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Calculate all properties of a sphere from any single measurement. Enter radius, diameter, volume, or surface area.
A sphere is a perfectly round 3D shape where every point on the surface is exactly the same distance (the radius) from the center. It's the 3D equivalent of a circle.
The factor of 4/3 comes from calculus—integrating infinitely thin circular slices from the bottom to the top of the sphere. Archimedes famously discovered this by comparing a sphere to a cylinder.
A great circle is any circle on the sphere's surface whose center is the center of the sphere. The equator of Earth is a great circle. Great circles are the largest circles possible on a sphere and represent the shortest path between two points (used in navigation).
A sphere minimizes surface area for any given volume. This is why bubbles are spherical—nature minimizes surface tension energy. It's also why planets are roughly spherical.
A sphere with diameter d has volume V = (π/6)d³ ≈ 0.524d³. A cube with the same edge length d has volume d³. So the sphere uses only about 52% of the cube's volume.
No, Earth is an oblate spheroid—slightly flattened at the poles and bulging at the equator due to its rotation. The equatorial radius is about 21 km larger than the polar radius.
Archimedes proved that a sphere fits perfectly inside a cylinder (same height and diameter). The sphere's volume is 2/3 of the cylinder's, and its surface area is also 2/3 of the cylinder's total.
Rearrange V = (4/3)πr³ to get r = ∛(3V/(4π)). For example, if V = 100, then r = ∛(75/π) ≈ 2.88.
Balls (basketball, soccer, tennis), marbles, planets and stars (approximately), bubbles, oranges (approximately), ball bearings, and many atoms can be modeled as spheres.