I would love to be able to write a formula for this, but I'm afraid it's beyond my ability. It would include temperature, medium viscosity, fluorescence lifetime of the fluorophore, and concentration of quencher, and it would take into account the geometry of the system. I feel confident that there would be a close correlation between quenching effect and quencher concentration because that is what would determine the likelihood that the quencher would come into contact with the fluorophore while the fluorophore is in its excited state.

The simplest such system consisting of fluorophore and collisional quencher, when both are free in solution, is described by the Stern-Volmer equation. Fo/F = 1+ Ksv[Q], where the constant Ksv = 8RT(tau)/(3(eta)), where tau is the excited state lifetime, eta is the viscosity of the solution, R is the ideal gas constant, T is absolute temperatue, Fo is the unquenched fluorescence intensity, and F is the intensity at quencher concentration [Q]. It seems to me that some modification of this equation would be required because of the physical constraint of the caged quencher enclosed within the fluorophore.

Thank you for your answers. I will think about a way to calculate this, but I may not have enough information of my system yet to be able to make this correlation. Stern-Volmer I have already looked into, but it does not properly account for binding equilibria, and therefore is an oversimplification of my system.