During single phase earth faults in distribution networks it is often insufficient to use current information only to perform directional fault detection. If the residual voltage angle is also available, the fault direction can be identified more easily. Due to the additional cost of voltage transformers they are often not available in distribution networks. This paper presents a method to estimate residual voltage angle with low-cost voltage presence indication system. The distribution networks are classified into groups according to their neutral earthing types. Different calculation methods are given for each group. The calculation methods have been validated by co-simulation with EMTP/ATP and MATLAB. The result shows that directional fault detection of single phase earth fault with the estimated residual voltage angle can achieve a promising accuracy. This method can also be applied in distribution networks with distributed energy resources.