Why round bar dia calculator with different spacing for same area in a same width need?

Some times we can not use random spacing due to links bar, so we will take manageable spacing and calculate dia of bar.

What is the round bar dia calculator with different spacing for same area in a same width formula?

d1= Round bar-1 dia
s1= Round bar-1 spacing
s2= Round bar-2 spacing
Let round bar-2 dia, d2
For same area of round bar in particular breadth (b) of any structure-
Area-1 = Area-2
(π*d1^²*b)/(4*s1) = (π*d2^²*b)/(4*s2)
(d1^²)/(s1) = (d2^²)/(s2)
s2/s1 = (d2/d1)^²
d2 = (s2/s1)^^0.5*(d1)