Volume Calculator
Pick a shape, enter its dimensions in any unit and get its volume in cubic units, liters, milliliters and US gallons. The formula used is shown with your numbers substituted.
Result
- Liters
- 0.7854 L
- Milliliters
- 785.4 ml
- US gallons
- 0.2075 US gal
- Cubic meters
- 0.000785 m³
- Cubic feet
- 0.0277 ft³
- Formula used
- π × 5² × 10
What is volume?
Volume is the amount of three-dimensional space an object occupies or a container encloses. Where area counts unit squares on a surface, volume counts unit cubes, so it is measured in cubic units: cubic centimeters (cm³), cubic meters (m³), cubic inches (in³) or cubic feet (ft³). You need it to size a water tank or aquarium, order concrete or soil, work out how much a box can ship, or convert the dimensions of a pot into liters of capacity.
Volume formulas
| Shape | Formula | Dimensions |
|---|---|---|
| Cube | a³ | side a |
| Rectangular box | l × w × h | length, width, height |
| Cylinder | π × r² × h | radius, height |
| Sphere | 4/3 × π × r³ | radius |
| Cone | 1/3 × π × r² × h | base radius, height |
| Square pyramid | 1/3 × a² × h | base side, height |
There is a pattern worth remembering. Boxes and cylinders are prisms: their volume is the base area times the height. Cones and pyramids taper to a point and hold exactly one third of the matching prism with the same base and height. So if you already know a base area from the area calculator, multiply it by the height (and divide by 3 for a pointed solid).
Worked example: a cylinder with radius 5 cm and height 10 cm. The base area is π × 5² = π × 25 = 78.54 cm². Multiply by the height: 78.54 × 10 = 785.4 cm³. Because 1 cm³ is exactly 1 ml, that is 785.4 ml or 0.7854 liters, and dividing by 3.785 gives 0.2075 US gallons. If you measured the diameter (10 cm) rather than the radius, halve it first; using the diameter by mistake quadruples the answer.
Converting volume units
| Unit | Liters | Notes |
|---|---|---|
| 1 mm³ | 0.000001 L | 0.001 ml |
| 1 cm³ | 0.001 L | 1 ml |
| 1 m³ | 1,000 L | 1,000,000 cm³ |
| 1 in³ | 0.016387 L | 16.387 ml |
| 1 ft³ | 28.3168 L | 1,728 in³ or 7.4805 US gal |
| 1 yd³ | 764.555 L | 27 ft³ |
| 1 US gallon | 3.78541 L | an imperial (UK) gallon is 4.54609 L |
To convert a volume between cubic units, cube the length factor. There are 100 cm in a meter, so a cubic meter contains 100 × 100 × 100 = 1,000,000 cm³, and there are 12 in in a foot, so a cubic foot is 12³ = 1,728 in³. The easiest way to avoid this trap is to convert the dimensions into the unit you want before calculating; the unit converter handles the lengths.
How to use this calculator
- Choose the shape. The input fields change to match its formula, which is shown above them.
- Select the unit your measurements are in. The volume is reported in that unit cubed, plus liters and gallons.
- Enter the dimensions. Use the radius (half the diameter) for round shapes and the perpendicular height for cones and pyramids.
- Read the result. The "formula used" row shows your numbers in place, so you can check the working or repeat it by hand.
Tips and common mistakes
- Capacity needs inside dimensions. For a tank, box or pot, subtract the wall thickness from each outside measurement (twice, for opposite walls). A 50 cm cube with 1 cm walls holds 48³ = 110,592 cm³, not 125,000 cm³.
- Radius, not diameter. Cylinders, spheres and cones all use the radius. Measuring across the full width and entering it as the radius overstates the volume four times (eight times for a sphere).
- Height is perpendicular height. For a cone or pyramid, measure straight up from the center of the base to the apex, not along the sloping side (the slant height).
- Use one unit throughout. Mixing centimeters for the radius with meters for the height gives nonsense. Convert first.
- Add a margin for materials. When ordering concrete, soil or gravel, add 5–10% for spillage and uneven ground; the concrete calculator does this and converts to bags or cubic yards.
- Irregular shapes: break them into simple solids and add the volumes, or use water displacement for small objects.
Frequently asked questions
How do I find the volume of a cylinder?
Multiply the area of the circular base by the height: V = π × r² × h. Measure the diameter across the widest part, halve it to get the radius, square that, multiply by π (about 3.1416) and then by the height. A can 6.6 cm across and 12 cm tall holds π × 3.3² × 12 ≈ 410 cm³, which is 410 ml.
How many liters are in a cubic meter?
Exactly 1,000 liters, because a liter is defined as 1,000 cm³ and a cubic meter is 1,000,000 cm³. A cubic foot holds 28.317 liters or 7.48 US gallons, and a cubic inch is 16.387 ml.
What is the difference between volume and capacity?
Volume is the space an object takes up; capacity is how much a container can hold. For a tank or box, capacity is the volume calculated from the inside dimensions, so subtract the wall thickness from each outside measurement before you calculate. Capacity is usually quoted in liters or gallons rather than cubic units.
How do I calculate the volume of an irregular object?
Either split it into simple solids (a house shape is a box plus a triangular prism) and add the volumes, or measure it by displacement: submerge the object in a container of water and measure how much the water level rises. 1 ml of displaced water equals 1 cm³ of volume.
Why is my calculated volume different from the capacity printed on a bottle?
Real containers are rarely perfect cylinders: shoulders, necks, tapered sides and a domed base all remove volume, and a bottle is filled with some headspace. Treat a cylinder calculation from the outside diameter as an upper estimate and expect the stated capacity to be 5–15% lower.