What is the impact of the (mean) diameter on the spring rate of extension springs, compression springs or torsion springs?

n the denominator of the formula of the spring rate of extension and compression springs [8nD^3 ] it seems that the mean diameter [D] is raised to the power of three. When the heart-on-heartmean diameter increases by 10%, the formula , and the spring rate thus decreases by 0.75 and 25%.

The mean diameter counts one by one in the denominator of the formula of the spring rate of torsion springs . When the mean diameter increases by 10%, the denominator in the formula increases by 10% and the spring rate is 1/1.1=0.91 lower and the spring rate thus decreases by almost 10%.