Hong Life CalculatorsUnderstanding the engine displacement calculator — concept and principle
This calculator works out an engine's displacement from its bore, stroke and number of cylinders, in cubic centimetres, litres and cubic inches. It also shows the swept volume per cylinder, the piston area and whether the engine is square, oversquare or undersquare. Mechanics, students and engine builders use it to check a spec sheet or plan a rebuild.
How it is calculated
Swept volume of one cylinder: Vd = π/4 × B² × L
Engine displacement = Vd × number of cylinders
- B = bore (cylinder diameter) and L = stroke (distance the piston travels), both converted to cm so the result is in cm³ (cc).
- Litres = cc ÷ 1000; cubic inches = cc ÷ 16.387064.
- Piston area = π/4 × B²; bore/stroke ratio = B ÷ L.
The principle
As the piston moves from top dead centre to bottom dead centre it sweeps a cylinder of air whose cross-section is the piston area and whose length is the stroke. That swept volume, multiplied by the number of cylinders, is the displacement: the volume of air the engine can draw in over one complete cycle. It sets roughly how much fuel can be burned per cycle, which is why displacement is a common size measure. The combustion chamber above the piston is not included; it affects the compression ratio, not the displacement. The bore-to-stroke ratio describes the shape: a larger bore allows bigger valves and higher revs, while a longer stroke favours low-speed torque.
Worked example
Default inputs: bore 86 mm, stroke 86 mm, 4 cylinders.
- Piston area = π/4 × 8.6² = 58.09 cm².
- Per cylinder = 58.09 × 8.6 = 499.6 cc.
- Displacement = 499.6 × 4 = 1,998 cc = 2 litres (a "2.0-litre" engine).
- Cubic inches = 1,998 ÷ 16.387 = 121.9.
- Bore ÷ stroke = 86 ÷ 86 = 1, so the engine is square (bore = stroke).
| Bore — cylinder diameter (mm) | Engine displacement (cc) |
|---|---|
| 21.5 | 125 |
| 43 | 500 |
| 64.5 | 1,124 |
| 86 | 1,998 |
| 108 | 3,122 |
| 129 | 4,496 |
| 172 | 7,993 |
How to read the result
Makers usually round displacement for marketing, so a 1,998 cc engine is sold as 2.0 L. Comparing bore and stroke tells you about character: oversquare engines tend to rev higher, undersquare engines tend to pull strongly at low speed. A rebore by 0.5 mm adds a little displacement; use the calculator to see how much before you choose oversize pistons.
Common mistakes
- Using the radius instead of the diameter for the bore.
- Mixing millimetres and centimetres, which gives results off by a factor of 10 or 1,000.
- Adding the combustion-chamber volume.
- Expecting the rounded marketing figure to match the exact result.
Frequently asked questions
How do I calculate engine displacement?
Multiply π/4 by the bore squared, by the stroke, and by the number of cylinders.
How many cc is a 2.0 L engine?
About 2,000 cc; an 86 × 86 mm four-cylinder gives 1,998 cc.
What does oversquare mean?
The bore is larger than the stroke, which usually suits higher engine speeds.
Sources: J. B. Heywood, Internal Combustion Engine Fundamentals, 2nd ed. (McGraw-Hill, 2018), ch. 2 · NIST Special Publication 811 (2008), Appendix B (1 in³ = 16.387064 cm³)