That moment, when your manager says to you … we are introducing 360 degree assessments into the business …

Say what?

How flat, How retro. How old school. How two dimensionaL. How **wrong**.

We are people in a three dimensional world - surely our assessments deserve more than two dimensions.

Me - I assess a full **4Pi Steradian** view!

**Steradian** … An area on the surface of the sphere equivalent to the square of its radius.

## Explanation

Angular measurement on a circle is defined by the ratio of the arc length to the radius of the circle, so a full rotation is 2 pi r / r = 2 pi radians, or 360 degrees if you want to use Babylonian units.

For a sphere, the idea is similar. You take the ratio of the area of the part of the sphere that you can travel to, to the square of the radius. These “angles” are called solid angles, and since the area of a sphere is 4 pi r^2, a sphere subtends a solid angle of 4 pi, the units being steradians. So the mathematical analog for a 360 view would be a 4 pi steradian view.

Someone, Somewhere.

## From Wikipedia

A square degree has sides of one degree, projected on a sphere.

There are (360)^2/pi square degrees on a sphere, which is approximately 41252 square degrees.

You can also use stereo-radians, or steradians, which is an area on the surface of the sphere equivalent to the square of its radius.

It is commonly used in radiant energy measurements, like in “X watts per steradian”.

A full sphere has 4*pi steradian.

In short, a 3D equivalent of a plane 360 degree view is 41252 square degrees or 12.5 steradians.