The gradients of vibrational coordinates are needed in order to form the exact vibrational kinetic energy operator of a polyatomic molecule. The conventional methods used to obtain these gradients are often quite laborious. However, by the methods of geometric algebra, the gradients for any vibrational coordinate can be easily calculated. Examples are given, and special attention is directed to ring coordinates. (C) 2000 American Institute of Physics. [S0021-9606(00)01106-5].