The strength is dependent mainly on the angle between the two ropes form, on which the hammock is hung, and the weight you want the hammock to support.
For a traditional hammock the angles of the ropes (measured to the horizontal) are about
A=30° (just an estimate). Lets assume we want to design the system for a person weighing
W=200lbs. Then we can derive a formula for the force ( acting on the ropes using trigonometry:
Force on each rope (in the same unit as the weight W):
F = 0.5 * W / sin(A)
(Note that the Force gets extremely high, the closer to horizontal the ropes are / the close
a is at
With the assumptions from above we get
F = 200lbs, but this is just static loading, as soon as you "dynamically" sit down in it the forces can be higher. I'd go with a safety factor of about 5 to be on the absolute safe (that means 5 times the static weight it absolutely needs to support, consider that any knots weaken the rope, a knot can reduce the strength by up to
50%), so that results in about
I have no experience using parachord, but this site also suggests to use rope of at least
700lbs - 1000lbs.
Another reference I just found is this online hammock anchor calculator.