In this article, we give an explicit relationship of SLE partition functions with Coulomb gas formalism of conformal field theory. We first construct a family of SLE$(κ)$ partition functions as Coulomb gas integrals and derive their various properties. In accordance with an interpretation as probabilistic correlations in loop $O(n)$ models, they are always positive when $κ\in (8/3,8)$, while they may have zeroes for $κ\le 8/3$. They also admit a Frobenius series expansion that matches with the algebraic content from CFT. Moreover, we check that at the first level of fusion, they have logarithmic asymptotic behavior when $κ= 8/3$ and $κ= 8$, in accordance with logarithmic minimal models $M(2,1)$ and $M(2,3)$, respectively. Second, we construct $\SLE_κ$ pure partition functions and show that they are real-analytic in $κ\in (0,8)$ and decay to zero as a polynomial of $(8-κ)$ as $κ\to 8$. We explicitly relate the Coulomb gas integrals and pure partition functions together in terms of the meander matrix. As a by-product, our results yield a construction of global non-simple multiple chordal SLE$(κ)$ measures ($κ\in (4,8)$) uniquely determined by their re-sampling property.