Volume Calculator
Pick a shape, choose your unit and enter its dimensions: this volume calculator returns the volume, the total surface area and the capacity in US gallons, liters and cubic feet, plus a table in nine units. It covers 11 solids, from boxes and cylinders to cones, spheres, capsules and frustums, so you can size a pool, a tank, an aquarium or a pile of mulch.
Updated
Results
- Total surface areaAll faces of the closed solid
- Surface area accuracyEllipsoid only
- US gallons1 gal = 231 in³
- Liters
- Cubic feet
- Slant heightCone and frustum only
- Volume formula
- Surface area formula
| Unit | Volume |
|---|
Results are estimates. See the methodology below.
How to use the calculator
- Choose the shape. Only the dimensions that shape needs are shown.
- Choose the unit (inches, feet, yards, centimeters or meters) and enter every dimension in it. Convert mixed measurements first: 4 ft 6 in is 4.5 ft.
- Read the volume in cubic units, then the gallons, liters and cubic feet below. The table repeats the volume in in³, ft³, yd³, cm³, m³, L, US gallons, quarts and fluid ounces.
Use radius, not diameter: half the distance across. For a pool or tank, enter the water depth rather than the wall height to get the water volume. Slant height appears only for the cone and the frustum.
Formulas used
| Shape | Volume | Total surface area |
|---|---|---|
| Cube | s³ | 6s² |
| Box | l × w × h | 2(lw + lh + wh) |
| Cylinder | πr²h | 2πr(r + h) |
| Cone | πr²h ÷ 3 | πr(r + √(r² + h²)) |
| Sphere | (4/3)πr³ | 4πr² |
| Hemisphere | (2/3)πr³ | 3πr² (dome plus flat base) |
| Rectangular pyramid | l × w × h ÷ 3 | base plus four triangular faces |
| Triangular prism | T × l | 2T + (a + b + c) × l |
| Capsule | πr²h + (4/3)πr³ | 2πr(2r + h) |
| Ellipsoid | (4/3)πabc | approximation |
| Conical frustum | πh(R² + Rr + r²) ÷ 3 | π(R + r)√((R − r)² + h²) + π(R² + r²) |
Notes: the pyramid's apex sits above the center of its base. The triangular prism takes the triangle's three sides and finds its area T with Heron's formula. The capsule's height is the straight middle section only; its total length is h + 2r. The ellipsoid uses semi-axes a, b and c, and its surface area uses Knud Thomsen's approximation, with a maximum error of 1.061%. A frustum with top radius 0 is a cone. Surface areas count every face of a closed solid.
Conversions use exact definitions: 1 in = 2.54 cm, 1 ft = 0.3048 m, 1 yd = 0.9144 m and 1 L = 0.001 m³. One US gallon is taken as 231 in³, or 3.785411784 L.
Worked examples
1. Pools and tanks
| Shape and dimensions | Volume | US gallons |
|---|---|---|
| Cylinder tank, radius 2 ft, height 5 ft | 62.8319 ft³ | about 470.01 |
| Round pool, 24 ft across (radius 12 ft), water 4 ft deep | 1,809.5574 ft³ | about 13,536 |
| Rectangular pool, 32 × 16 ft, average depth 5 ft | 2,560 ft³ | about 19,150 |
For a pool with a sloped floor, use the average of the shallow and deep ends as the height. The tank holds about 1,779.2 liters.
2. Aquarium
A tank measuring 48 × 13 × 21 inches has a volume of 13,104 in³, or 56.727273 US gallons. That's from the outside dimensions; glass thickness and the gap below the rim mean it holds less water.
3. A pile of mulch
A cone-shaped pile 8 ft across (radius 4 ft) and 3 ft high holds 50.2655 ft³. In the table, that's 1.861684535 yd³ if your supplier sells by the cubic yard. Its slant height is 5 ft.
4. A quick check
A box of 11 × 7 × 3 inches is 231 in³: exactly 1 US gallon in the table. A 1-meter cube is 1,000 L, or 264.17205 gallons.
Frequently asked questions
How many gallons are in a cubic foot?
About 7.48 US gallons, since a cubic foot is 1,728 in³ and a gallon is 231 in³. Enter a 1-ft cube to see the exact figure in the table.
How do I calculate the volume of a round pool?
Choose cylinder, enter half the pool's width as the radius and the water depth as the height. A 24-ft pool with 4 ft of water holds about 13,536 gallons.
Are these US or imperial gallons?
US liquid gallons only. The imperial gallon used in the UK is a different unit, so don't use these figures for it; the liters column works anywhere.
Can it find the water in a partly filled horizontal tank?
No. It calculates full solids only. For an upright tank or a pool you can enter the water depth as the height, but a lying cylinder needs a different formula. Hollow shapes, wall thickness and oblique solids aren't modeled either.
What's the difference between volume and surface area?
Volume is the space inside, in cubic units; surface area is the total area of the outside, in square units. For the 2-ft by 5-ft cylinder: 62.8319 ft³ inside, 87.9646 ft² of surface, top and bottom included.
How do I order concrete or soil by the cubic yard?
Read the yd³ row in the table. For slabs and round columns, the concrete calculator also adds bag counts and a waste allowance; to convert between other volume units, use the volume converter.
Sources
Results are for idealized shapes and are rounded for display. Real pools, tanks and piles are rarely perfect solids, so add a margin when you buy water treatment, fill or materials by volume.