Engine displacement is the total volume swept by every piston as it travels from top dead centre to bottom dead centre — the amount of air and fuel the engine can draw in during one complete cycle of all its cylinders. It is the single number that gets stamped on a badge, written into a tax bracket, and used to sort engines into classes, and it comes from three measurements: the bore, the stroke and the cylinder count.
This calculator turns those three figures into displacement in litres, cubic centimetres and cubic inches at once, which matters because the automotive world never settled on one unit. Arb Digital added the bore-to-stroke ratio alongside the volume because two engines of identical displacement can behave completely differently depending on how that volume is distributed between diameter and travel.
What This Engine Displacement Calculator Does
It computes the swept volume of one cylinder as the area of the bore multiplied by the stroke length, then multiplies by the number of cylinders. The result appears in three units simultaneously, so a metric bore and stroke give you the cubic-inch figure without a second conversion step, and an American engine quoted in inches gives you litres.
Two features go beyond the basic arithmetic. The overbore field adds a machining allowance to the bore, which is how you answer the practical question of what a rebuilt block will displace after boring — a calculation that trips people up because the allowance is a diameter increase, not a radius increase, and it enters the formula squared. The bore-to-stroke ratio in the results grid classifies the engine as oversquare, square or undersquare and the note explains what that implies.
What this page deliberately does not do is compute compression ratio. That requires combustion chamber volume, piston dish or dome volume, head gasket thickness and deck clearance, none of which are displacement inputs. Arb Digital covers it separately on the engine compression ratio calculator; displacement is the swept volume alone, and compression ratio is the relationship between that swept volume and what remains above the piston at the top of its travel.
How to Use It
- Pick the unit before typing. Bore and stroke must share a unit. Mixing a bore in millimetres with a stroke in inches is the most common way to get an answer that is wrong by a factor of twenty-five.
- Enter the bore as a diameter. It is the cylinder's internal diameter, not its radius. The formula halves it internally; halving it yourself gives a quarter of the true displacement.
- Enter the stroke as total travel. The stroke is twice the crankshaft throw, because the journal offset moves the piston by that distance both up and down. Specification sheets quote the stroke, not the throw.
- Count every cylinder. Six for a V6, eight for a V8, four for an inline or flat four. The number of banks is irrelevant to the volume.
- Add an overbore only if the block has been machined. Leave it at zero for a standard engine. The allowance is added to the diameter, so a 0.030 in overbore makes each bore 0.030 in larger across, not 0.060 in.
The Formula: Area of a Circle, Times Stroke, Times Cylinders
Displacement = (π ÷ 4) × bore² × stroke × number of cylinders. The first two terms are just the area of a circle written in terms of diameter instead of radius, since πr² with r = d/2 becomes πd²/4. That area multiplied by the stroke gives a cylinder of volume, and multiplying by the cylinder count gives the engine total.
This is exactly how the definition is written into United States emissions regulation. Title 40 of the Code of Federal Regulations, Part 1054, covering small nonroad spark-ignition engines, defines an engine's displacement as the intended swept volume of all its cylinders — the internal cross-sectional area multiplied by the stroke length multiplied by the cylinder count — and works a one-cylinder example with a 6.00 cm bore and a 6.25 cm stroke that rounds to 177 cc. The regulatory worked-example button loads exactly that case so you can confirm the tool reproduces it.
Work the defaults instead. An 86 mm bore and an 86 mm stroke across four cylinders: the bore area is π ÷ 4 × 86² = 5,809 mm². Multiplied by the 86 mm stroke that is 499,556 mm³, or 499.6 cc per cylinder. Four cylinders give 1,998 cc — the engine everyone calls a 2.0 litre. Dividing by 16.387064, the exact cubic centimetres in a cubic inch under the international inch defined in NIST Special Publication 811, the Guide for the Use of the International System of Units, gives 121.9 cubic inches.
Why Badges Round and Real Displacement Rarely Ends in Zeros
Almost no engine displaces the round number on its badge. The 2.0 litre above is 1,998 cc. The famous 350 small-block is 349.85 cubic inches. A 1.6 is usually 1,591 or 1,598. Manufacturers round to the nearest tenth of a litre for marketing, and tax and racing classes are written as upper limits precisely because nothing lands exactly on the boundary.
This has a practical consequence for anyone modifying an engine. Class rules are typically stated as "up to 2,000 cc", and a 1,998 cc engine has 2 cc of headroom — which an overbore of even a quarter of a millimetre will consume. Run the overbore field before the machining, not after: a 0.5 mm overbore on that engine takes it to 2,021 cc and out of the class entirely.
The same rounding explains why converted figures disagree between sources. A 5.7 litre and a 350 cubic inch engine are the same engine, but 350 cubic inches is 5,735 cc, which rounds to 5.7. Convert in the other direction from a rounded 5.7 litre and you get 347.8 cubic inches, which is not 350. Always convert from the bore and stroke, never from the badge.
Bore-to-Stroke Ratio: Two Ways to Get the Same Litres
Divide the bore by the stroke and you get a ratio that describes the engine's shape. Above 1.0 the engine is oversquare — wide bores and short strokes. Below 1.0 it is undersquare, or long-stroke. At exactly 1.0 it is square, which is what the default 86 × 86 configuration is.
The ratio matters because mean piston speed, which is what limits engine revs, depends on stroke rather than displacement. A short stroke lets the crankshaft turn faster before the piston is moving unsustainably quickly, which is why high-revving motorcycle and racing engines are strongly oversquare. A long stroke gives a longer effective lever on the crank throw and better low-speed torque at the cost of revs, which is why diesels and large truck engines are undersquare.
Two engines can therefore share a displacement figure and share almost nothing else. A 2.0 litre four with a 100 mm bore and a 63.7 mm stroke and a 2.0 litre four with a 75 mm bore and a 113 mm stroke are the same size and completely different machines. The engine RPM calculator covers the road-speed side of that relationship, and the torque calculator the rotational side.
Two-Stroke, Rotary and the Limits of Swept Volume
Displacement as computed here assumes a conventional reciprocating piston engine, and the assumption quietly fails in two well-known cases.
A two-stroke engine fires once per crankshaft revolution rather than once every two, so it processes roughly twice the air and fuel per revolution as a four-stroke of the same swept volume. Racing bodies deal with this by applying an equivalence factor rather than comparing raw displacement, because the swept volume genuinely does not mean the same thing. The formula on this page still gives the correct swept volume for a two-stroke — it just stops being a fair comparison against a four-stroke.
A Wankel rotary has no cylinders and no stroke, so the formula does not apply at all. Its capacity is quoted as the volume of one chamber multiplied by the number of rotor faces that complete a cycle, and the long-running disagreement over whether to multiply by two or three for classification purposes is exactly a disagreement about what counts as a swept volume. If you are working on a rotary, this calculator is the wrong tool, and the raw chamber volume from the cylinder volume calculator is closer to what you need.
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Browse All Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Entering the bore radius instead of the diameter — the formula already divides by two. Using the radius gives a quarter of the true displacement.
- Mixing units between bore and stroke — both fields share one unit selector for a reason. A millimetre bore with an inch stroke is nonsense the arithmetic cannot detect.
- Using the crank throw as the stroke — the stroke is twice the throw. Taking the throw halves the displacement.
- Counting banks rather than cylinders — a V8 is eight cylinders, not two. Displacement is a whole-engine figure.
- Converting from the badge instead of the measurements — a badge is rounded. Two conversions from a rounded figure can miss the true capacity by several per cent.
Related Free Tools From Arb Digital
Compression ratio needs chamber and deck volumes as well as swept volume, and is handled by the engine compression ratio calculator. For revs against road speed and gearing, use the engine RPM calculator, and for output figures the horsepower calculator and the torque calculator. Mixture work is covered by the air fuel ratio calculator. The underlying geometry, for a single chamber or any other cylindrical volume, is on the cylinder volume calculator, and unit changes between litres, cc and cubic inches on the volume converter. The full free online tools hub lists everything else Arb Digital publishes.
Frequently Asked Questions
Multiply pi divided by four by the bore squared, then by the stroke, then by the number of cylinders. The first part is the area of the cylinder bore, multiplying by the stroke gives the swept volume of one cylinder, and multiplying by the cylinder count gives the engine total.
The bore is the internal diameter of the cylinder. The formula divides it by two internally to get the radius, so entering a radius yourself produces a displacement four times too small, since the term is squared.
There are exactly 1,000 cubic centimetres in a litre and exactly 16.387064 cubic centimetres in a cubic inch, following from the internationally agreed definition of the inch as 25.4 millimetres. A 350 cubic inch engine is therefore 5,735 cc, or 5.7 litres when rounded.
Because bore and stroke are chosen for engineering reasons and rarely produce a round volume. Manufacturers round to the nearest tenth of a litre for badging, so the true swept volume almost always sits slightly below or above the advertised figure.
More than people expect, because bore enters the formula squared while stroke enters it linearly. A half-millimetre overbore on an 86 millimetre bore adds a little over one per cent to the capacity, which is enough to push a 1,998 cc engine past a 2,000 cc class limit.
An oversquare engine has a bore larger than its stroke, giving a ratio above one; an undersquare engine has a stroke larger than its bore. Oversquare designs tolerate higher revs because piston speed depends on stroke, while undersquare designs favour low-speed torque.
No. A Wankel rotary has no bore, stroke or cylinders in the reciprocating sense, so the formula does not apply. Rotary capacity is quoted as chamber volume multiplied by the number of rotor faces, and the correct multiplier is a matter of classification convention rather than geometry.
This tool is provided for educational and reference use. It computes theoretical swept volume from nominal dimensions and does not account for machining tolerances, and it is not a substitute for the official capacity figure used for taxation, insurance or motorsport class eligibility.
