# How many cubic inches is it?

Finds a volume in cubic inches from the sides of a box, the diameter and height of a cylinder, or an engine’s bore, stroke and cylinders, with the same volume in cc, litres, cubic feet and gallons.

- Page: https://www.acalculator.org/math/cubic-inches-calculator
- JSON spec: https://www.acalculator.org/math/cubic-inches-calculator.json
- Version: e6d0a2481c09

## Default answer

Example with the default inputs (Shape Box, Length 12 in, Width 10 in, Height 8 in): The volume is 960 cubic inches (15.732 litres).

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| shape | Shape | What you are measuring: a box, a cylinder, or the cylinders of an engine. |
| l | Length | The length of the box. |
| w | Width | The width of the box. |
| h | Height | The height of the box or the cylinder. |
| d | Diameter | The inside diameter of the cylinder. |
| bore | Bore | The diameter of one engine cylinder. |
| stroke | Stroke | How far the piston travels from the bottom to the top. |
| cyl | Cylinders | How many cylinders the engine has. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| cubicInches | Cubic inches | The volume in cubic inches (in³). |
| cc | Cubic centimetres (cc) | The volume in cubic centimetres; 1 in³ = 16.387064 cm³. |
| liters | Litres | The volume in litres; 1 L = 1,000 cm³. |
| cubicFeet | Cubic feet | The volume in cubic feet; 1 ft³ = 1,728 in³. |
| gallons | US gallons | The volume in US liquid gallons; 1 gal = 231 in³. |

## Method

Box: V = l × w × h. Cylinder: V = π ÷ 4 × d² × h. Engine: V = π ÷ 4 × bore² × stroke × cylinders. 1 in³ = 16.387064 cm³; 1 ft³ = 1,728 in³; 1 gal = 231 in³.

## Assumptions

- Engine displacement is the swept volume: the volume each piston moves through, times the number of cylinders. It leaves out the combustion chamber above the piston.
- A typed length is read as the exact decimal you typed in its unit (1 in = 2.54 cm exactly).

## Worked examples

1. shape = box, l = 0.3048, w = 0.254, h = 0.2032 gives cubicInches = 960, cc = 15,731.58144, liters = 15.731581, cubicFeet = 0.555556, gallons = 4.155844. Source: OpenStax, Contemporary Mathematics, §10.7 Volume and Surface Area (rectangular prism V = l·w·h; right cylinder V = πr²h), https://openstax.org/books/contemporary-mathematics/pages/10-7-volume-and-surface-area; NIST Special Publication 811, Appendix B (1 in = 2.54 cm exactly; 1 gal = 231 in³ exactly), https://www.nist.gov/pml/special-publication-811.
2. shape = box, l = 0.1, w = 0.2, h = 0.3 gives cc = 6,000, liters = 6, cubicInches = 366.142465. Source: OpenStax, Contemporary Mathematics, §10.7 Volume and Surface Area (rectangular prism V = l·w·h; right cylinder V = πr²h), https://openstax.org/books/contemporary-mathematics/pages/10-7-volume-and-surface-area; NIST Special Publication 811, Appendix B (1 in = 2.54 cm exactly; 1 gal = 231 in³ exactly), https://www.nist.gov/pml/special-publication-811.
3. shape = cylinder, d = 0.1016, h = 0.1524 gives cubicInches = 75.398224. Source: OpenStax, Contemporary Mathematics, §10.7 Volume and Surface Area (rectangular prism V = l·w·h; right cylinder V = πr²h), https://openstax.org/books/contemporary-mathematics/pages/10-7-volume-and-surface-area.
4. shape = engine, bore = 0.1016, stroke = 0.088392, cyl = 8 gives cubicInches = 349.847758, liters = 5.732978. Source: OpenStax, Contemporary Mathematics, §10.7 Volume and Surface Area (rectangular prism V = l·w·h; right cylinder V = πr²h), https://openstax.org/books/contemporary-mathematics/pages/10-7-volume-and-surface-area (each cylinder sweeps a right cylinder of diameter bore and height stroke); NIST Special Publication 811, Appendix B (1 in = 2.54 cm exactly; 1 gal = 231 in³ exactly), https://www.nist.gov/pml/special-publication-811.

## FAQ

### How do I calculate cubic inches?

Measure the length, width and height in inches and multiply them. A box 12 in long, 10 in wide and 8 in high holds 12 × 10 × 8 = 960 cubic inches.

### How do I find the cubic inches of a cylinder?

Multiply the area of the round end by the height: V = π × r² × h, or π ÷ 4 × d² × h with the diameter. A can 4 in across and 6 in tall holds π × 2² × 6 = 75.40 in³.

### How do I work out engine displacement in cubic inches?

Each cylinder sweeps a round column the size of the bore and the length of the stroke. Displacement = π ÷ 4 × bore² × stroke × number of cylinders. A V8 with a 4.00 in bore and a 3.48 in stroke displaces about 349.85 in³, or 5.7 litres.

### How many cc are in a cubic inch?

Exactly 16.387064 cm³, because an inch is exactly 2.54 cm and 2.54³ = 16.387064. So 100 in³ is 1,638.7 cc, or 1.64 litres.

### How many cubic inches are in a cubic foot or a gallon?

A cubic foot is 12 × 12 × 12 = 1,728 in³. A US liquid gallon is defined as exactly 231 in³.

### Can I type the sizes in centimetres?

Yes. Each length has its own unit, and the page changes it to inches before it multiplies. A 10 × 20 × 30 cm box is 6,000 cm³, which is 366.14 in³.

## Sources

- OpenStax, Contemporary Mathematics, §10.7 Volume and Surface Area: volume of a rectangular prism (V = B·h) and of a right cylinder (V = πr²h). https://openstax.org/books/contemporary-mathematics/pages/10-7-volume-and-surface-area (retrieved 2026-10-02)
- NIST Special Publication 811, Guide for the Use of the International System of Units, Appendix B: 1 in = 2.54 cm exactly, 1 US gallon = 231 in³ exactly. https://www.nist.gov/pml/special-publication-811 (retrieved 2026-10-02)