There are several methods to calculate the error function erf x,the first one is based on the power series of integrated function e~(-t~2).The expression of erf x from this method is mathematical con-vergent,and for the relative deviations in the significant range,it is also numerical convergent.However,the numerical integration,such as trapezoidal rule,applied to calculate erf x with controllable computational error seems to bo the best one,with excellent results obtained.