 litre
Since 1 cc is exactly 1,000 mm³, dividing by a thousand gets you there. This engine is also perfectly square — bore equals stroke — which is unusual and generally a deliberate design compromise.
| Convert | Multiply by | Example |
|---|---|---|
| Cubic inches → cc | 16.387064 | 350 ci = 5,735 cc |
| cc → cubic inches | 0.0610237 | 2,000 cc = 122.0 ci |
| cc → litres | ÷ 1,000 | 5,735 cc = 5.74 L |
| Litres → cubic inches | 61.0237 | 5.7 L = 347.8 ci |
Why Bore Counts Twice as Much as Stroke
This is the part that catches people out. Displacement rises with the square of bore but only linearly with stroke. Increase bore by 10% and displacement rises 21%. Increase stroke by 10% and it rises exactly 10%.
That is why a modest overbore adds more capacity than the numbers suggest, and why engine builders reach for boring first. A common 0.030" overbore on a 4.000" bore small block takes 349.8 ci to 355 ci — the famous "355" — from a change of thirty thousandths of an inch.
The limit is cylinder wall thickness. Bore too far and you break into the water jacket, which ends the block. Sonic testing before machining is standard practice on any block being taken near its limit.
What Displacement Does Not Tell You
- Not power. A 2.0 turbo can make triple what a 2.0 naturally aspirated engine makes. Displacement sets potential airflow, not output — see HP per litre for how efficiently an engine uses its capacity.
- Not compression ratio. That depends on combustion chamber volume, which the displacement formula ignores entirely. Use our compression ratio calculator for that.
- Not character. Two engines of identical displacement behave completely differently depending on how it is split between bore and stroke — see the bore-to-stroke ratio section for what that changes.
To run the numbers without the arithmetic, use our engine displacement calculator, or the engine size converter to move between cc, litres and cubic inches.
Frequently Asked Questions
Displacement = (π ÷ 4) × bore² × stroke × cylinders. Keep bore and stroke in the same units and the answer comes out in those units cubed.
Same formula with bore and stroke in mm, then divide by 1,000 (1 cc = 1,000 mm³). An 86 mm bore and stroke four-cylinder gives 1,998 cc.
Manufacturers round to a marketable figure. A 4.000" bore and 3.480" stroke across eight cylinders calculates to 349.8 ci, sold as a 350.
Bore, by a factor of two. Displacement rises with the square of bore but only linearly with stroke — a 10% bore increase adds 21%, a 10% stroke increase adds 10%.
Multiply cubic inches by 16.387064. 350 ci = 5,735 cc = 5.7 litres. Reverse it by multiplying cc by 0.0610237.
No. A V8, flat-eight and straight-eight with identical bore and stroke displace exactly the same. Layout affects packaging and balance, not swept volume.
Not necessarily. Displacement sets potential airflow, but forced induction, compression and head design matter enormously. A 2.0 turbo routinely beats a much larger NA engine.