Library / Automotive and vehicle dynamics / VEH-06
Automotive and vehicle dynamics
Engine swept displacement
Total volume swept by the pistons in all cylinders, from bore and stroke.
- Ref
- VEH-06
- Rev
- v1
- Field
- Automotive and vehicle dynamics
- Result
- Vd [L]
nc is the number of cylinders, Be the bore (cylinder diameter) and S the stroke (distance the piston travels), both in mm. The swept volume of one cylinder is the piston area π B²/4 times the stroke; the engine displacement is nc times that. The result is in litres (1 L = 10⁶ mm³). It excludes the clearance volume above the piston at the top of its stroke.
Total volume swept by the pistons in all cylinders, from bore and stroke. Engines are commonly rated by this number in litres.
Calculator
- Displacement per cylinder, π B²S/40.4996 L
- Bore to stroke ratio, Be / S1
- Displacement in cubic centimetres1,998 cm³
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- Four cylinders of 86 mm bore and 86 mm stroke give 1.998 L, the “2.0 litre” engine. The bore is squared, so a 10 % larger bore adds 21 % to the displacement while 10 % more stroke adds only 10 %.
- A bore larger than the stroke (oversquare) gives the same capacity with a shorter stroke and so a lower piston speed at a given rpm, which is why high-revving engines favour it.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (L) | Local step | Change in result |
|---|---|---|---|---|---|---|
| nc Number of cylinders | 1 to 12 | 0.4996 | 5.995 | 5.495 | +1 | +25 % |
| Be Cylinder bore | 50 to 150 mm | 0.6754 | 6.079 | 5.404 | +10% | +21 % |
| S Piston stroke | 40 to 200 mm | 0.9294 | 4.647 | 3.718 | +10% | +10 % |
Sweep of Cylinder bore
| Cylinder bore (mm) | Swept displacement (L) |
|---|---|
| 50 | 0.6754 |
| 62.5 | 1.055 |
| 75 | 1.52 |
| 87.5 | 2.069 |
| 100 | 2.702 |
| 112.5 | 3.419 |
| 125 | 4.222 |
| 137.5 | 5.108 |
| 150 | 6.079 |
Sweep one variable
Variables and how each one contributes
Swept displacement
What the equation gives you. Everything else feeds it.
Number of cylinders
How many cylinders the engine has (a whole number). Directly proportional: every extra cylinder adds an equal share. Raising it by 1 (to 5) moves the result by +25 %, from 1.998 to 2.498 L.
Cylinder bore
The cylinder bore (inside diameter), in mm. Enters squared, so a small change in bore matters twice as much as the same change in stroke. Raising it by 10 % (to 94.6) moves the result by +21 %, from 1.998 to 2.418 L.
Piston stroke
The piston stroke, in mm. Directly proportional, since the swept volume is the piston area times the stroke. Raising it by 10 % (to 94.6) moves the result by +10 %, from 1.998 to 2.198 L.
Worked example with the values above
- Piston area: π B²/4 = π × 86² / 4 = 5,809 mm².
- Swept volume of one cylinder: 5,809 × 86 = 499,600 mm³ = 0.4996 L.
- Vd = nc × that = 4 × 0.4996 = 1.998 L.
Assumptions and limits
- A reciprocating piston engine with circular cylinders and a constant bore and stroke.
- Swept volume only, excluding the combustion chamber volume at top dead centre.
Common mistakes
- Entering the radius instead of the bore (the diameter). This gives one quarter of the true volume.
- Mixing units: the result is in litres only when bore and stroke are in millimetres.
Statistics and uncertainty
Bore and stroke are measured to a fraction of a millimetre, so the computed displacement is far more precise than the rounded value in the marketing name. Because the bore is squared, a 0.1 mm error in an 86 mm bore changes the displacement by about 0.23 %, twice the relative error in the bore itself.
Where it is used
- Converting bore and stroke data from a datasheet to displacement.
- Comparing engines on a like-for-like basis and finding BMEP from torque.
Maths you need
- Area of a circle: π d² / 4
- Volume: area × length