Volume Calculator
Calculate the volume of common 3D shapes: cube, rectangular box, sphere, cylinder, cone, pyramid, and ellipsoid.
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How to use this calculator
Cube: s³. Box: lwh. Sphere: (4/3)πr³. Cylinder: πr²h. Cone: (1/3)πr²h. Pyramid: (1/3)b²h. Ellipsoid: (4/3)πabc.
- 1
Select the 3D shape from the dropdown.
- 2
Enter the required dimensions (radius, height, side length, etc.).
- 3
The volume is calculated immediately in the units you entered (cubed).
- 4
For an ellipsoid enter three semi-axes a, b, c; for a cone enter base radius and height.
Frequently asked questions
Which box do I put each measurement in?
The first box is the side of a cube, the length of a box, or the radius of a sphere, cylinder or cone, or semi-axis a of an ellipsoid. The second is the width of a box, the height of a cylinder, cone or square pyramid, or semi-axis b. The third is the height of a box or semi-axis c. Unused boxes are ignored, so a leftover value there does not matter.
What is the pyramid’s base?
A square whose side is the first box, with the perpendicular height in the second. Its volume is one-third of side² × height, so a base of 5 and a height of 4 gives 33.333333. Rectangular or triangular bases are not supported.
Is the height the slanted edge or the straight-up height?
The straight-up, perpendicular height. Using the slant length of a cone or pyramid overstates the volume. The same holds for a leaning cylinder: the perpendicular height still gives the correct volume.
Why are cylinder and cone volumes related?
For the same radius and height, a cone holds exactly one-third of a cylinder’s volume. With radius 5 and height 4, the cylinder gives 314.159265 and the cone 104.719755, which is a ratio of 3 to 1. The same one-third relation links a pyramid and a box with the same base and height.
What are the rules for invalid input?
The first box must be above zero for every shape. A box also needs a positive width and height, a cylinder, cone or pyramid needs a positive height, and an ellipsoid needs positive second and third semi-axes. Otherwise an error message explains what is missing. Negative values are rejected, not treated as lengths.
Which units are used for the answer?
The result is the unit you entered, cubed. Dimensions in centimetres give cm³ and dimensions in metres give m³. Keep every dimension in one unit: 1000 cm³ equals one litre, so a 10 cm cube is a litre, but mixing metres and centimetres would give nonsense.
Does it give surface area?
No, only volume. Use the sphere calculator for a sphere’s surface area. For the other shapes you would need a separate formula. It also does not handle hollow shapes, frustums (cut-off cones) or composite solids.
How is an ellipsoid different from a sphere?
An ellipsoid has three independent semi-axes, a, b and c, and the volume is 4/3 × π × a × b × c. If all three are equal it becomes a sphere. For semi-axes 5, 4 and 3 the volume is 251.327412, compared with 523.598776 for a sphere of radius 5.
Volumes of seven common solids
Formulas behind the calculator
Each solid uses a standard formula: a cube is s³, a box is length × width × height, a sphere is 4/3 × π × r³, a cylinder is π × r² × h, a cone is one-third of that, a square pyramid is one-third of side² × height, and an ellipsoid is 4/3 × π × a × b × c. Pick the shape first, then enter the dimensions in the order the labels indicate; the output is the volume in your unit cubed.
| Shape | Dimensions used | Volume |
|---|---|---|
| Cube | side 5 | 125 |
| Rectangular box | 5 × 4 × 3 | 60 |
| Sphere | radius 5 | 523.598776 |
| Cylinder | radius 5, height 4 | 314.159265 |
| Cone | radius 5, height 4 | 104.719755 |
| Square pyramid | side 5, height 4 | 33.333333 |
| Ellipsoid | semi-axes 5, 4, 3 | 251.327412 |
Worked example: a small cylinder
A cylindrical can with radius 0.5 and height 2 returns a volume of 1.570796. In centimetres that would be 1.570796 cm³, which is about 1.57 millilitres, since one cubic centimetre equals one millilitre. Radius is half the diameter, so a common mistake is entering the diameter into the radius box, which makes the result four times too large.
Worked example: cylinder against cone
Using radius 5 and height 4, the cylinder is 314.159265 and the cone is 104.719755. Dividing the first by the second gives exactly 3, because a cone is one-third of the cylinder that encloses it. The same ratio explains why the pyramid with side 5 and height 4 is 33.333333, a third of the 100 you would get from a 5 × 5 × 4 box.
Planning materials and containers
For a 10 cm cube the calculator returns 1000, which equals 1000 cm³, or one litre. The same approach converts bin, tank or planter dimensions into capacity. Use inside dimensions for containers, because wall thickness reduces the usable volume, and use the perpendicular height for anything that slopes or leans. For soil, concrete or water, add a margin for settling or waste.
Boundaries of the tool
It computes volume only, for the seven listed solids. Pyramids need a square base, frustums and hollow shapes are not included, and the ellipsoid shortcut assumes three perpendicular semi-axes. Results are rounded to six decimals. If your object is irregular, break it into these shapes and add the volumes.
Learn more from an authoritative source:
WikipediaCone Calculator
Calculate the volume, slant height, lateral surface area, and total surface area of a cone from its base radius and height.
Sphere Calculator
Calculate radius, diameter, surface area, and volume of a sphere from any one known measurement.
Cylinder Calculator
Calculate the volume, lateral surface area, total surface area, and base area of a cylinder from its radius and height.
Percentage Difference Calculator
Calculate the symmetric percentage difference between two values — useful when neither value is a reference baseline.
Percent Error Calculator
Calculate the percent error between an experimental measurement and the accepted theoretical value, including absolute error and sign.
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Calculate the absolute value of any real number, with a step-by-step explanation of the result.
Results are estimates for informational purposes only and do not constitute professional financial, medical, legal, or technical advice. Read full disclaimer →