EngineeringFormulaMechanical
Engine Displacement Calculator
Calculate total engine displacement in cubic inches, cc and liters from bore, stroke and cylinder count, or solve the bore or stroke for a target size.
Engine displacement is the volume the pistons sweep in one stroke, added up over every cylinder. It is what an engine's size label means: a 350 cubic inch V8, a 2.0 L four, a 600 cc motorcycle. This engine displacement calculator multiplies the bore area by the stroke and the cylinder count, and shows the answer in cubic inches, cc and liters (litres) at once. It can also work backwards to find the bore or stroke needed for a target displacement, for example when planning a stroker or a bored-out block. It measures swept volume only, so it is separate from the Compression Ratio Calculator, which also needs the chamber, gasket and piston volumes.
B · Finished diameter, after any overbore
S · Full piston travel
n · Whole number; 1 for a single
Solution
Enter bore, stroke and cylinder count to get the engine displacement.
V = n π B² S / 4
Formula Sheet
- VTotal Displacement
- BCylinder Bore
- SStroke
- nCylinder Count
Variables & Units
| Symbol | Variable | Description | Common Units |
|---|---|---|---|
| V | Total Displacement | Swept volume of all cylinders combined. | in³, cc, L |
| B | Cylinder Bore | Diameter of the cylinder. | in, mm |
| S | Stroke | Distance the piston travels from bottom to top dead center. | in, mm |
| n | Cylinder Count | Number of cylinders in the engine. |
How to Use This Calculator
- 01Choose Displacement to find engine size, Find Bore to solve the bore for a target size, or Find Stroke to solve the stroke.
- 02Optionally pick a common engine from the list to fill in its factory bore, stroke and cylinder count, then edit any value.
- 03Enter the bore and stroke in inches or millimeters. Use the finished bore after any overbore, not the stock size.
- 04Enter the number of cylinders. For a single-cylinder motorcycle or scooter engine, enter 1.
- 05In the Find Bore and Find Stroke modes, enter the target displacement in cubic inches, cc or liters.
- 06Read the total in your chosen unit, plus the other two units, the displacement of one cylinder, and the bore-to-stroke ratio.
How the Formula Works
One piston sweeps a cylinder: the circular bore area multiplied by the stroke. Swept volume per cylinder is Vs = πB²S / 4, where B is the bore diameter and S is the stroke.
Total displacement is the swept volume of one cylinder times the number of cylinders: V = n × πB²S / 4. Only the diameter, stroke and count matter, so a V8, an inline four and a flat six all use the same formula.
Because the bore is squared, it has more effect than the stroke. A 1% wider bore adds about 2% displacement, while a 1% longer stroke adds 1%.
To find the bore for a target, the formula is rearranged to B = √(4V / (π S n)). To find the stroke, S = 4V / (π B² n).
Cubic inches, cc and liters are the same volume in different units: 1 cubic inch is 16.387 cc, and 1000 cc is 1 liter. Engine names round the result, so a 302 ci engine (4.95 L) is sold as a 5.0 L.
Worked Example 01
Chevrolet small-block 350: 4.000 in bore, 3.480 in stroke, 8 cylinders
Known
- Bore: 4.000 in (101.6 mm)
- Stroke: 3.480 in (88.39 mm)
- Cylinders: 8
Formula
V = n π B² S / 4
Substitution
V = 8 × π × 4.000² × 3.480 / 4 = 349.85 in³ (inches)
Result
349.85 in³ = 5733 cc = 5.73 L
The factory 350 is really 349.85 cubic inches, which is why it is named 350. In liters it is 5.73 L, sold as a 5.7 L.
Worked Example 02
Honda K20A: 86 mm bore, 86 mm stroke, 4 cylinders
Known
- Bore: 86 mm
- Stroke: 86 mm
- Cylinders: 4
Formula
V = n π B² S / 4
Substitution
V = 4 × π × 8.6² × 8.6 / 4 = 1998.2 cm³ (lengths in cm)
Result
1998 cc = 2.00 L = 121.94 in³
One cylinder sweeps 499.6 cc, and four of them make 1998 cc. Bore equals stroke, so this is a square engine.
Worked Example 03
Stroke needed for a 400 in³ V8 with a 4.125 in bore
Known
- Target displacement: 400 in³ (6555 cc)
- Bore: 4.125 in (104.78 mm)
- Cylinders: 8
Formula
S = 4V / (π B² n)
Substitution
S = 4 × 6555 / (π × 10.478² × 8) = 9.503 cm
Result
3.741 in (95.03 mm)
To reach exactly 400 cubic inches with that bore the stroke has to be 3.741 in. A 3.750 in stroke, a common crank size, gives 400.9 in³.
Applications
- 01Working out the size of an engine from its bore and stroke
- 02Converting an engine size between cubic inches, cc and liters
- 03Planning a stroker or bored engine by finding the stroke or bore for a target size
- 04Checking whether an engine fits a racing or sanctioning-body displacement class
Common Engines: Factory Bore and Stroke to Displacement
| Engine | Bore × stroke | Cylinders | cc | Cubic inches | Liters |
|---|---|---|---|---|---|
| Chevrolet small-block 327 V8 | 4.001 × 3.250 in | 8 | 5357 | 326.9 | 5.36 |
| Chevrolet small-block 350 V8 | 4.000 × 3.480 in | 8 | 5733 | 349.8 | 5.73 |
| Chevrolet big-block 454 V8 | 4.250 × 4.000 in | 8 | 7439 | 454.0 | 7.44 |
| Ford 302 V8 | 4.000 × 3.000 in | 8 | 4942 | 301.6 | 4.94 |
| GM LS3 6.2 L V8 | 103.25 × 92.0 mm | 8 | 6162 | 376.1 | 6.16 |
| Ford Coyote 5.0 L V8 | 92.2 × 92.7 mm | 8 | 4951 | 302.1 | 4.95 |
| Chrysler 5.7 L Hemi V8 | 99.5 × 90.9 mm | 8 | 5654 | 345.1 | 5.65 |
| Honda K20A 2.0 L four-cylinder | 86 × 86 mm | 4 | 1998 | 121.9 | 2.00 |
| Volkswagen Type 1 1600 flat-four | 85.5 × 69 mm | 4 | 1585 | 96.7 | 1.58 |
| Yamaha YZF-R6 600 cc inline-four | 67 × 42.5 mm | 4 | 599 | 36.6 | 0.60 |
Cubic Inches, cc and Liters
| Cubic inches | cc | Liters |
|---|---|---|
| 100 | 1639 | 1.64 |
| 122 | 1999 | 2.00 |
| 151 | 2474 | 2.47 |
| 200 | 3277 | 3.28 |
| 250 | 4097 | 4.10 |
| 302 | 4949 | 4.95 |
| 350 | 5735 | 5.74 |
| 400 | 6555 | 6.55 |
| 454 | 7440 | 7.44 |
| 500 | 8194 | 8.19 |
| 572 | 9373 | 9.37 |
Bore-to-Stroke Ratio
| Bore ÷ stroke | Name | Typical tendency |
|---|---|---|
| Above 1.02 | Oversquare | Room for larger valves and higher rpm at a given piston speed |
| 0.98 to 1.02 | Square | Balanced bore and stroke |
| Below 0.98 | Undersquare | Long stroke, usually tuned for low-rpm torque |
Assumptions
- 01Every cylinder has the same bore and stroke.
- 02Displacement is swept volume only. It excludes the combustion chamber, head gasket and piston crown volumes.
- 03Bore and stroke are the actual finished dimensions, not catalog values from before machining.
- 041 cubic inch = 16.387064 cc. Liters are cc divided by 1000, and the rounded size is that value to one decimal. Badge names are marketing choices and can differ.
Where This Model Stops
- 01Does not cover rotary (Wankel) engines, which use a different displacement definition.
- 02Does not calculate compression ratio, power, torque, or volumetric efficiency. Displacement alone does not predict performance.
- 03Engines built with different cylinder sizes cannot be handled with one bore and stroke.
- 04Factory bore and stroke values in the engine list are nominal. Real engines vary by production tolerance, overbore and machining.
References
- [1]Piston Displacement
ScienceDirect Topics (Elsevier)
Definition of displacement as the volume swept by the pistons, from bore, stroke and cylinder count.
- [2]
- [3]
Guide for the Use of the International System of Units (SI), Appendix B: conversion factors
NIST
Exact conversion of the cubic inch to cubic meters (1 in = 25.4 mm, so 1 in³ = 16.387064 cm³).
- [4]How to Calculate Engine Compression Ratio and Displacement
JE Pistons
Piston maker's worked displacement formula from bore, stroke and cylinder count.
Frequently Asked Questions
How do you calculate engine displacement?
Multiply the bore area by the stroke to get one cylinder's swept volume, then multiply by the number of cylinders: V = n × π × B² × S / 4. Use the same length unit for bore and stroke. For example, an 86 mm × 86 mm four-cylinder sweeps 1998 cc.
How do I convert cubic inches to liters or cc?
Multiply cubic inches by 16.387 to get cc, or by 0.016387 to get liters. To go the other way, divide cc by 16.387 or multiply liters by 61.02. A 350 ci engine is 5735 cc, or 5.74 L.
Why is a 302 not exactly 5.0 liters?
302 cubic inches is 4.95 L, and the factory 4.000 × 3.000 in bore and stroke give 4.94 L. Ford badged it a 5.0 L, so the name is a marketing round-up and not the exact size. The size you calculate from the dimensions is the real one.
What bore do I enter after boring the engine?
Enter the finished bore: the stock bore plus the overbore. For a 4.000 in block bored 0.030 in over, enter 4.030 in. Displacement rises with the square of the bore, so 0.030 in over adds about 1.5%.
Does displacement include the combustion chamber?
No. Displacement is the swept volume only. The chamber, head gasket and piston crown volumes are extra volume that remains at top dead center and matter for compression ratio. Use the Compression Ratio Calculator for that.
What does the bore-to-stroke ratio tell me?
A ratio above 1 is oversquare (bore larger than stroke), around 1 is square, and below 1 is undersquare. Oversquare engines tend to allow larger valves and higher rpm at the same piston speed, while undersquare engines are usually built for low-rpm torque. It is a design tendency, not a performance guarantee.
How do I calculate displacement for a motorcycle or single-cylinder engine?
Use the same formula with one cylinder. A 66 mm bore and 58.7 mm stroke single gives about 200 cc. Two-stroke and four-stroke engines are both sized by swept volume.