OneTaskBy Tim King · Updated
Volume Calculator
Cone, Sphere, Cylinder and Frustum Volume in Cubic Units and Litres
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How the Volume Calculator works
This volume calculator works out how much space eleven common solids take up: cubes, boxes, cylinders, cones, spheres, hemispheres, square pyramids, triangular prisms, capsules, cone frustums and ellipsoids. Pick the solid, enter its measurements in any one unit, and it shows the formula, each line of working, and the answer in litres and gallons.
Volume is the three-dimensional space inside a solid, measured in cubic units. A box 1 cm on every side holds 1 cm³, which is exactly one millilitre, so 1,000 cm³ makes a litre and a cubic metre holds 1,000 litres.
How the volume calculator works
Every prism and cylinder follows one formula pattern: the area of the base times the height. A cylinder is πr² × h and a box is l × w × h. Anything that comes to a point, a cone or a pyramid, holds exactly a third of the matching prism. A sphere is ⁴⁄₃πr³, and a hemisphere is half that.
First example. A cylinder with radius 3 and height 10 holds π × 9 × 10 ≈ 282.74 cubic units. In centimetres that is about 0.283 litres, a little under a can of drink.
Second example. A ball 22 cm across has a radius of 11 cm, so its volume is ⁴⁄₃ × π × 1,331 ≈ 5,575 cm³, or about 5.6 litres.
How many litres does a 1 m × 0.5 m × 0.4 m tank hold? 1 × 0.5 × 0.4 = 0.2 m³, which is 200 litres.
Volume of a cube, and of a cylinder, sphere and cone that fit inside it, for sizes 1 to 24
| Size s | Cube (s³) | Cylinder (d = h = s) | Sphere (d = s) | Cone (d = h = s) |
|---|---|---|---|---|
| 1 | 1 | 0.79 | 0.52 | 0.26 |
| 2 | 8 | 6.28 | 4.19 | 2.09 |
| 3 | 27 | 21.21 | 14.14 | 7.07 |
| 4 | 64 | 50.27 | 33.51 | 16.76 |
| 5 | 125 | 98.17 | 65.45 | 32.72 |
| 6 | 216 | 169.65 | 113.1 | 56.55 |
| 7 | 343 | 269.39 | 179.59 | 89.8 |
| 8 | 512 | 402.12 | 268.08 | 134.04 |
| 9 | 729 | 572.56 | 381.7 | 190.85 |
| 10 | 1,000 | 785.4 | 523.6 | 261.8 |
| 11 | 1,331 | 1,045.36 | 696.91 | 348.45 |
| 12 | 1,728 | 1,357.17 | 904.78 | 452.39 |
| 13 | 2,197 | 1,725.52 | 1,150.35 | 575.17 |
| 14 | 2,744 | 2,155.13 | 1,436.76 | 718.38 |
| 15 | 3,375 | 2,650.72 | 1,767.15 | 883.57 |
| 16 | 4,096 | 3,216.99 | 2,144.66 | 1,072.33 |
| 17 | 4,913 | 3,858.66 | 2,572.44 | 1,286.22 |
| 18 | 5,832 | 4,580.44 | 3,053.63 | 1,526.81 |
| 19 | 6,859 | 5,387.05 | 3,591.36 | 1,795.68 |
| 20 | 8,000 | 6,283.19 | 4,188.79 | 2,094.4 |
| 21 | 9,261 | 7,273.57 | 4,849.05 | 2,424.52 |
| 22 | 10,648 | 8,362.92 | 5,575.28 | 2,787.64 |
| 23 | 12,167 | 9,555.94 | 6,370.63 | 3,185.31 |
| 24 | 13,824 | 10,857.34 | 7,238.23 | 3,619.11 |
Tips
- Use one unit throughout. Mixing metres and centimetres is the most common mistake.
- Radius, not diameter. Halve the measurement across a pipe or ball before entering it.
- Cubic units grow fast. Double every dimension and the volume goes up eight times.
FAQ
How do you calculate the volume of a cylinder?
Square the radius, multiply by π and then by the height: V = πr²h. A tin 8 cm across and 11 cm tall has a radius of 4 cm, so its volume is π × 16 × 11 ≈ 553 cm³, a little over half a litre. Choose Cylinder above and enter the radius and height to see each step.
Why is a cone a third of a cylinder?
A cone with the same base and height as a cylinder holds exactly one third as much. You can prove it with calculus, or by filling a cone with water three times to fill the cylinder. The same third applies to a pyramid and the box around it, which is why both formulas start with ⅓.
How do you convert cubic centimetres to litres?
Divide by 1,000. One cubic centimetre is one millilitre, so 5,000 cm³ is 5 litres. For cubic metres, multiply by 1,000 instead. The calculator shows both conversions under the answer, so you only need to read the line that matches the unit you measured in.
What is a cone frustum?
It is a cone with its tip cut off parallel to the base, the shape of a bucket, a lampshade or a flowerpot. Its volume is ⅓πh(R² + Rr + r²), where R and r are the bottom and top radii. Measure the inside of a bucket that way to find how many litres it holds.
See also: all Algebra and Geometry tools, Arithmetic, Number Theory, Statistics, Trigonometry and Calculus.
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