Why converting rotary degrees to linear travel matters
A rotary axis is programmed in degrees, but the actual surface speed and feed relationship at a given radius behaves like linear travel along an arc. Converting a rotation into the equivalent linear distance traveled at a specific radius is what lets you sanity-check a rotary feed rate against the same intuition you use for a linear axis.
How the number is calculated
Equivalent linear travel equals the radius from the rotary center multiplied by the rotation angle expressed in radians, or equivalently the radius times the angle in degrees times pi divided by 180. This is the same arc length relationship used anywhere a rotation needs to be expressed as a distance: a larger radius covers more linear distance for the same angle of rotation.
Practical tips
Use this to convert a rotary feed rate given in degrees per minute into an equivalent surface feed in inches per minute at the tool contact point, which is especially useful when working out chip load or surface speed on a 4th or 5th axis part where the cutting point sits at a known radius from the rotary center. Remember that the equivalent linear travel changes with radius, so a single rotary feed rate produces a different surface speed at the outside of a part than it does closer to the rotary center.