I am amazed that nobody noticed that Iosif asks for the calculation of the transfinite diameter of the interval $[0,1]$. This notion applies to arbitrary compact domains $K$ in ${\mathbb R}^n$ :
$$d(K)=\lim_{k\rightarrow+\infty}\sup_{x_1,\ldots,x_k\in K}\left(\prod_{\alpha<\beta}|x_\alpha-x_\beta|\right)^{2/k(k-1)}.$$
In the particular case where $K\subset{\mathbb C}$ is simply connected, then the inverse of $d(K)$ is the conformal radius of ${\mathbb C}\setminus K$.