A simpler algorithm for computing probability values of a Chi-square (?2) random variable X is provided. This algorithm accurately compute a comprehensive ?2 probability values for all the range of X at specified degrees of freedom without further need to extrapolate before some desired ?2 probability values are obtained as a result of their non-availability in some of the currently available statistical tables. It is further demonstrated that, the P-values for any ?2-tests could be readily obtained from the ?2 probability values computed by our method.