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

Some times a particular dia of steel not available at site, hence we have to change with the adjacent dia of steel, so new bar spacing will change. Round bar spacing calculator calculates the diffrent dia spacing.

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

d1= Round bar-1 dia
s1= Round bar-1 spacing
d2= Round bar-2 dia
Let round bar-2 spacing, s2
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 = (d2/d1)^²*s1)