Circle, Sphere: Contact | Fill Level
Fill Level Calculator Circle and Sphere
Calculates, to how many percent a circle or sphere is filled at a given fill height. Please enter the radius and the fill height. The fill level will be calculated, this is the percentual value of the filling. The fill height can be twice the radius at the most, in this case, the fill level is 100 percent.
Example: a circle with the radius 1 and the fill height 0.77 (see image above) is filled to 35.5 percent. A sphere with these values is filled to 33 percent.
If the fill height is less than the radius, then a circle is more filled than a sphere of the same radius. If, on the other hand, the fill height is greater than the radius and less than twice the radius, then the circle is less filled than the sphere. If the fill height equals the radius, then the fill level of both the circle and the sphere is exactly 50 percent. If the fill height is the diameter, then the fill level is 100 percent in each case. Of course, it can't be any more than that.
For the formulas to calculate this, see the calculators for circle, circular segment, sphere and spherical cap.
The fill height can also be referred to as level. This is especially a term for the water level, particularly in lakes and rivers, but this can also be applied to vessels and containers. With spheres, as well as with similar elliptical containers that are filled, the level rises quickly at first, slowly in the middle and quickly again towards the end. The reason for this is, of course, that the volume is smaller at the narrower points and is therefore filled more quickly. Filling such shapes is therefore difficult to estimate when filling by hand. At the beginning and end, there is a great risk of filling too quickly, and if this happens towards the end, some of the water will of course spill over.
Last updated on 07/01/2025. Author: Jürgen Kummer
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