The displacement formula
Each cylinder is a tube. The piston moves from bottom dead center to top dead center, a distance called the stroke, and the tube's diameter is the bore. The volume it sweeps is a cylinder: area of the circle × height.
- Swept volume of one cylinder = π/4 × bore² × stroke (π/4 × bore² is the same as π × radius²)
- Engine displacement = swept volume of one cylinder × number of cylinders
The formula is the same for petrol and diesel, four-stroke and two-stroke engines. It does not include the combustion chamber above the piston at top dead center: that volume belongs to the compression ratio, not to the displacement. Rotary (Wankel) engines are rated by a different convention.
Units: mm, cc, liters and cubic inches
Engine specs usually give bore and stroke in millimetres. Divide both by 10 to get centimetres, and the formula returns cubic centimetres directly, because 1 cc = 1 cm³. In Excel: =PI()/4*(B2/10)^2*(C2/10)*D2. If you calculate in millimetres, divide the result by 1,000 instead: =PI()/4*B2^2*C2*D2/1000.
- Liters = cc ÷ 1,000. The 1,998.2 cc inline-4 is 2.00 liters.
- Cubic inches = cc ÷ 16.387064, the exact number of cc in one cubic inch. 1,998.2 cc = 121.9 cubic inches.
- With bore and stroke in inches, the same formula gives cubic inches directly. The classic small-block V8 with a 4.00 in bore and 3.48 in stroke: π/4 × 4² × 3.48 × 8 = 349.8 cubic inches, the famous "350", or 5,733 cc (5.7 liters).
Advertised sizes are rounded: a 998.8 cc inline-3 is sold as a 1.0, and the 3,604.6 cc V6 as a 3.6.
Worked example: displacement of six engines, compression ratio and an overbore
Rows 2 to 6 calculate the displacement of five engines from bore and stroke in millimetres (inputs in yellow). Row 9 does the same for a classic V8 specified in inches. Rows 12 to 19 work out liters, the compression ratio and the effect of boring the cylinders out.
| A | B | C | D | E | F | |
|---|---|---|---|---|---|---|
| 1 | Engine | Bore (mm) | Stroke (mm) | Cylinders | Displacement (cc) | Cubic inches |
| 2 | Inline-4 petrol | 86.0 | 86.0 | 4 | 1,998.2 | 121.9 |
| 3 | Inline-3 petrol | 71.9 | 82.0 | 3 | 998.8 | 61.0 |
| 4 | V6 petrol | 96.0 | 83.0 | 6 | 3,604.6 | 220.0 |
| 5 | Single, motorcycle | 105.0 | 80.0 | 1 | 692.7 | 42.3 |
| 6 | Inline-6 diesel | 107.0 | 124.0 | 6 | 6,690.1 | 408.3 |
| 7 | ||||||
| 8 | Inch specs | Bore (in) | Stroke (in) | Cylinders | Cubic inches | Displacement (cc) |
| 9 | Classic small-block V8 | 4.00 | 3.48 | 8 | 349.8 | 5,733 |
| 10 | ||||||
| 11 | Inline-4: liters, compression ratio and overbore | Value | ||||
| 12 | Displacement in liters | 2.00 | ||||
| 13 | Swept volume per cylinder (cc) | 499.6 | ||||
| 14 | Clearance (chamber) volume per cylinder (cc) | 52.6 | ||||
| 15 | Compression ratio = (swept + clearance) ÷ clearance | 10.50 | ||||
| 16 | Clearance volume needed for 11.0:1 (cc) | 50.0 | ||||
| 17 | Displacement after a 0.5 mm overbore (cc) | 2,021.5 | ||||
| 18 | Increase from the overbore | 1.17% | ||||
| 19 | Bore ÷ stroke of the V6 (above 1 = oversquare) | 1.16 | ||||
- E2
=PI()/4*(B2/10)^2*(C2/10)*D2π/4 × bore² × stroke × cylinders, mm converted to cm so the result is in cc - F2
=E2/16.3870641 cubic inch = 16.387064 cc exactly - E9
=PI()/4*B9^2*C9*D9The same formula with inches gives cubic inches directly - F15
=(F13+F14)/F14Compression ratio - F17
=PI()/4*((B2+0.5)/10)^2*(C2/10)*D2Displacement with the bore 0.5 mm larger
Illustrative engine dimensions for practice, not the specifications of any particular manufacturer's engine, and no affiliation with any vehicle or parts maker. Always use the manufacturer's service data for real work.
Bore, stroke and the shape of the engine
Because the bore is squared, it has more influence on displacement than the stroke. The bore-to-stroke ratio describes the engine's shape: exactly 1 is a square engine (the 86 × 86 mm inline-4), above 1 is oversquare (the V6 with 96 × 83 mm, ratio 1.16), below 1 undersquare (the diesel with 107 × 124 mm). Oversquare engines leave room for bigger valves and rev higher, long-stroke engines tend to deliver more torque low in the rev range, which is why many diesels are undersquare. Displacement alone does not say which is which: the 692.7 cc single-cylinder motorcycle engine and the 6,690.1 cc inline-6 diesel are built for very different jobs.
From displacement to compression ratio
The compression ratio compares the volume in a cylinder with the piston at the bottom with the volume left at the top: CR = (swept volume + clearance volume) ÷ clearance volume, both per cylinder. The inline-4 sweeps 1,998.2 ÷ 4 = 499.6 cc per cylinder. With a combustion chamber, gasket and piston clearance of 52.6 cc in total, CR = (499.6 + 52.6) ÷ 52.6 = 10.50:1. Solving for the chamber gives the clearance a target ratio needs: for 11.0:1, clearance = swept ÷ (11 − 1) = 50.0 cc. This is the calculation behind milling a cylinder head or changing the head gasket thickness.
What an overbore does to displacement
When worn cylinders are bored out and fitted with oversize pistons, displacement grows with the square of the bore. A 0.5 mm overbore on the 86 mm inline-4 gives π/4 × 8.65² × 8.6 × 4 = 2,021.5 cc, an increase of 1.17%. The quick check is (new bore ÷ old bore)² − 1 = (86.5 ÷ 86)² − 1, the same percent change. The compression ratio also rises slightly, because the swept volume grows while the chamber stays the same.
Displacement is not power
Displacement measures size, not output. Power depends on how much air the engine moves per minute (displacement × rpm × volumetric efficiency), how efficiently it burns the fuel and whether a turbocharger or supercharger forces more air in. A modern turbocharged 2.0-liter can outperform an older 3.6-liter V6. Displacement still matters in practice: it is part of the engine code, it decides the parts that fit, and in some countries it affects vehicle tax and insurance classes.
Common mistakes
- Using the radius as the diameter. π × bore² overstates displacement four times. Use π/4 × bore², or π × (bore/2)².
- Mixing millimetres and centimetres. π/4 × 86² × 86 × 4 is 1,998,229 cubic millimetres. Divide by 1,000 for cc, or convert to cm first.
- Forgetting the cylinder count. π/4 × bore² × stroke is one cylinder. Multiply by the number of cylinders for the engine.
- Wrong cubic inch factor. One cubic inch is 16.387064 cc. Dividing by 16 or 16.4 adds noticeable errors on large engines.
- Adding the chamber to displacement. The clearance volume is part of the compression ratio, not of displacement.
- Trusting the badge. A "2.0" is rarely exactly 2,000 cc. Calculate from bore and stroke when the exact value matters.
Frequently asked questions
How do you calculate engine displacement?
Multiply π/4 by the bore squared, by the stroke and by the number of cylinders. With bore and stroke in centimetres the result is in cc. For example, 86 mm bore, 86 mm stroke and 4 cylinders give 1,998.2 cc.
How do you convert cc to cubic inches?
Divide the cc by 16.387064. A 1,998.2 cc engine is 121.9 cubic inches, and a 350 cubic inch V8 is about 5,733 cc or 5.7 liters.
Is engine displacement the same as engine size?
Yes. Engine size, capacity and displacement all mean the swept volume of all cylinders, usually given in liters, cc or cubic inches.
Does a bigger bore or a longer stroke add more displacement?
The bore is squared in the formula, so a 1% larger bore adds about 2% displacement, while a 1% longer stroke adds 1%.