An approximate method for determining the maturity time is presented for applications in low neutron source nuclear reactor startup simulations. This new method relies only on the calculation of the mean neutron density and does not require the additional calculation of the variance in the neutron density as the traditional method does. The most accurate method for determining the safe neutron source strength, required to sufficiently mitigate the probability of a rogue transient during nuclear reactor startup, uses the Pál-Bell equations. However, as space and energy dependencies are included, the numerical computation become computationally demanding. Therefore, approximate methods that significantly reduce the computation time and improve the computational efficiency of the simulation while remaining very accurate are extremely useful. The approximate method for determining the maturity time presented in this study has shown excellent agreement with traditional methods while offering an order of magnitude reduction in computation time.