Volume Calculator
The volume of a box, cube, cylinder, sphere, cone, pyramid, capsule, hemisphere, frustum, tube or triangular prism, in cubic units, litres and gallons.
Result
Volume: 24 ft³
A measurement, not a material estimate. Nothing is added for waste or settlement.
- Surface area
- 52 ft² (7,488 in², 4.831 m²)
https://calcgallery.com/geometry/volume-calculator/
Results follow the mathematical operation and values shown. Check that you selected the intended operation, convention and dataset type before relying on the result. Read the full disclaimer
How to use the Volume Calculator
- Choose the solid.
- Enter its dimensions in whatever units you measured them in. For a cone, pyramid or frustum, use the vertical height, not the sloping side.
- Read the volume in cubic feet or cubic metres, with litres and US gallons beside it.
The formulas
| Solid | Volume | Notes |
|---|---|---|
| Box | l × w × h | also called a rectangular prism or cuboid |
| Cube | s³ | a box with all three sides equal |
| Cylinder | π × r² × h | the circular base area times the height |
| Sphere | 4/3 × π × r³ | |
| Cone | 1/3 × π × r² × h | h is the vertical height |
| Rectangular pyramid | 1/3 × l × w × h | apex over the centre of the base |
| Capsule | π × r² × L + 4/3 × π × r³ | a cylinder of length L with a hemisphere on each end |
| Hemisphere | 2/3 × π × r³ | half a sphere |
| Frustum of a cone | 1/3 × π × h × (R² + R × r + r²) | R and r the bottom and top radii, h vertical |
| Tube | π × (R² − r²) × h | a hollow cylinder, R outer and r inner radius |
| Triangular prism | A × L | A the triangle’s area from its three sides (Heron) |
A third of the prism
The cone and the pyramid each hold exactly one third of the cylinder or box that encloses them. A cone of radius 3 and height 4 has a third of the volume of a cylinder of the same size. This rule is easy to forget when working by hand. The page carries a separate check for each solid with the third, so a slip in one does not hide behind another.
Height, not slant
For the cone and the pyramid, the height is measured straight up from the centre of the base to the tip. It is not the length of the sloping side, which is always longer. Using the slope overstates the volume. If you only have the slant height s of a cone, its vertical height is √(s² − r²).
The capsule
A capsule is a cylinder with a hemisphere on each end, the shape of many propane tanks, pills and pipe fittings. The straight length is the cylindrical middle only. The two rounded ends together make one whole sphere, so the page adds a sphere of the same radius to the cylinder.
Units, litres and gallons
Enter lengths in any unit. Everything is converted to metres before multiplying, so the volume comes out in cubic metres and is then shown in the units you are working in. Volume scales with the cube of length. A box twice as long, wide and high holds eight times as much, so a mistake in one measurement affects the answer more than you might expect. Gallons here are US liquid gallons, about 3.785 litres each.
Hemisphere, frustum, tube and prism
A hemisphere holds exactly half a sphere of the same radius, 2/3 × π × r³. A frustum is a cone with its tip cut off parallel to the base; its formula is the difference between two cones, and with equal radii it becomes a cylinder, which is how the page checks it. A tube is the outer cylinder minus the inner one, so its volume is the material in the wall, not what it holds. A triangular prism takes the three sides of its triangular end, so the end does not need a right angle: the area comes from Heron’s formula and is multiplied by the length.
With your numbers
- Volume = 4 ft × 3 ft × 2 ft
- Volume = 24 ft³
Quick reference
A measurement, not a material estimate. Nothing is added for waste or settlement.
| Example | Volume |
|---|---|
| Box, 4 × 3 × 2 ft | 24 ft³ |
| Cube, 3 ft sides | 27 ft³ |
| Cylinder, radius 0.5 m, 2 m high | 1.5708 m³ |
| Sphere, radius 3 m | 113.0973 m³ |
| Cone, radius 3 m, 4 m high | 37.6991 m³ |
| Square pyramid, 4 m base, 6 m high | 32 m³ |
| Capsule, radius 2 m, 6 m straight | 108.9085 m³ |
| Hemisphere, radius 3 m | 56.5487 m³ |
| Frustum, radii 3 and 1 m, 4 m high | 54.4543 m³ |
| Tube, radii 0.5 and 0.4 m, 2 m long | 0.5655 m³ |
| Triangular prism, 3-4-5 ft end, 10 ft long | 60 ft³ |
Common questions about the Volume Calculator
- What is the difference between volume and capacity?
- Volume is the space a solid takes up. Capacity is how much a container holds. For a thin-walled container they are nearly the same if you measure the inside. For a thick-walled tank, planter or pool, measure the inside dimensions to get the capacity. The outside dimensions give the volume of the whole object, walls included.
- How many litres are in a cubic metre?
- Exactly 1,000. A litre is a cube 10 cm on each side, and a cubic metre holds ten of those along each edge: 10 × 10 × 10. A cubic foot is about 28.3 litres, or about 7.48 US gallons.
- How do I find the volume of an irregular object?
- By displacement. Submerge it in a container of water and measure how far the level rises. The volume of water pushed up equals the volume of the object. For a large irregular space, such as a hole or a pond, break it into boxes and cylinders, work out each, and add them.
- How do I find the volume of a bucket or a tapered planter?
- Choose the frustum of a cone and enter the radius across the bottom, the radius across the top and the vertical height. Measure the inside to get what it holds. Averaging the two radii and treating it as a cylinder always gives a little less than the true volume.
- How much material is in a pipe or tube?
- Choose the tube and enter the outer radius, the inner radius and the length. The volume is the ring of the wall times the length, the outer cylinder minus the hole. For what the pipe holds, use the cylinder with the inner radius instead.
- Why is a cone a third of a cylinder?
- A cone with the same base and height as a cylinder holds exactly a third as much, and the same is true of a pyramid and the box around it. It is not an approximation. It follows from the way the cross-section shrinks steadily to a point, and it can be checked by filling a cone with water three times to fill the cylinder.