Compression ratio calculator

How is compression ratio calculated?

CR = (swept volume + clearance volume) ÷ clearance volume. The swept volume of one cylinder is π ÷ 4 × bore² × stroke; the clearance volume is everything left above the piston at top dead center.

What goes into the clearance volume?

The combustion chamber in the head, the head gasket (π ÷ 4 × gasket bore² × compressed thickness), the gap between the piston top and the deck at top dead center, and the piston’s dish or dome.

How do I enter a dish or a dome?

A dish, valve reliefs and the small space above the top ring add volume — enter them as a positive number of cc. A dome takes up space — enter it as negative, or add everything up as one net figure. If the piston rises above the deck, enter the deck clearance as negative.

Example

Ford Performance’s engine-building guide works a 4.000 in bore and 3.500 in stroke: swept volume 720.7 cc. The clearance volume is 60.2 cc of chamber + 8.7 cc of gasket + 2.1 cc of deck + 4.0 cc of valve notches + 0.9 cc above the top ring − 10.4 cc of dome = 65.5 cc, so CR = (720.7 + 65.5) ÷ 65.5 = 12.0 : 1.

Is this the same as dynamic compression?

No — this is the static ratio from the engine’s geometry. The effective (dynamic) ratio also depends on when the intake valve closes, which is set by the camshaft.

How much does a thinner head gasket raise the compression ratio?

Slightly: in the example below, compressing the gasket from 0.041 in to 0.027 in changes the ratio from 9.77:1 to 10.10:1. Each part of the clearance volume matters, because a small volume sits in the denominator, so a few cubic centimeters make a visible difference.

Why does the ratio matter?

A higher compression ratio improves thermal efficiency, but it raises the temperature and pressure of the unburned mixture, which makes knock more likely on a given fuel. The ratio an engine can run is therefore limited by the fuel's octane rating, the combustion chamber design and the engine management, so look at the manufacturer's recommendation before changing anything.

Where the volumes come from

The swept volume of one cylinder is π ÷ 4 × bore² × stroke, converted to cubic centimeters (1 cubic inch is 16.387064 cc). The clearance volume adds the combustion chamber volume measured in the head, the gasket volume (π ÷ 4 × gasket bore² × compressed thickness), the gap between the piston and the block deck at top dead center, and the piston's dish or valve reliefs as positive volumes (a dome is negative). Everything above the piston at top dead center counts.

Worked example: a 4.030 in bore and 3.480 in stroke

The swept volume is π ÷ 4 × 4.030² × 3.480 = 44.4 in³, or 727.4 cc. With a 64 cc chamber, a gasket volume of 8.9 cc (4.100 in bore, 0.041 in compressed), 2.1 cc for a 0.010 in deck clearance and an 8 cc dish, the clearance volume is 83.0 cc and the ratio is (727.4 + 83.0) ÷ 83.0 = 9.77:1. Removing the dish raises it to 10.70:1, while swapping to 72 cc heads lowers it to 9.00:1.

Common mistakes

Mixing inches and cubic centimeters is the first: bore, stroke, gasket and deck are in inches here and the chamber and dish are in cc. Using the uncompressed gasket thickness (the manufacturer's number) instead of the compressed one is the second. A third is entering the dish as negative, which treats it as a dome and raises the ratio instead of lowering it. Finally, the static ratio calculated here is not the dynamic one: a camshaft that closes the intake valve late gives a lower effective compression than the number suggests.

Sources: Ford Performance engine-building guide (compression ratio worksheet, volume terms); the conversion of 16.387064 cc per cubic inch is exact (NIST SP 811). Related: engine displacement calculator, horsepower calculator, Carnot efficiency calculator and torque calculator.