How to Calculate Cubic Inches of a Cylinder

How to work it out

1. Measure across the circular end — the diameter or radius.
2. If you measured the diameter, halve it to get the radius r.
3. Square the radius and multiply by π to get the base area.
4. Multiply the base area by the height h: V = π r² h.
5. Convert the result into your preferred unit above.

Getting an accurate measurement

If you can only reach the top, measure the diameter across the opening and halve it. Keep every measurement in the same system, and let the tool convert between units for you.

How the volume is worked out

The volume of a cylinder is:

A worked example

Worked example. Take a cylinder with a diameter of 3 in (so a radius of 1.5 in) and a height of 8 in. The base area is π × 1.5² = 7.07 in², and multiplying by the height gives a volume of about 0.2 US gallons (57 in³ · 0.9 litres).

Conversions use standard factors: 1 US gallon = 231 in³, 1 Imperial gallon = 4.54609 L, 1 litre = 1000 cm³.

Follow-on questions, answered

The figure above is usually the start, not the finish. These are the questions that tend to come next, answered here so you do not have to run another search:

What is it in cc (cubic centimetres)?

One cubic inch is about 16.39 cc, so the cm3 figure in the breakdown is the metric version that engine builders usually quote.

How do I turn cubic inches into gallons?

Divide by 231 for US gallons — that is the exact definition of a US gallon — or by about 277.42 for Imperial. Both gallon values are shown with the result.

Is this the same as engine displacement?

For a single cylinder, yes: the bore radius and the stroke give the swept volume in cubic inches. Multiply by the number of cylinders for total displacement.

Common uses

A few of the jobs it gets used for:

• Blueprinting an engine's displacement
• Sizing a small precision reservoir
• Converting a machined bore to gallons

Where people go wrong

Two things trip people up: squaring the wrong number, and forgetting that the answer is cubic. If a result looks four times too big or too small, you have probably swapped radius and diameter somewhere, so it is always worth re-reading the measurement you are least sure of. It also helps to glance at the equivalent units; if the litre and gallon figures are both off by the same factor, the input is the culprit, not the maths.

One result, every unit

One number, many units. Whatever you enter, the result lists the same volume as litres, US gallons, Imperial gallons, millilitres, cubic centimetres, cubic inches, cubic feet, cubic yards and cubic metres at the same time. You almost never have to convert by hand: read the figure in the unit your job uses and copy any of the others straight from the breakdown. If you need a shareable version, the copy-link button preserves your exact inputs so a colleague opens the page with the same calculation already filled in.

What to work out next

Once you have your answer you may also want to work in gallons cubic feet volume formula. These related calculators pick up where this one leaves off:

The bottom line: with the radius or diameter and the height, the volume follows immediately, and the breakdown lets you hand the same number to anyone in the unit they prefer. Measure inside dimensions for anything that holds liquid, leave a little headspace at the top of a real container, and treat the geometric figure as a clean maximum rather than the final word on usable capacity.

Questions people ask