What this calculator does
A bore and stroke calculator answers the reverse of the usual engine displacement question: instead of starting from a known bore and stroke and calculating the resulting displacement, this works backwards from a target total displacement and one known dimension to find the other. It is the same underlying relationship as the engine displacement formula, rearranged to solve for whichever measurement is missing.
The result also reports the bore-to-stroke ratio, which describes the engine's basic design character. An oversquare engine has a bore larger than its stroke, which tends to allow higher engine speeds; an undersquare engine has a stroke larger than its bore, which tends to favour low-speed torque; a square engine has bore and stroke approximately equal.
The formula
Total displacement equals (π/4) × bore² × stroke × number of cylinders. Dividing by the cylinder count gives the displacement per cylinder, then the formula is rearranged: to solve for bore, divide the per-cylinder displacement by ((π/4) × stroke) and take the square root; to solve for stroke, divide the per-cylinder displacement by ((π/4) × bore²).
| Term | Meaning |
|---|---|
| Bore | The diameter of each cylinder. |
| Stroke | The distance the piston travels from top to bottom of the cylinder. |
| Bore:stroke ratio | Bore divided by stroke; above 1 is oversquare, below 1 is undersquare, at 1 is square. |
The inputs explained
| Field | What to enter |
|---|---|
| Solve for | Choose whether you know the stroke and want the required bore, or know the bore and want the required stroke. |
| Target total displacement (cc) | The total target displacement for the whole engine, across all cylinders. |
| Known value (stroke if solving bore; bore if solving stroke) (mm) | The dimension you already know: stroke, if solving for bore, or bore, if solving for stroke. |
| Number of cylinders | The number of cylinders sharing that total displacement. |
When to use it
Planning an engine build around a target capacity
Given a target displacement class, such as 2.0 litres, and a stroke fixed by an existing crankshaft, this works out the bore a new set of pistons and cylinders would need.
Exploring oversquare versus undersquare options
Trying a few different known values for the same target displacement shows how the resulting bore-to-stroke ratio, and therefore the engine's basic character, shifts.
Checking a spec sheet against a stated displacement
If a spec sheet gives displacement and one dimension but not the other, this fills in the missing figure so both numbers can be checked against each other.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How does required bore change with a fixed stroke as target displacement rises?
A fixed 86 mm stroke across 4 cylinders, at a range of target total displacements.
| Target displacement | Result | Bore:stroke ratio |
|---|---|---|
| 1600 cc | 76.95 mm | 0.89 |
| 1800 cc | 81.62 mm | 0.95 |
| 2000 cc | 86.04 mm | 1.00 |
| 2200 cc | 90.24 mm | 1.05 |
| 2400 cc | 94.25 mm | 1.10 |
| 2600 cc | 98.10 mm | 1.14 |
How does required stroke change with a fixed bore as cylinder count changes?
A fixed 2,000 cc target displacement and 86 mm bore, across a range of cylinder counts.
Questions
How is this different from the engine displacement calculator?
The engine displacement calculator starts from a known bore, stroke and cylinder count and works out the resulting displacement. This calculator runs that relationship in reverse, starting from a target displacement and one known dimension to find the other.
What does an oversquare engine actually mean in practice?
Oversquare (bore larger than stroke) generally allows an engine to safely rev higher, since a shorter stroke means lower piston speed at a given RPM, which is common in performance-oriented engines. Undersquare engines, with a longer stroke relative to bore, tend to produce more low-speed torque and are common in engines tuned for efficiency or towing.
Does this account for real-world factors like deck clearance or head gasket thickness?
No. This is a purely geometric calculation based on the swept volume formula. Real engine building involves additional factors such as compression height, deck clearance and combustion chamber volume, which this calculator does not model.
Can I use this for a single-cylinder engine?
Yes, set the cylinder count to 1 and the target displacement to the single cylinder's swept volume.
To check displacement in the forward direction from a known bore and stroke, see the engine displacement calculator.