Estimating formation permeability is crucial for production estimation, hydraulic fracturing design optimization and rate transient analysis. Laboratory experiments can be used to measure the permeability of rock samples, but the results may not be representative at a field scale because of reservoir heterogeneity and pre-existing natural fracture systems. Diagnostic Fracture Injection Tests (DFIT) have now become standard practice to estimate formation pore pressure and formation permeability. However, in low permeability reservoirs, after-closure radial flow is often absent, which can cast significant uncertainties in interpreting DFIT data. Without knowing the fracture dimension prior, open fracture stiffness/compliance can't be determined, which is required for formation permeability estimation. Previous work has to assume a fracture radius or fracture height in order to estimate formation permeability, thus dent the confidence in the interpretation results. In the study, we present a new approach to determine fracture dimension, leak-off coefficient and formation permeability uniquely based on material balance and basic fracture mechanics, using data from shut-in to after-closure linear flow. Field examples are also presented to demonstrate the simplicity and effectiveness of this new approach.