Plain Angles and Solid Angles

All units of light can be derived from each other. They are linked by two geometrical units:-

For a better understanding, it might be helpful to recall the concept of the plane angle. The unit of the plane angle is radians. It is defined as the lenght of an arc divided by its radius.

a plain angle
A plain angle

If the arc (i.e. the part of a circle´s periphery) that is subtended by the angle is exactly as long as the radius of the circle, the angle spans 1 radian. This is equivalent to 57°. A full circle covers an angle of or 2Pi radians or 360°.

Solid angles