A general numerical error propagation procedure is developed to calculate the error in a quantity derived from measurements which are subject to errors. It is an alternative to computer intensive techniques such as Monte Carlo and can be applied to quite complex analytical problems where correlation among the measurement errors and among the final errors in results are present. Previous formulations have usually ignored correlated errors. Some of the assumptions involved in error propagation can also be checked numerically. This is an advantage over analytical formulations which cannot assess the validity of the calculated errors. Formulation as computer subroutines permits the analysis to be added to existing programs. Examples from the fields of geochronology and thermodynamics are used to highlight the advantages and the flexibility of the method.