Parsec is the radius of the circle such that its arc of length 1 AU subtends 1" at the center.
1" =
Use the formula Arc length = radius X (angle subtended by the arc at the center, in radian measure).
So, 1 parsec = 648000/
1 AU = semi-minor axis of Earth's orbit = Average Earth-Sun distance..
= 149597870.7 km
I think that this definition is a disambiguation-definition, despite that the notion of parallax is not explicit in this definition.