Now I'm not positive if I am correct with this but from the example and some thinking I have an educated guess of how this could be calculated.
Starting with your square with rounded corners, and an equilateral triangle with side lengths that are equal to the lengths of the square.
To calculate the arcs of the reulaeaux triangle I believe you would use the following formula.
r = (H/2) + [(W^2)/(8*H)]
H = [W sqrt(3)]/2
Where r is the radius of the arc of the reuleaux triangle. W is the length of the square edges.
H is going the be the radius of the corners of the square.
I'm not 100% positive yet but if someone could check this out for me I would be grateful.
Hopefully this helps!
EDIT: Under further review of this I've noticed that the relationship between a reuleaux triangle and a square with rounded corners is very specific (only 1 square will work with a specific triangle). I've updated my above formula and believe that this is the correct correlation between the two.