Piston displacement is calculated using the volume formula for a cylinder: multiply π by the radius squared by the stroke length, then multiply by the number of cylinders. The full formula looks like this: Total Displacement = π × r² × stroke × number of cylinders. If you know your engine’s bore and stroke specs, you can calculate displacement in under a minute.
The Core Formula
Displacement measures the total volume swept by all pistons as they travel from the top of the cylinder to the bottom. The formula is based on basic cylinder geometry:
- Bore: the diameter of the cylinder
- Stroke: the distance the piston travels from top dead center to bottom dead center
- Number of cylinders: how many cylinders the engine has
The single-cylinder formula is: Volume = π × (bore ÷ 2)² × stroke. You can also write this as: bore² × π ÷ 4 × stroke. Both versions give the same result. To get total engine displacement, multiply the single-cylinder volume by the number of cylinders.
One important distinction: displacement only accounts for the volume the piston actually sweeps through, sometimes called “swept volume.” It does not include the small pocket of space between the piston and the cylinder head when the piston is at the very top of its travel. That leftover space is the clearance volume, and it factors into compression ratio rather than displacement.
Step-by-Step Example: Chevy 350
The Chevrolet 350 Small-Block V8 is one of the most common engines in the world, so it makes a good test case. Chevy lists the bore at 101.6 mm and the stroke at 88.39 mm, with 8 cylinders.
First, find the radius by dividing the bore in half: 101.6 ÷ 2 = 50.8 mm. Next, square the radius: 50.8² = 2,580.64 mm². Multiply by π: 2,580.64 × 3.14159 = 8,106.6 mm². Now multiply by the stroke: 8,106.6 × 88.39 = 716,582 mm³, which is 716.58 cc per cylinder. Finally, multiply by 8 cylinders: 716.58 × 8 = 5,732.6 cc, or roughly 5.7 liters. That matches Chevy’s official spec of 350 cubic inches (5.7L).
Working in Cubic Inches
If your bore and stroke are in inches rather than millimeters, the process is identical, and the result comes out in cubic inches. Many American engine builders use a slightly rearranged version of the formula that skips the step of dividing the bore by two:
Single-cylinder displacement = bore² × 3.14159 × stroke ÷ 4
This is mathematically equivalent. You square the full bore diameter, multiply by π, multiply by the stroke, then divide by 4 (because dividing the diameter by 2 and then squaring it is the same as dividing the squared diameter by 4). Multiply by the number of cylinders for total displacement.
Converting Between Units
Engine displacement gets expressed in three common units: cubic inches (ci), cubic centimeters (cc), and liters (L). Converting between them is straightforward.
One cubic inch equals 16.387 cubic centimeters. So a 350 cubic inch engine is 350 × 16.387 = 5,735 cc. To convert cubic centimeters to liters, divide by 1,000: 5,735 ÷ 1,000 = 5.735 L, which manufacturers round to 5.7L.
Going the other direction, divide cubic centimeters by 16.387 to get cubic inches. A 2,000 cc engine, for example, is about 122 cubic inches.
Accounting for an Overbore
When an engine is rebuilt, the cylinders are often bored slightly larger to clean up wear on the cylinder walls. This increases the bore diameter and, consequently, the displacement. A common overbore is 0.030 inches (sometimes written as “.030 over”).
To calculate displacement after an overbore, simply add the overbore amount to the original bore diameter before plugging it into the formula. For the Chevy 350 with a stock bore of 4.000 inches and a .030 overbore, the new bore becomes 4.030 inches. Running the formula with 4.030 instead of 4.000 gives you about 355 cubic inches rather than 350. That small change in bore diameter adds roughly 5 cubic inches because the increase gets squared in the formula, amplifying its effect across all 8 cylinders.
How to Measure Bore and Stroke
If you’re working with an engine and don’t have the factory specs, you’ll need to measure the bore and stroke directly. Bore is measured using a telescoping bore gauge inserted into the cylinder, then transferring that measurement to a micrometer for a precise reading. The bore gauge expands to contact the cylinder walls, and you lock it in place, remove it, and measure across it with the micrometer. When reading the micrometer, apply only slight resistance on the thimble. If your micrometer has a torque limiter on the end, use it to prevent overtightening, which would skew the measurement.
Stroke is easier to measure. With the piston at the very bottom of its travel (bottom dead center), measure the distance to the top of the cylinder deck, then move the piston to top dead center and measure again. The difference between those two positions is the stroke. Accuracy matters here. Even a few thousandths of an inch off on your bore measurement gets magnified when you square it and multiply across all cylinders.
Why Displacement Matters
Displacement is the single most basic indicator of an engine’s size and potential output. Larger displacement means the engine can take in more air and fuel per cycle, which translates directly to more torque. Engines with greater displacement typically produce that torque at lower RPM, which is why large trucks use big-displacement engines for pulling power rather than high-revving small ones.
Horsepower is a function of torque multiplied by engine speed, so displacement influences horsepower as well, though the relationship is less direct. Two engines with the same displacement can produce very different horsepower numbers depending on how well they breathe, what compression ratio they run, and how high they rev. Still, displacement gives you a useful baseline. It’s also the number used for vehicle registration, emissions classification, and racing class rules, which is why knowing how to calculate it accurately has practical value beyond curiosity.