The celebrated Verlinde formula expresses the fusion coefficients in rational two-dimensional conformal field theories (CFTs) as a sum over a ratio of modular S-kernels. In his seminal work on the Jones polynomial, Witten provided a proof of this formula by invoking the dual description of a rational CFT via a three-dimensional Chern-Simons topological quantum field theory (TQFT) with a compact gauge group. Motivated by this approach and the challenge of understanding non-rational two-dimensional CFTs, which remain largely elusive, we will use the recently developed 3D Virasoro TQFT to derive an integral identity that we interpret as a non-rational generalization of the Verlinde formula for the Virasoro algebra at central charge c ≥ 25. After describing its essential properties, we will discuss some interesting applications of the formula both in 2d CFTs and 3d gravity.