A luminescent solar concentrator focuses solar light spectrallyand spatially to convert it to electricity. Due to a large numberof input parameters and their complex effect on the device efficiency,it is typically described by numerical simulations. Here,an analytical solution is presented, which significantly reducesthe complexity of the optical efficiency evaluation. The equationswere derived using probabilistic approach and validatedby simulations. The implementation by a computer algebra programyields instant results for any set of input parameters. Itallows a higher level of analysis, where an inverse task of findingparameters for a given efficiency can be readily solved. The obtainedexplicit expressions provide a clear standard for theoreticaldescription of such devices.