# What is my compression ratio?

Computes the static compression ratio of a piston engine from the bore, the stroke and the clearance volume, or any one of them from the other three.

- Page: https://www.acalculator.org/physics/compression-ratio-calculator
- JSON spec: https://www.acalculator.org/physics/compression-ratio-calculator.json
- Version: 40dd467aa3ee

## Default answer

Example with the default inputs (Bore 3.38582677165354 in, Stroke 3.38582677165354 in, Clearance volume 50 cm³): A 3.386 in bore and 3.386 in stroke with 50 cm³ of clearance volume gives a compression ratio of 10.99:1.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| bore | Bore | The diameter of the cylinder. |
| stroke | Stroke | How far the piston travels from the bottom to the top of its stroke. |
| vc | Clearance volume | The volume above the piston at top dead center: combustion chamber, head gasket, deck clearance, and piston dome or dish. |
| cr | Compression ratio | The cylinder volume at bottom dead center divided by the volume at top dead center. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| bore | Bore | The diameter of the cylinder. |
| stroke | Stroke | How far the piston travels from the bottom to the top of its stroke. |
| clearance | Clearance volume | The volume above the piston at top dead center: combustion chamber, head gasket, deck clearance, and piston dome or dish. |
| cr | Compression ratio | The cylinder volume at bottom dead center divided by the volume at top dead center. |
| swept | Swept volume per cylinder | The volume the piston displaces in one stroke: π ÷ 4 × bore² × stroke. |
| total | Cylinder volume at bottom dead center | The swept volume plus the clearance volume. |

## Method

CR = (Vs + Vc) ÷ Vc, with Vs = π ÷ 4 × bore² × stroke (Heywood 1988).

## Assumptions

- This is the static (geometric) compression ratio. The dynamic ratio, which depends on when the intake valve closes, is lower.
- The clearance volume is the whole volume above the piston at top dead center: the combustion chamber, the compressed head gasket, the deck clearance, and the piston dome (subtract) or dish (add).
- The cylinder is a round bore of the given diameter. Every cylinder of the engine is the same, so the ratio for one cylinder is the ratio for the engine.

## Worked examples

1. bore = 0.086, stroke = 0.086, vc = 0.00005 gives swept = 0.0005, cr = 10.991144. Source: hand calculation in content.mdx: Vs = π ÷ 4 × 8.6² × 8.6 = 499.56 cm³; CR = (499.56 + 50) ÷ 50 = 10.99 (Heywood 1988, chapter 2).
2. bore = 0.1016, stroke = 0.088392, cr = 10 gives vc = 0.00008. Source: hand calculation in content.mdx: Vs = π ÷ 4 × 4² × 3.48 = 43.731 in³ = 716.62 cm³; Vc = Vs ÷ (10 − 1) = 79.62 cm³.
3. stroke = 0.09, vc = 0.00006, cr = 9.5 gives bore = 0.084941. Source: hand calculation in content.mdx: bore = √(4 × (9.5 − 1) × 60 cm³ ÷ (π × 9 cm)) = √72.15 cm² = 8.494 cm = 84.94 mm.

## FAQ

### How do I calculate an engine's compression ratio?

Divide the cylinder volume with the piston at the bottom by the volume with the piston at the top: CR = (Vs + Vc) ÷ Vc. Vs is the swept volume, π ÷ 4 × bore² × stroke, and Vc is the clearance volume above the piston at top dead center.

### What goes into the clearance volume?

Everything above the piston at top dead center: the combustion chamber in the head, the volume of the compressed head gasket (π ÷ 4 × gasket bore² × gasket thickness), the deck clearance (π ÷ 4 × bore² × deck height), and the piston dish or valve reliefs. Subtract the volume of a domed piston.

### How do I raise or lower the compression ratio?

Make the clearance volume smaller to raise it (a thinner head gasket, a smaller chamber, a domed piston, or a milled head or deck) or larger to lower it. A longer stroke or bigger bore also raises it, because the swept volume grows while the clearance volume stays the same.

### What is the difference between static and dynamic compression ratio?

The static ratio is pure geometry and is what this calculator gives. The dynamic ratio counts only the part of the stroke after the intake valve closes, so it is always lower, and it depends on the camshaft.

### What is a typical compression ratio?

Heywood gives 8 to 12 for spark-ignition (petrol) engines and 12 to 24 for diesel engines. The right value for your engine also depends on the fuel octane, boost and cam timing.

## Sources

- Heywood, J. B. Internal Combustion Engine Fundamentals. McGraw-Hill (1988), chapter 2, Engine design and operating parameters: displaced volume V_d = π ÷ 4 × B² × L and compression ratio r_c = (V_d + V_c) ÷ V_c, with typical values 8 to 12 (spark ignition) and 12 to 24 (compression ignition).
- NIST Special Publication 811 (2008), Appendix B.8: 1 in = 2.54 cm exactly and 1 in³ = 16.387064 cm³. https://www.nist.gov/pml/special-publication-811