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1.
the degree to which a person, place, thing, or action is radical.
"that band rocked my ass off with their supreme radicality"
by ryan ingersol March 07, 2005
 
2.
A quality that describes a person with radical thoughts and ideas. Radical, as in an extremist, rebellious, and revolutionary kind of way.

It can't really be used in a sentence, because it may not sound right, but hey, it's better than radicalness.

See radical.
The leader rallies up his men with his mountainous voice, his left fist raised up high, his own eyes burning with the fires of radicality that boil forth from within the recesses of his mind, his heart, and his soul.
by Merc Julian August 08, 2004
 
3.
As defined by: a level of excellence achieved by a group, or individual.
"You've reached Radicality, congratulations"
by Mr Blue August 16, 2012