Volume of everyday shapes
How much water does a tank hold, how much soil fills a planter, how much concrete goes into a round pier? Each question comes down to the volume of a simple solid. This calculator handles six shapes, gives the volume in cubic inches, cubic feet, gallons or liters, and adds the total surface area, useful for paint, wrapping or insulation.
The formulas
| Shape | Volume | Surface area |
|---|---|---|
| Rectangular box | l × w × h | 2(lw + lh + wh) |
| Cube | s³ | 6s² |
| Cylinder | πr²h | 2πr(r + h) |
| Sphere | 4/3 πr³ | 4πr² |
| Cone | πr²h ÷ 3 | πr(r + √(r² + h²)) |
| Square pyramid | s²h ÷ 3 | s² + 2s√(s²/4 + h²) |
The cone and the pyramid hold exactly one third of the cylinder or box with the same base and height.
Worked example: a cylinder 6 inches across
A container has a radius of 3 inches and a height of 8 inches.
- Base area: π × 3² = 28.27 sq in.
- Volume: 28.27 × 8 = 226.19 cubic inches.
- In gallons: 226.19 ÷ 231 = 0.979 gal, just under a gallon, or 3.71 liters.
- Surface area: 2π × 3 × (3 + 8) = 207.35 sq in.
Cylinder volume by height (radius 3 in)
| Height | Volume | Capacity |
|---|---|---|
| 4 in | 113.10 in³ | 0.490 gal |
| 6 in | 169.65 in³ | 0.734 gal |
| 8 in | 226.19 in³ | 0.979 gal |
| 10 in | 282.74 in³ | 1.224 gal |
| 12 in | 339.29 in³ | 1.469 gal |
Volume grows in direct proportion to height, but with the square of the radius: doubling the radius quadruples the volume.
Units that matter
- 1 cubic foot = 1,728 cubic inches = 7.48 US gallons.
- 1 US gallon = 231 cubic inches = 3.785 liters.
- 1 cubic yard = 27 cubic feet, the unit used for concrete, mulch and topsoil.
- 1 liter = 1,000 cubic centimeters = 61.02 cubic inches.
Enter every dimension in the same unit; you can switch each field between inches, feet, centimeters and meters, and choose the unit of each result.
Practical examples
- Planters: a box 36 × 12 × 10 inches holds 4,320 cu in, or 2.5 cu ft of potting mix. Bags are often sold in 1 or 2 cu ft sizes.
- Round concrete piers: a 12-inch tube 4 ft deep holds π × 0.5² × 4 = 3.14 cu ft, so about 0.12 cubic yard each.
- Water heaters and tanks: a cylinder 20 inches across and 48 inches tall holds about 65 gallons.
- Balls and domes: a basketball, about 9.4 inches across, encloses roughly 435 cubic inches of air.
Inside versus outside
For containers, use the inside dimensions: walls take up space. A cooler that measures 24 inches on the outside may have only 20 inches inside, which cuts its capacity by more than a third.