Calculations at a sphere. A sphere is the set of all points in a space with the same distance (the radius) to a certain point, which is called center.
Enter one value and choose the number of decimal places. Then click Calculate.
Formulas:
d = 2 r
A = 4 π r²
V = 4/3 π r³
A/V = 3 / r
pi:
π = 3.141592653589793...
Radius and diameter have the same unit (e.g. meter), the surface area has this unit squared (e.g. square meter), the volume has this unit to the power of three (e.g. cubic meter). A/V has this unit -1.
The sphere was considered a perfect form in ancient times. It is the extension of the circle into the three-dimensional. The expansion of the sphere by another dimension is the hypersphere. A sphere can be divided into spherical cap, spherical segment and spherical sector. The sphere has an infinite number of planes of symmetry, all of which pass through its center, to which it is point-symmetrical. It is also rotationally symmetrical to any rotation. The pure spherical shape rarely occurs in nature. Water drops are spherical in weightlessness. But as soon as forces act on a spherical shape, it distorts. An example are stars and planets, which would only be spherical if they did not rotate. But the rotation flattens them into oblate spheroids.
Due to their ability to roll in any direction, spheres are widely used in technology and games. Examples here are a ball bearing, marbles and game balls. The football (soccer ball) is often a truncated icosahedron inflated into a sphere.
If you stack spheres in the usual way, in the close-packing of equal spheres, with one sphere resting on top of the middle of other spheres, then the packing density is about 75 percent, with 26 percent of the volume being gaps.