For a uniform semicircular wire of radius $a$, the centroid distance from the diameter is $\bar{y} = \dfrac{2a}{\pi}$. This is derived by: $\bar{y} = \dfrac{\int_0^\pi a\sin\theta\cdot a\,d\theta}{\pi a} = \dfrac{a\int_0^\pi \sin\theta\,d\theta}{\pi} = \dfrac{2a}{\pi}$.