A unified analysis is presented to calculate the incoherent spontaneous power of cooperative radiations based on self-amplified spontaneous emission. Using quantum mechanical tools, we derive analytical expressions for the incoherent spontaneous power of undulator and Cherenkov free-electron lasers (FELs). The undulator and Cherenkov FELs are considered as two different examples for the radiation that accumulate cooperatively. In the case of the undulator FEL, we show an excellent agreement between an expression for the incoherent radiation power derived in the present work and that obtained using a completely different approach [Phys. Rev. E 65 (2002) 026501]. For the Cherenkov radiation, we demonstrate a satisfactory agreement between the incoherent power predicted in our analysis and previous experimental results.