Guide
How to Calculate Engine Displacement from Bore and Stroke
Engine displacement is π/4 × bore² × stroke × number of cylinders. Measure bore and stroke in inches and the answer is in cubic inches (CID); multiply by 16.387064 for cubic centimeters (cc), or divide by 61.0237 for liters. This guide works the formula through by hand, converts between the three units, and shows why the number on the badge almost never matches the arithmetic.
The formula, and why it has π/4 in it
Each cylinder is a plain geometric cylinder. Its volume is the area of the bore circle times the distance the piston travels, which is the stroke. The area of a circle is π × radius², and the radius is half the bore, so the area is π × (bore ÷ 2)² = (π ÷ 4) × bore². That is all the π/4 is: the halving of the diameter, squared, moved out front so you can work with the bore figure exactly as it is published. Numerically π/4 is 0.785398 — a circle fills about 78.5% of the square drawn around it.
Multiply one cylinder's swept volume by the cylinder count and you have the engine's displacement. Cylinder layout never enters it: an inline-six and a V6 with the same bore and stroke displace exactly the same. Displacement also says nothing about compression ratio, turbocharging, or power — it is the volume the pistons sweep, nothing more.
Worked example: 4.000 in bore, 3.480 in stroke, eight cylinders
These are the engine calculator's default values, and they are the published bore and stroke of the Chevrolet 350 small-block V8:
- Bore area = 0.785398 × 4.000² = 0.785398 × 16 = 12.566 in²
- One cylinder = 12.566 × 3.480 = 43.73 in³
- Eight cylinders = 43.731 × 8 = 349.85 in³
- In cc = 349.85 × 16.387064 = 5,733 cc
- In liters = 5,733 cc ÷ 1,000 = 5.73 L
Type 4.000, 3.480 and 8 into the calculator in US units and it reads 349.8 CID, 5.73 L, 5,733 cc, and 43.73 in³ per cylinder. Carry the extra digits through the middle steps when you do this by hand: rounding to 349.8 before converting gives 5,732 cc, one cc short of the unrounded answer.
The same method works in millimeters. A 95 mm bore and 105 mm stroke gives (π ÷ 4) × 95² × 105 = 744,263 mm³ per cylinder, which is 744.26 cc because 1 cc is 1,000 mm³. Eight of those make 5,954 cc, or 5.95 L — enter 95, 105 and 8 with the calculator set to Metric and it shows exactly that.
Cubic inches to cc and liters
One inch is exactly 2.54 cm by definition, so one cubic inch is exactly 2.54³ = 16.387064 cm³, and a cubic centimeter is the same volume as a milliliter. A liter is 1,000 cm³, so liters are cc ÷ 1,000. Going the other way, one liter is 1,000 ÷ 16.387064 = 61.0237 cubic inches (rounded). The table uses the exact factor; cc are rounded to the nearest whole cc and liters to two decimals.
| Cubic inches (CID) | Cubic centimeters (cc) | Liters (L) |
|---|---|---|
| 100 | 1,639 | 1.64 |
| 200 | 3,277 | 3.28 |
| 250 | 4,097 | 4.10 |
| 300 | 4,916 | 4.92 |
| 350 | 5,735 | 5.74 |
| 400 | 6,555 | 6.55 |
| 454 | 7,440 | 7.44 |
| 500 | 8,194 | 8.19 |
| 1,000 | 16,387 | 16.39 |
And the reverse, for the liter figures that most engines are now sold under. Cubic inches are rounded to one decimal, the same precision the calculator shows:
| Liters (L) | Cubic centimeters (cc) | Cubic inches (CID) |
|---|---|---|
| 1.0 | 1,000 | 61.0 |
| 2.0 | 2,000 | 122.0 |
| 3.0 | 3,000 | 183.1 |
| 4.0 | 4,000 | 244.1 |
| 5.0 | 5,000 | 305.1 |
| 5.7 | 5,700 | 347.8 |
| 6.0 | 6,000 | 366.1 |
| 6.7 | 6,700 | 408.9 |
| 7.3 | 7,300 | 445.5 |
| 10.0 | 10,000 | 610.2 |
| 15.0 | 15,000 | 915.4 |
The calculator itself multiplies by 16.3871 and 0.0163871 — the exact factor rounded to six significant figures. At the precision it displays, that gives the same cc and liter figures as the exact factor for every cubic-inch row above.
Why the badge rarely matches the arithmetic
A displacement on a badge or in a brochure is a name, rounded to a tidy figure, and the rounding goes in whichever direction the maker chose. Run published bore and stroke figures through the calculator and the gap shows up immediately. Each row below can be typed straight in; the metric row is entered with the toggle set to Metric.
| Engine | Calculator inputs (bore, stroke, cylinders) | Calculator reads | Sold as |
|---|---|---|---|
| Chevrolet 350 small-block | 4.000 in, 3.480 in, 8 | 349.8 CID / 5.73 L | 350 / 5.7 L |
| Ford 6.0L Power Stroke | 95 mm, 105 mm, 8 (Metric) | 5,954 cc / 5.95 L | 6.0 L |
| Ford 6.7L Power Stroke | 3.900 in, 4.250 in, 8 | 406.2 CID / 6.66 L | 6.7 L |
| Ford 7.3L Power Stroke | 4.11 in, 4.18 in, 8 | 443.6 CID / 7.27 L | 7.3 L / 444 cu in |
The 350 is rounded up to 350 in cubic inches and down to 5.7 in liters — the same engine, rounded in opposite directions depending on the unit. That is why converting a badge back gives the wrong answer: 5.7 L is 347.8 in³, not 350, and 350 in³ is 5.74 L, not 5.7. If you need the real number, start from bore and stroke, never from the badge.
Overbores and strokers: what each actually adds
Bore is squared and stroke is not, so the two behave differently. A 1% larger bore adds about 2% displacement; a 1% longer stroke adds 1%. Starting from the same 4.000 × 3.480 in eight-cylinder, these are the calculator's own readouts, and each gain is simply the difference between two readouts:
| Change | Bore | Stroke | Calculator reads | Gain |
|---|---|---|---|---|
| Standard | 4.000 in | 3.480 in | 349.8 CID | — |
| +0.030 in overbore | 4.030 in | 3.480 in | 355.1 CID | +5.3 in³ |
| +0.040 in overbore | 4.040 in | 3.480 in | 356.9 CID | +7.1 in³ |
| +0.060 in overbore | 4.060 in | 3.480 in | 360.4 CID | +10.6 in³ |
| Longer stroke only | 4.000 in | 3.750 in | 377 CID | +27.2 in³ |
| Overbore and longer stroke | 4.030 in | 3.750 in | 382.7 CID | +32.9 in³ |
The 4.040 in row is a 1% overbore, and it lands 2.0% above standard — the squared bore at work. Two practical points follow. A rebuilt engine that has been bored over no longer has the displacement on its badge, so enter the bore it has now. And how far a particular block can safely be bored is a question for a machinist with the block in front of them, not for a formula.
Where this goes wrong
- Mixing millimeters and inches. A 101.6 mm bore typed into an inch field, with a 3.480 in stroke, comes out at 225,707.8 CID — absurd enough to notice. The quieter version is converting a metric spec to inches by hand and rounding: 95 × 105 mm entered as 3.74 × 4.13 in reads 363 CID and 5,948 cc, six cc short of the 5,954 cc the millimeter figures give. Enter the numbers in the units they were published in and let the unit toggle do the conversion.
- Using the radius instead of the diameter. Bore is the full diameter of the cylinder. Entering half of it divides the answer by four: a 2.000 in “bore” on the 3.480 in-stroke eight reads 87.5 CID instead of 349.8.
- Rounding the bore before you start. Because bore is squared, small rounding there costs twice as much as in the stroke. At a 3.750 in stroke, 4.0 in place of 4.030 drops the answer from 382.7 to 377 CID — 5.7 in³ lost to one dropped digit.
- Rounding the marketed size and converting it back. A 5.7 L badge converts to 347.8 in³, while the engine measures 349.8. Badges are rounded names, so treat any conversion from them as approximate.
- Reading the per-cylinder line as the total. The calculator shows both. 43.73 in³ is one cylinder of the worked example; 349.8 is the engine.
- Expecting displacement to predict power. It fixes the volume the pistons sweep and nothing else. Boost, compression, cam timing, and fueling all change output without changing displacement at all.
Run your own numbers
The engine displacement calculator does all of the above in one step: enter bore, stroke, and cylinder count in inches or millimeters and it returns cubic inches, liters, cc, and the per-cylinder volume, using the same formula and rounding shown on this page.
Where these numbers come from
The conversion factors are definitions, not measurements; the engine dimensions are the published bore and stroke figures for each engine, which the calculator turns into displacement.
- NIST Guide to the SI, Appendix B.8 — Lists the inch as exactly 2.54 cm, which is where the exact 16.387064 cm³ per cubic inch comes from.
- NIST Guide to the SI, Chapter 5 — Defines the liter as one cubic decimeter, 1,000 cm³.
- Chevrolet small-block engine (1954–2003) — Bore and stroke of the 350 (4.000 × 3.480 in).
- Ford Power Stroke engine — Bore and stroke of the 6.0L (95 × 105 mm), 6.7L (3.9 × 4¼ in) and 7.3L (4.11 × 4.18 in).
Is CID the same as cubic inches?
Yes. CID stands for cubic inch displacement, and it is the engine's total displacement expressed in cubic inches (in³). A 350 CID engine and a 350 in³ engine are the same thing written two ways.
How many cc are in one cubic inch?
Exactly 16.387064 cc. The inch is defined as exactly 2.54 cm, and 2.54 cubed is 16.387064, so the factor has no rounding in it at all. Going the other way, one liter is about 61.0237 cubic inches.
Does a turbocharger or supercharger change displacement?
No. Forced induction packs more air into the same cylinders, which raises power, but the volume the pistons sweep is unchanged. Only bore, stroke, and cylinder count change displacement.
Why do metric engines land on odd cubic-inch figures?
Because their bore and stroke are usually whole or half millimeters, and nothing about a round metric dimension produces a round number of cubic inches. The 95 × 105 mm example above is 5,954 cc — 363.3 in³ by the exact factor.