Using binomial coefficients the Clebsch-Gordan and Gaunt coefficients were calculated for extremely large quantum numbers. The main advantage of this approach is directly calculating these coefficients, instead of using recursion relations. Accuracy of the results is quite high for quantum numbers I1 and I2 up to 100. Despite direct calculation, the CPU times are found comparable with those given in the related literature. © 1995 by Academic Press, Inc.