In the case of a significant well storage, the initial period of the drawdown observation is significantly influenced by the well storage. The duration of this period is so far estimated with formulae which use the transmissivity of the aquifer. But this parameter should be determined with the interpretation of the ongoing pumping test. This paper gives an alternative formula, which does not use the aquifer parameters. The formula uses only parameters which can be determined easily during a pumping test. Furthermore, the derived formula is also valid for a large diameter pumping well. In addition, a straight-line equation with well storage effect is given for the estimation of aquifer parameters. This explicitly shows the effect of pumping well storage on observation wells and becomes equivalent to the well-known Cooper and Jacob (CJ) method after large pumping duration. Moreover, simple unique formulae are offered for estimating both transmissivity and storativity parameters at large observation times. The application of the developed methodology is presented for the pumping test data, which are available in the literature.