How to calculate volume
Volume is the amount of three-dimensional space a shape takes up, measured in cubic units such as cubic feet (ft³) or cubic meters (m³). To calculate volume, measure the lengths the formula needs, convert them to the same unit, and put them into the formula for your shape. This volume calculator does the conversion for you, so you can enter each length in a different unit.
When you mix units, the result is shown in every unit you used. For example, a cone with a 3 ft radius and a 24 in height has a volume of 1⁄3 × π × 3² × 2 ≈ 18.85 ft³, which is the same as about 32,572 in³.
Volume formulas
Here r is a radius, h a height, l a length, w a width, a an edge or semi-axis, and d a diameter.
| Shape | Volume formula |
|---|---|
| Rectangular prism | V = l × w × h |
| Cylinder | V = πr²h |
| Sphere | V = 4⁄3 πr³ |
| Cone | V = 1⁄3 πr²h |
| Cube | V = a³ |
| Square pyramid | V = 1⁄3 a²h |
| Capsule | V = πr²h + 4⁄3 πr³ |
| Spherical cap | V = 1⁄3 πh²(3R − h) |
| Conical frustum | V = 1⁄3 πh(r² + rR + R²) |
| Ellipsoid | V = 4⁄3 πabc |
| Tube (pipe) | V = π(d₁² − d₂²)l ⁄ 4 |
Volume of a rectangular prism
Multiply length by width by height. A box or tank that is 10 ft long, 6 ft wide, and 4 ft high holds 10 × 6 × 4 = 240 cubic feet, or about 1,795 US gallons. This is how a cubic feet calculator or tank volume calculator works for any box-shaped space.
Volume of a cylinder
Find the area of the circular base, πr², and multiply it by the height. A cylinder with a 2 ft radius and a 6 ft height holds π × 2² × 6 ≈ 75.4 cubic feet. If you know the diameter instead, halve it to get the radius. For a hollow pipe, use the tube shape, which subtracts the inner circle from the outer one.
Volume of a sphere
A sphere's volume is 4⁄3 πr³, so a ball with a 3 in radius holds about 113.1 cubic inches. A hemisphere is half of that.
Volume of a cone
The volume of a cone is exactly one third of a cylinder with the same base and height, 1⁄3 πr²h. A cone with a 2 ft radius and a 5 ft height holds about 20.94 cubic feet. A square pyramid is likewise one third of the box around it, 1⁄3 a²h.
What the result includes
- The volume in the cubic version of each length unit you entered.
- The same volume in common units: cubic feet, cubic yards, cubic inches, US gallons, liters, and cubic meters.
- For a spherical cap, the missing third value. Enter any two of the base radius, ball radius, and height. If you give both radii, two caps fit, a shallow one and a deep one, so both volumes are shown. If you fill in all three, the calculator uses the two radii.
| Unit | Equals |
|---|---|
| 1 cubic foot | 1,728 cubic inches ≈ 7.48 US gallons ≈ 28.32 liters |
| 1 cubic yard | 27 cubic feet ≈ 0.765 cubic meters |
| 1 US gallon | 231 cubic inches ≈ 3.785 liters |
| 1 cubic meter | 1,000 liters ≈ 35.31 cubic feet |
Frequently asked questions
What is the volume formula for a box?
Volume = length × width × height. Measure all three in the same unit first; the answer is in that unit cubed.
How do I convert cubic feet to gallons?
Multiply cubic feet by about 7.48 to get US gallons. One US gallon is defined as exactly 231 cubic inches, and a cubic foot is 1,728 cubic inches.
Can I use this as a cubic yard calculator?
Yes. Enter your lengths in feet or yards and read the cubic yards row under the result. There are 27 cubic feet in a cubic yard.
How many cubic feet are in a cubic yard?
There are 27 cubic feet in a cubic yard, because a yard is 3 feet and 3 × 3 × 3 = 27. Divide cubic feet by 27 to get cubic yards, which is how mulch, soil, and concrete are usually sold.
Is volume the same as capacity?
Not quite. Volume is the space a shape takes up, while capacity is how much a container can hold. For a container with thin walls they are nearly the same; for thick walls, measure the inside dimensions.
Limitations
The formulas assume ideal shapes: perfectly flat faces, right angles, and circular cross sections. Real objects such as tanks with rounded corners or uneven ground can hold somewhat more or less. Results are rounded to 10 significant digits, or 8 when shown in scientific notation.
What's changed
- Launched.
References
- Wolfram MathWorld, Spherical Cap
cap volume and the relation between its height and radii
- Wolfram MathWorld, Conical Frustum
frustum volume formula
- Wolfram MathWorld, Ellipsoid
ellipsoid volume formula
- NIST Guide to the SI, Appendix B.9: Factors for units listed by kind of quantity
US gallon and cubic unit conversion factors