What is the impact of a thicker wire on the spring rate of extension springs, compression springs or torsion springs?

From the numerator in the formula of the spring rate of extension and compression springs (Gd^4) it seems that the wire thickness [d] is raised to the power of four. When the wire becomes 10% thicker, the numerator in the formula [1,1]4 increases, and the spring rate 1.46 and thus more than 45% higher.

For torsion springs, the wire thickness is as important as with an extension or compression spring. When the wire gets 10% thicker, the spring rate is then also 45% higher. Voor torsieveren telt de draaddikte even zwaar mee als bij een drukveer of trekveer. Wanneer de draad 10% dikker wordt, wordt de veerconstante dus ook ruim 45% hoger.